//Reed Solomon Program
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//Reed Solomon Program
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//This program is based on Phil Karn
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//This program is based on Phil Karn
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//Rewritten for YACC CPU (has no C library) by Tak.Sugawara Apr.3.2005
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//Rewritten for YACC CPU (has no C library) by Tak.Sugawara Apr.3.2005
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//Consideration for embedded CPU
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//Consideration for embedded CPU
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// 1) Has no C library. Ex. Not have printf/random...
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// 1) Has no C library. Ex. Not have printf/random...
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// 2) Not have plenty of stack
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// 2) Not have plenty of stack
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#define POLY 0x80000057
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#define POLY 0x80000057
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#define print_port 0x3ff0
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#define print_port 0x3ff0
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#define print_char_port 0x3ff1
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#define print_char_port 0x3ff1
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#define print_int_port 0x3ff2
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#define print_int_port 0x3ff2
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#define print_long_port 0x3ff4
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#define print_long_port 0x3ff4
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#define uart_port 0x03ffc //for 16KRAM
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#define uart_port 0x03ffc //for 16KRAM
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#define uart_wport uart_port
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#define uart_wport uart_port
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#define uart_rport uart_port
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#define uart_rport uart_port
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#define int_set_address 0x03ff8 //for 16KRAM
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#define int_set_address 0x03ff8 //for 16KRAM
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//#define PC
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//#define PC
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void print_uart(unsigned char* ptr)//
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void print_uart(unsigned char* ptr)//
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{
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{
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unsigned int uport;
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unsigned int uport;
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#define WRITE_BUSY 0x0100
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#define WRITE_BUSY 0x0100
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while (*ptr) {
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while (*ptr) {
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do {
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do {
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uport=*(volatile unsigned*) uart_port;
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uport=*(volatile unsigned*) uart_port;
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} while (uport & WRITE_BUSY);
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} while (uport & WRITE_BUSY);
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*(volatile unsigned char*)uart_wport=*(ptr++);
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*(volatile unsigned char*)uart_wport=*(ptr++);
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}
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}
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//*(volatile unsigned char*)uart_wport=0x00;//Write Done
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//*(volatile unsigned char*)uart_wport=0x00;//Write Done
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}
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}
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void putc_uart(unsigned char c)//
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void putc_uart(unsigned char c)//
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{
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{
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unsigned int uport;
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unsigned int uport;
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do {
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do {
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uport=*(volatile unsigned*) uart_port;
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uport=*(volatile unsigned*) uart_port;
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} while (uport & WRITE_BUSY);
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} while (uport & WRITE_BUSY);
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*(volatile unsigned char*)uart_wport=c;
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*(volatile unsigned char*)uart_wport=c;
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}
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}
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unsigned char read_uart()//Verilog Test Bench Use
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unsigned char read_uart()//Verilog Test Bench Use
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{
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{
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unsigned uport;
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unsigned uport;
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uport= *(volatile unsigned *)uart_rport;
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uport= *(volatile unsigned *)uart_rport;
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return uport;
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return uport;
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}
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}
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void print(unsigned char* ptr)//Verilog Test Bench Use
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void print(unsigned char* ptr)//Verilog Test Bench Use
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{
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{
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while (*ptr) {
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while (*ptr) {
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#ifdef PC
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#ifdef PC
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putchar(*(ptr++));
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putchar(*(ptr++));
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#else
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#else
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*(volatile unsigned char*)print_port=*(ptr++);
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*(volatile unsigned char*)print_port=*(ptr++);
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#endif
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#endif
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}
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}
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#ifndef PC
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#ifndef PC
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*(volatile unsigned char*)print_port=0x00;//Write Done
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*(volatile unsigned char*)print_port=0x00;//Write Done
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#endif
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#endif
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}
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}
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void print_char(unsigned char val)//Little Endian write out 16bit number
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void print_char(unsigned char val)//Little Endian write out 16bit number
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{
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{
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#ifdef PC
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#ifdef PC
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putchar(val);
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putchar(val);
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#else
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#else
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*(volatile unsigned char*)print_port=(unsigned char)val ;
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*(volatile unsigned char*)print_port=(unsigned char)val ;
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#endif
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#endif
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}
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}
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void print_uchar(unsigned char val)//Little Endian write out 16bit number
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void print_uchar(unsigned char val)//Little Endian write out 16bit number
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{
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{
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#ifdef PC
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#ifdef PC
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printf("%x",val);
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printf("%x",val);
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#else
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#else
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*(volatile unsigned char*)print_char_port=(unsigned char)val ;
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*(volatile unsigned char*)print_char_port=(unsigned char)val ;
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#endif
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#endif
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}
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}
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static unsigned lfsr_state=1;
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static unsigned lfsr_state=1;
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unsigned random (void)
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unsigned random (void)
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{
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{
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if (lfsr_state & 0x1)
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if (lfsr_state & 0x1)
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{
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{
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lfsr_state = (lfsr_state >> 1) ^ POLY;
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lfsr_state = (lfsr_state >> 1) ^ POLY;
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}
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}
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else
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else
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{
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{
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lfsr_state = (lfsr_state >> 1);
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lfsr_state = (lfsr_state >> 1);
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}
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}
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return lfsr_state;
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return lfsr_state;
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}
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}
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/*
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/*
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void print(unsigned char* ptr)
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void print(unsigned char* ptr)
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{
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{
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while(*(ptr)) putchar(*(ptr++));
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while(*(ptr)) putchar(*(ptr++));
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}
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}
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*/
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*/
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void print_num(unsigned long num)
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void print_num(unsigned long num)
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{
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{
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unsigned long digit,offset;
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unsigned long digit,offset;
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for(offset=1000;offset;offset/=10) {
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for(offset=1000;offset;offset/=10) {
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digit=num/offset;
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digit=num/offset;
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print_char(digit+'0');//putchar(digit+'0');
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print_char(digit+'0');//putchar(digit+'0');
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num-=digit*offset;
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num-=digit*offset;
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}
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}
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}
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}
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void memcpy(unsigned char* dest,unsigned char* source,unsigned size)
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void memcpy(unsigned char* dest,unsigned char* source,unsigned size)
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{
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{
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unsigned i;
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unsigned i;
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for (i=0;i< size;i++){
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for (i=0;i< size;i++){
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*(dest++)=*(source++);
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*(dest++)=*(source++);
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}
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}
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}
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}
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unsigned memcmp(unsigned char* dest,unsigned char* source,unsigned size)
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unsigned memcmp(unsigned char* dest,unsigned char* source,unsigned size)
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{
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{
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unsigned i;
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unsigned i;
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for (i=0;i< size;i++){
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for (i=0;i< size;i++){
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if (*(dest++)!=*(source++) ) return 1;
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if (*(dest++)!=*(source++) ) return 1;
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}
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}
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return 0;
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return 0;
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}
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}
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/*
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/*
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* Reed-Solomon coding and decoding
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* Reed-Solomon coding and decoding
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* Phil Karn (karn@ka9q.ampr.org) September 1996
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* Phil Karn (karn@ka9q.ampr.org) September 1996
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*
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*
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* This file is derived from the program "new_rs_erasures.c" by Robert
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* This file is derived from the program "new_rs_erasures.c" by Robert
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* Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari Thirumoorthy
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* Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari Thirumoorthy
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* (harit@spectra.eng.hawaii.edu), Aug 1995
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* (harit@spectra.eng.hawaii.edu), Aug 1995
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*
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*
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* I've made changes to improve performance, clean up the code and make it
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* I've made changes to improve performance, clean up the code and make it
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* easier to follow. Data is now passed to the encoding and decoding functions
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* easier to follow. Data is now passed to the encoding and decoding functions
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* through arguments rather than in global arrays. The decode function returns
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* through arguments rather than in global arrays. The decode function returns
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* the number of corrected symbols, or -1 if the word is uncorrectable.
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* the number of corrected symbols, or -1 if the word is uncorrectable.
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*
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*
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* This code supports a symbol size from 2 bits up to 16 bits,
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* This code supports a symbol size from 2 bits up to 16 bits,
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* implying a block size of 3 2-bit symbols (6 bits) up to 65535
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* implying a block size of 3 2-bit symbols (6 bits) up to 65535
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* 16-bit symbols (1,048,560 bits). The code parameters are set in rs.h.
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* 16-bit symbols (1,048,560 bits). The code parameters are set in rs.h.
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*
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*
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* Note that if symbols larger than 8 bits are used, the type of each
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* Note that if symbols larger than 8 bits are used, the type of each
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* data array element switches from unsigned char to unsigned int. The
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* data array element switches from unsigned char to unsigned int. The
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* caller must ensure that elements larger than the symbol range are
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* caller must ensure that elements larger than the symbol range are
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* not passed to the encoder or decoder.
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* not passed to the encoder or decoder.
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*
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*
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*/
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*/
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//#include <stdio.h>
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//#include <stdio.h>
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#include "rs.h"
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#include "rs.h"
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#if (KK >= NN)
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#if (KK >= NN)
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#error "KK must be less than 2**MM - 1"
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#error "KK must be less than 2**MM - 1"
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#endif
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#endif
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/* This defines the type used to store an element of the Galois Field
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/* This defines the type used to store an element of the Galois Field
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* used by the code. Make sure this is something larger than a char if
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* used by the code. Make sure this is something larger than a char if
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* if anything larger than GF(256) is used.
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* if anything larger than GF(256) is used.
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*
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*
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* Note: unsigned char will work up to GF(256) but int seems to run
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* Note: unsigned char will work up to GF(256) but int seems to run
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* faster on the Pentium.
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* faster on the Pentium.
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*/
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*/
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typedef int gf;
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typedef int gf;
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/* Primitive polynomials - see Lin & Costello, Appendix A,
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/* Primitive polynomials - see Lin & Costello, Appendix A,
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* and Lee & Messerschmitt, p. 453.
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* and Lee & Messerschmitt, p. 453.
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*/
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*/
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#if(MM == 2)/* Admittedly silly */
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#if(MM == 2)/* Admittedly silly */
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int Pp[MM+1] = { 1, 1, 1 };
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int Pp[MM+1] = { 1, 1, 1 };
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#elif(MM == 3)
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#elif(MM == 3)
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/* 1 + x + x^3 */
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/* 1 + x + x^3 */
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int Pp[MM+1] = { 1, 1, 0, 1 };
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int Pp[MM+1] = { 1, 1, 0, 1 };
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#elif(MM == 4)
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#elif(MM == 4)
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/* 1 + x + x^4 */
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/* 1 + x + x^4 */
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int Pp[MM+1] = { 1, 1, 0, 0, 1 };
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int Pp[MM+1] = { 1, 1, 0, 0, 1 };
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#elif(MM == 5)
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#elif(MM == 5)
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/* 1 + x^2 + x^5 */
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/* 1 + x^2 + x^5 */
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int Pp[MM+1] = { 1, 0, 1, 0, 0, 1 };
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int Pp[MM+1] = { 1, 0, 1, 0, 0, 1 };
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#elif(MM == 6)
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#elif(MM == 6)
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/* 1 + x + x^6 */
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/* 1 + x + x^6 */
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int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1 };
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#elif(MM == 7)
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#elif(MM == 7)
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/* 1 + x^3 + x^7 */
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/* 1 + x^3 + x^7 */
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int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 1 };
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#elif(MM == 8)
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#elif(MM == 8)
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/* 1+x^2+x^3+x^4+x^8 */
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/* 1+x^2+x^3+x^4+x^8 */
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int Pp[MM+1] = { 1, 0, 1, 1, 1, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 0, 1, 1, 1, 0, 0, 0, 1 };
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#elif(MM == 9)
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#elif(MM == 9)
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/* 1+x^4+x^9 */
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/* 1+x^4+x^9 */
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int Pp[MM+1] = { 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
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#elif(MM == 10)
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#elif(MM == 10)
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/* 1+x^3+x^10 */
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/* 1+x^3+x^10 */
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int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 11)
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#elif(MM == 11)
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/* 1+x^2+x^11 */
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/* 1+x^2+x^11 */
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int Pp[MM+1] = { 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 12)
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#elif(MM == 12)
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/* 1+x+x^4+x^6+x^12 */
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/* 1+x+x^4+x^6+x^12 */
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int Pp[MM+1] = { 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 13)
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#elif(MM == 13)
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/* 1+x+x^3+x^4+x^13 */
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/* 1+x+x^3+x^4+x^13 */
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int Pp[MM+1] = { 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 14)
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#elif(MM == 14)
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/* 1+x+x^6+x^10+x^14 */
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/* 1+x+x^6+x^10+x^14 */
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int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 };
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#elif(MM == 15)
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#elif(MM == 15)
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/* 1+x+x^15 */
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/* 1+x+x^15 */
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int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 16)
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#elif(MM == 16)
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/* 1+x+x^3+x^12+x^16 */
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/* 1+x+x^3+x^12+x^16 */
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int Pp[MM+1] = { 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 };
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int Pp[MM+1] = { 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 };
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#else
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#else
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#error "MM must be in range 2-16"
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#error "MM must be in range 2-16"
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#endif
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#endif
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/* Alpha exponent for the first root of the generator polynomial */
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/* Alpha exponent for the first root of the generator polynomial */
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#define B0 1
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#define B0 1
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/* index->polynomial form conversion table */
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/* index->polynomial form conversion table */
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gf Alpha_to[NN + 1];
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gf Alpha_to[NN + 1];
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/* Polynomial->index form conversion table */
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/* Polynomial->index form conversion table */
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gf Index_of[NN + 1];
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gf Index_of[NN + 1];
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/* No legal value in index form represents zero, so
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/* No legal value in index form represents zero, so
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* we need a special value for this purpose
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* we need a special value for this purpose
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*/
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*/
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#define A0 (NN)
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#define A0 (NN)
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/* Generator polynomial g(x)
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/* Generator polynomial g(x)
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* Degree of g(x) = 2*TT
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* Degree of g(x) = 2*TT
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* has roots @**B0, @**(B0+1), ... ,@^(B0+2*TT-1)
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* has roots @**B0, @**(B0+1), ... ,@^(B0+2*TT-1)
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*/
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*/
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gf Gg[NN - KK + 1];
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gf Gg[NN - KK + 1];
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/* Compute x % NN, where NN is 2**MM - 1,
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/* Compute x % NN, where NN is 2**MM - 1,
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* without a slow divide
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* without a slow divide
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*/
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*/
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static inline gf
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static inline gf
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modnn(int x)
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modnn(int x)
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{
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{
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// print("modnn input="); print_num(x);
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// print("modnn input="); print_num(x);
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while (x >= NN) {
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while (x >= NN) {
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x -= NN;
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x -= NN;
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x = (x >> MM) + (x & NN);
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x = (x >> MM) + (x & NN);
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}
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}
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// print("modnn output=");print_num(x);
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// print("modnn output=");print_num(x);
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// print("\n");
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// print("\n");
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return x;
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return x;
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}
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}
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#define min(a,b) ((a) < (b) ? (a) : (b))
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#define min(a,b) ((a) < (b) ? (a) : (b))
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#define CLEAR(a,n) { int ci; for(ci=(n)-1;ci >=0;ci--) (a)[ci] = 0; }
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#define CLEAR(a,n) { int ci; for(ci=(n)-1;ci >=0;ci--) (a)[ci] = 0; }
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#define COPY(a,b,n) { int ci; for(ci=(n)-1;ci >=0;ci--) (a)[ci] = (b)[ci]; }
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#define COPY(a,b,n) { int ci; for(ci=(n)-1;ci >=0;ci--) (a)[ci] = (b)[ci]; }
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#define COPYDOWN(a,b,n) { int ci; for(ci=(n)-1;ci >=0;ci--) (a)[ci] = (b)[ci]; }
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#define COPYDOWN(a,b,n) { int ci; for(ci=(n)-1;ci >=0;ci--) (a)[ci] = (b)[ci]; }
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void init_rs(void)
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void init_rs(void)
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{
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{
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generate_gf();
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generate_gf();
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gen_poly();
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gen_poly();
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}
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}
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/* generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m]
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/* generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m]
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lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
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lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
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polynomial form -> index form index_of[j=alpha**i] = i
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polynomial form -> index form index_of[j=alpha**i] = i
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alpha=2 is the primitive element of GF(2**m)
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alpha=2 is the primitive element of GF(2**m)
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HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
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HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
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Let @ represent the primitive element commonly called "alpha" that
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Let @ represent the primitive element commonly called "alpha" that
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is the root of the primitive polynomial p(x). Then in GF(2^m), for any
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is the root of the primitive polynomial p(x). Then in GF(2^m), for any
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0 <= i <= 2^m-2,
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0 <= i <= 2^m-2,
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@^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
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@^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
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where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
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where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
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of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
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of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
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example the polynomial representation of @^5 would be given by the binary
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example the polynomial representation of @^5 would be given by the binary
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representation of the integer "alpha_to[5]".
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representation of the integer "alpha_to[5]".
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Similarily, index_of[] can be used as follows:
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Similarily, index_of[] can be used as follows:
|
As above, let @ represent the primitive element of GF(2^m) that is
|
As above, let @ represent the primitive element of GF(2^m) that is
|
the root of the primitive polynomial p(x). In order to find the power
|
the root of the primitive polynomial p(x). In order to find the power
|
of @ (alpha) that has the polynomial representation
|
of @ (alpha) that has the polynomial representation
|
a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
|
a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
|
we consider the integer "i" whose binary representation with a(0) being LSB
|
we consider the integer "i" whose binary representation with a(0) being LSB
|
and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
|
and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
|
"index_of[i]". Now, @^index_of[i] is that element whose polynomial
|
"index_of[i]". Now, @^index_of[i] is that element whose polynomial
|
representation is (a(0),a(1),a(2),...,a(m-1)).
|
representation is (a(0),a(1),a(2),...,a(m-1)).
|
NOTE:
|
NOTE:
|
The element alpha_to[2^m-1] = 0 always signifying that the
|
The element alpha_to[2^m-1] = 0 always signifying that the
|
representation of "@^infinity" = 0 is (0,0,0,...,0).
|
representation of "@^infinity" = 0 is (0,0,0,...,0).
|
Similarily, the element index_of[0] = A0 always signifying
|
Similarily, the element index_of[0] = A0 always signifying
|
that the power of alpha which has the polynomial representation
|
that the power of alpha which has the polynomial representation
|
(0,0,...,0) is "infinity".
|
(0,0,...,0) is "infinity".
|
|
|
*/
|
*/
|
|
|
void
|
void
|
generate_gf(void)
|
generate_gf(void)
|
{
|
{
|
register int i, mask;
|
register int i, mask;
|
|
|
mask = 1;
|
mask = 1;
|
Alpha_to[MM] = 0;
|
Alpha_to[MM] = 0;
|
for (i = 0; i < MM; i++) {
|
for (i = 0; i < MM; i++) {
|
Alpha_to[i] = mask;
|
Alpha_to[i] = mask;
|
Index_of[Alpha_to[i]] = i;
|
Index_of[Alpha_to[i]] = i;
|
/* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
|
/* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
|
if (Pp[i] != 0)
|
if (Pp[i] != 0)
|
Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
|
Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
|
mask <<= 1; /* single left-shift */
|
mask <<= 1; /* single left-shift */
|
}
|
}
|
Index_of[Alpha_to[MM]] = MM;
|
Index_of[Alpha_to[MM]] = MM;
|
/*
|
/*
|
* Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
|
* Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
|
* poly-repr of @^i shifted left one-bit and accounting for any @^MM
|
* poly-repr of @^i shifted left one-bit and accounting for any @^MM
|
* term that may occur when poly-repr of @^i is shifted.
|
* term that may occur when poly-repr of @^i is shifted.
|
*/
|
*/
|
mask >>= 1;
|
mask >>= 1;
|
for (i = MM + 1; i < NN; i++) {
|
for (i = MM + 1; i < NN; i++) {
|
if (Alpha_to[i - 1] >= mask)
|
if (Alpha_to[i - 1] >= mask)
|
Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
|
Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
|
else
|
else
|
Alpha_to[i] = Alpha_to[i - 1] << 1;
|
Alpha_to[i] = Alpha_to[i - 1] << 1;
|
Index_of[Alpha_to[i]] = i;
|
Index_of[Alpha_to[i]] = i;
|
}
|
}
|
Index_of[0] = A0;
|
Index_of[0] = A0;
|
Alpha_to[NN] = 0;
|
Alpha_to[NN] = 0;
|
print("index dump\n");
|
print("index dump\n");
|
for (i=0;i<NN;i++){
|
for (i=0;i<NN;i++){
|
print_uchar(Index_of[i]);
|
print_uchar(Index_of[i]);
|
print(" ");
|
print(" ");
|
}
|
}
|
print("\n");
|
print("\n");
|
print("Alpha_to dump\n");
|
print("Alpha_to dump\n");
|
for (i=0;i<NN;i++){
|
for (i=0;i<NN;i++){
|
print_uchar(Alpha_to[i]);
|
print_uchar(Alpha_to[i]);
|
print(" ");
|
print(" ");
|
}
|
}
|
print("\n");
|
print("\n");
|
|
|
}
|
}
|
|
|
|
|
/*
|
/*
|
* Obtain the generator polynomial of the TT-error correcting, length
|
* Obtain the generator polynomial of the TT-error correcting, length
|
* NN=(2**MM -1) Reed Solomon code from the product of (X+@**(B0+i)), i = 0,
|
* NN=(2**MM -1) Reed Solomon code from the product of (X+@**(B0+i)), i = 0,
|
* ... ,(2*TT-1)
|
* ... ,(2*TT-1)
|
*
|
*
|
* Examples:
|
* Examples:
|
*
|
*
|
* If B0 = 1, TT = 1. deg(g(x)) = 2*TT = 2.
|
* If B0 = 1, TT = 1. deg(g(x)) = 2*TT = 2.
|
* g(x) = (x+@) (x+@**2)
|
* g(x) = (x+@) (x+@**2)
|
*
|
*
|
* If B0 = 0, TT = 2. deg(g(x)) = 2*TT = 4.
|
* If B0 = 0, TT = 2. deg(g(x)) = 2*TT = 4.
|
* g(x) = (x+1) (x+@) (x+@**2) (x+@**3)
|
* g(x) = (x+1) (x+@) (x+@**2) (x+@**3)
|
*/
|
*/
|
void
|
void
|
gen_poly(void)
|
gen_poly(void)
|
{
|
{
|
register int i, j;
|
register int i, j;
|
|
|
Gg[0] = Alpha_to[B0];
|
Gg[0] = Alpha_to[B0];
|
Gg[1] = 1; /* g(x) = (X+@**B0) initially */
|
Gg[1] = 1; /* g(x) = (X+@**B0) initially */
|
for (i = 2; i <= NN - KK; i++) {
|
for (i = 2; i <= NN - KK; i++) {
|
Gg[i] = 1;
|
Gg[i] = 1;
|
/*
|
/*
|
* Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by
|
* Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by
|
* (@**(B0+i-1) + x)
|
* (@**(B0+i-1) + x)
|
*/
|
*/
|
for (j = i - 1; j > 0; j--){
|
for (j = i - 1; j > 0; j--){
|
if (Gg[j] != 0)
|
if (Gg[j] != 0)
|
Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + B0 + i - 1)];
|
Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + B0 + i - 1)];
|
else
|
else
|
Gg[j] = Gg[j - 1];
|
Gg[j] = Gg[j - 1];
|
|
|
// print("Gg[");print_num(j);print("]=");print_num(Gg[j]);print("\n");
|
// print("Gg[");print_num(j);print("]=");print_num(Gg[j]);print("\n");
|
// print("Gg[");print_num(j-1);print("]=");print_num(Gg[j-1]);print("\n");
|
// print("Gg[");print_num(j-1);print("]=");print_num(Gg[j-1]);print("\n");
|
}
|
}
|
/* Gg[0] can never be zero */
|
/* Gg[0] can never be zero */
|
Gg[0] = Alpha_to[modnn((Index_of[Gg[0]]) + B0 + i - 1)];
|
Gg[0] = Alpha_to[modnn((Index_of[Gg[0]]) + B0 + i - 1)];
|
}
|
}
|
/* convert Gg[] to index form for quicker encoding */
|
/* convert Gg[] to index form for quicker encoding */
|
for (i = 0; i <= NN - KK; i++)
|
for (i = 0; i <= NN - KK; i++)
|
Gg[i] = Index_of[Gg[i]];
|
Gg[i] = Index_of[Gg[i]];
|
|
|
print("Gg dump\n");
|
print("Gg dump\n");
|
for (i=0;i<=NN-KK;i++){
|
for (i=0;i<=NN-KK;i++){
|
print_uchar(Gg[i]);
|
print_uchar(Gg[i]);
|
print(" ");
|
print(" ");
|
}
|
}
|
print("\n");
|
print("\n");
|
}
|
}
|
|
|
|
|
/*
|
/*
|
* take the string of symbols in data[i], i=0..(k-1) and encode
|
* take the string of symbols in data[i], i=0..(k-1) and encode
|
* systematically to produce NN-KK parity symbols in bb[0]..bb[NN-KK-1] data[]
|
* systematically to produce NN-KK parity symbols in bb[0]..bb[NN-KK-1] data[]
|
* is input and bb[] is output in polynomial form. Encoding is done by using
|
* is input and bb[] is output in polynomial form. Encoding is done by using
|
* a feedback shift register with appropriate connections specified by the
|
* a feedback shift register with appropriate connections specified by the
|
* elements of Gg[], which was generated above. Codeword is c(X) =
|
* elements of Gg[], which was generated above. Codeword is c(X) =
|
* data(X)*X**(NN-KK)+ b(X)
|
* data(X)*X**(NN-KK)+ b(X)
|
*/
|
*/
|
int
|
int
|
encode_rs(dtype data[KK], dtype bb[NN-KK])
|
encode_rs(dtype data[KK], dtype bb[NN-KK])
|
{
|
{
|
register int i, j;
|
register int i, j;
|
gf feedback;
|
gf feedback;
|
|
|
CLEAR(bb,NN-KK);
|
CLEAR(bb,NN-KK);
|
for (i = KK - 1; i >= 0; i--) {
|
for (i = KK - 1; i >= 0; i--) {
|
#if (MM != 8)
|
#if (MM != 8)
|
if(data[i] > NN)
|
if(data[i] > NN)
|
return -1; /* Illegal symbol */
|
return -1; /* Illegal symbol */
|
#endif
|
#endif
|
feedback = Index_of[data[i] ^ bb[NN - KK - 1]];
|
feedback = Index_of[data[i] ^ bb[NN - KK - 1]];
|
if (feedback != A0) { /* feedback term is non-zero */
|
if (feedback != A0) { /* feedback term is non-zero */
|
for (j = NN - KK - 1; j > 0; j--)
|
for (j = NN - KK - 1; j > 0; j--)
|
if (Gg[j] != A0)
|
if (Gg[j] != A0)
|
bb[j] = bb[j - 1] ^ Alpha_to[modnn(Gg[j] + feedback)];
|
bb[j] = bb[j - 1] ^ Alpha_to[modnn(Gg[j] + feedback)];
|
else
|
else
|
bb[j] = bb[j - 1];
|
bb[j] = bb[j - 1];
|
bb[0] = Alpha_to[modnn(Gg[0] + feedback)];
|
bb[0] = Alpha_to[modnn(Gg[0] + feedback)];
|
} else { /* feedback term is zero. encoder becomes a
|
} else { /* feedback term is zero. encoder becomes a
|
* single-byte shifter */
|
* single-byte shifter */
|
for (j = NN - KK - 1; j > 0; j--)
|
for (j = NN - KK - 1; j > 0; j--)
|
bb[j] = bb[j - 1];
|
bb[j] = bb[j - 1];
|
bb[0] = 0;
|
bb[0] = 0;
|
}
|
}
|
}
|
}
|
return 0;
|
return 0;
|
}
|
}
|
|
|
/*
|
/*
|
* Performs ERRORS+ERASURES decoding of RS codes. If decoding is successful,
|
* Performs ERRORS+ERASURES decoding of RS codes. If decoding is successful,
|
* writes the codeword into data[] itself. Otherwise data[] is unaltered.
|
* writes the codeword into data[] itself. Otherwise data[] is unaltered.
|
*
|
*
|
* Return number of symbols corrected, or -1 if codeword is illegal
|
* Return number of symbols corrected, or -1 if codeword is illegal
|
* or uncorrectable.
|
* or uncorrectable.
|
*
|
*
|
* First "no_eras" erasures are declared by the calling program. Then, the
|
* First "no_eras" erasures are declared by the calling program. Then, the
|
* maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
|
* maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
|
* If the number of channel errors is not greater than "t_after_eras" the
|
* If the number of channel errors is not greater than "t_after_eras" the
|
* transmitted codeword will be recovered. Details of algorithm can be found
|
* transmitted codeword will be recovered. Details of algorithm can be found
|
* in R. Blahut's "Theory ... of Error-Correcting Codes".
|
* in R. Blahut's "Theory ... of Error-Correcting Codes".
|
*/
|
*/
|
int
|
int
|
eras_dec_rs(dtype data[NN], int eras_pos[NN-KK], int no_eras)
|
eras_dec_rs(dtype data[NN], int eras_pos[NN-KK], int no_eras)
|
{
|
{
|
int deg_lambda, el, deg_omega;
|
int deg_lambda, el, deg_omega;
|
int i, j, r;
|
int i, j, r;
|
gf u,q,tmp,num1,num2,den,discr_r;
|
gf u,q,tmp,num1,num2,den,discr_r;
|
gf recd[NN];
|
gf recd[NN];
|
gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
|
gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
|
* and syndrome poly */
|
* and syndrome poly */
|
gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
|
gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
|
gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
|
gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
|
int syn_error, count;
|
int syn_error, count;
|
|
|
/* data[] is in polynomial form, copy and convert to index form */
|
/* data[] is in polynomial form, copy and convert to index form */
|
for (i = NN-1; i >= 0; i--){
|
for (i = NN-1; i >= 0; i--){
|
#if (MM != 8)
|
#if (MM != 8)
|
if(data[i] > NN)
|
if(data[i] > NN)
|
return -1; /* Illegal symbol */
|
return -1; /* Illegal symbol */
|
#endif
|
#endif
|
recd[i] = Index_of[data[i]];
|
recd[i] = Index_of[data[i]];
|
}
|
}
|
/* first form the syndromes; i.e., evaluate recd(x) at roots of g(x)
|
/* first form the syndromes; i.e., evaluate recd(x) at roots of g(x)
|
* namely @**(B0+i), i = 0, ... ,(NN-KK-1)
|
* namely @**(B0+i), i = 0, ... ,(NN-KK-1)
|
*/
|
*/
|
syn_error = 0;
|
syn_error = 0;
|
for (i = 1; i <= NN-KK; i++) {
|
for (i = 1; i <= NN-KK; i++) {
|
tmp = 0;
|
tmp = 0;
|
for (j = 0; j < NN; j++)
|
for (j = 0; j < NN; j++)
|
if (recd[j] != A0) /* recd[j] in index form */
|
if (recd[j] != A0) /* recd[j] in index form */
|
tmp ^= Alpha_to[modnn(recd[j] + (B0+i-1)*j)];
|
tmp ^= Alpha_to[modnn(recd[j] + (B0+i-1)*j)];
|
syn_error |= tmp; /* set flag if non-zero syndrome =>
|
syn_error |= tmp; /* set flag if non-zero syndrome =>
|
* error */
|
* error */
|
/* store syndrome in index form */
|
/* store syndrome in index form */
|
s[i] = Index_of[tmp];
|
s[i] = Index_of[tmp];
|
}
|
}
|
if (!syn_error) {
|
if (!syn_error) {
|
/*
|
/*
|
* if syndrome is zero, data[] is a codeword and there are no
|
* if syndrome is zero, data[] is a codeword and there are no
|
* errors to correct. So return data[] unmodified
|
* errors to correct. So return data[] unmodified
|
*/
|
*/
|
return 0;
|
return 0;
|
}
|
}
|
CLEAR(&lambda[1],NN-KK);
|
CLEAR(&lambda[1],NN-KK);
|
lambda[0] = 1;
|
lambda[0] = 1;
|
if (no_eras > 0) {
|
if (no_eras > 0) {
|
/* Init lambda to be the erasure locator polynomial */
|
/* Init lambda to be the erasure locator polynomial */
|
lambda[1] = Alpha_to[eras_pos[0]];
|
lambda[1] = Alpha_to[eras_pos[0]];
|
for (i = 1; i < no_eras; i++) {
|
for (i = 1; i < no_eras; i++) {
|
u = eras_pos[i];
|
u = eras_pos[i];
|
for (j = i+1; j > 0; j--) {
|
for (j = i+1; j > 0; j--) {
|
tmp = Index_of[lambda[j - 1]];
|
tmp = Index_of[lambda[j - 1]];
|
if(tmp != A0)
|
if(tmp != A0)
|
lambda[j] ^= Alpha_to[modnn(u + tmp)];
|
lambda[j] ^= Alpha_to[modnn(u + tmp)];
|
}
|
}
|
}
|
}
|
#ifdef ERASURE_DEBUG
|
#ifdef ERASURE_DEBUG
|
/* find roots of the erasure location polynomial */
|
/* find roots of the erasure location polynomial */
|
for(i=1;i<=no_eras;i++)
|
for(i=1;i<=no_eras;i++)
|
reg[i] = Index_of[lambda[i]];
|
reg[i] = Index_of[lambda[i]];
|
count = 0;
|
count = 0;
|
for (i = 1; i <= NN; i++) {
|
for (i = 1; i <= NN; i++) {
|
q = 1;
|
q = 1;
|
for (j = 1; j <= no_eras; j++)
|
for (j = 1; j <= no_eras; j++)
|
if (reg[j] != A0) {
|
if (reg[j] != A0) {
|
reg[j] = modnn(reg[j] + j);
|
reg[j] = modnn(reg[j] + j);
|
q ^= Alpha_to[reg[j]];
|
q ^= Alpha_to[reg[j]];
|
}
|
}
|
if (!q) {
|
if (!q) {
|
/* store root and error location
|
/* store root and error location
|
* number indices
|
* number indices
|
*/
|
*/
|
root[count] = i;
|
root[count] = i;
|
loc[count] = NN - i;
|
loc[count] = NN - i;
|
count++;
|
count++;
|
}
|
}
|
}
|
}
|
if (count != no_eras) {
|
if (count != no_eras) {
|
print("\n lambda(x) is WRONG\n");
|
print("\n lambda(x) is WRONG\n");
|
return -1;
|
return -1;
|
}
|
}
|
#ifndef NO_PRINT
|
#ifndef NO_PRINT
|
print("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
|
print("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
|
for (i = 0; i < count; i++)
|
for (i = 0; i < count; i++)
|
print_num(loc[i]);
|
print_num(loc[i]);
|
print("\n");
|
print("\n");
|
#endif
|
#endif
|
#endif
|
#endif
|
}
|
}
|
for(i=0;i<NN-KK+1;i++)
|
for(i=0;i<NN-KK+1;i++)
|
b[i] = Index_of[lambda[i]];
|
b[i] = Index_of[lambda[i]];
|
|
|
/*
|
/*
|
* Begin Berlekamp-Massey algorithm to determine error+erasure
|
* Begin Berlekamp-Massey algorithm to determine error+erasure
|
* locator polynomial
|
* locator polynomial
|
*/
|
*/
|
r = no_eras;
|
r = no_eras;
|
el = no_eras;
|
el = no_eras;
|
while (++r <= NN-KK) { /* r is the step number */
|
while (++r <= NN-KK) { /* r is the step number */
|
/* Compute discrepancy at the r-th step in poly-form */
|
/* Compute discrepancy at the r-th step in poly-form */
|
discr_r = 0;
|
discr_r = 0;
|
for (i = 0; i < r; i++){
|
for (i = 0; i < r; i++){
|
if ((lambda[i] != 0) && (s[r - i] != A0)) {
|
if ((lambda[i] != 0) && (s[r - i] != A0)) {
|
discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
|
discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
|
}
|
}
|
}
|
}
|
discr_r = Index_of[discr_r]; /* Index form */
|
discr_r = Index_of[discr_r]; /* Index form */
|
if (discr_r == A0) {
|
if (discr_r == A0) {
|
/* 2 lines below: B(x) <-- x*B(x) */
|
/* 2 lines below: B(x) <-- x*B(x) */
|
COPYDOWN(&b[1],b,NN-KK);
|
COPYDOWN(&b[1],b,NN-KK);
|
b[0] = A0;
|
b[0] = A0;
|
} else {
|
} else {
|
/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
|
/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
|
t[0] = lambda[0];
|
t[0] = lambda[0];
|
for (i = 0 ; i < NN-KK; i++) {
|
for (i = 0 ; i < NN-KK; i++) {
|
if(b[i] != A0)
|
if(b[i] != A0)
|
t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
|
t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
|
else
|
else
|
t[i+1] = lambda[i+1];
|
t[i+1] = lambda[i+1];
|
}
|
}
|
if (2 * el <= r + no_eras - 1) {
|
if (2 * el <= r + no_eras - 1) {
|
el = r + no_eras - el;
|
el = r + no_eras - el;
|
/*
|
/*
|
* 2 lines below: B(x) <-- inv(discr_r) *
|
* 2 lines below: B(x) <-- inv(discr_r) *
|
* lambda(x)
|
* lambda(x)
|
*/
|
*/
|
for (i = 0; i <= NN-KK; i++)
|
for (i = 0; i <= NN-KK; i++)
|
b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
|
b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
|
} else {
|
} else {
|
/* 2 lines below: B(x) <-- x*B(x) */
|
/* 2 lines below: B(x) <-- x*B(x) */
|
COPYDOWN(&b[1],b,NN-KK);
|
COPYDOWN(&b[1],b,NN-KK);
|
b[0] = A0;
|
b[0] = A0;
|
}
|
}
|
COPY(lambda,t,NN-KK+1);
|
COPY(lambda,t,NN-KK+1);
|
}
|
}
|
}
|
}
|
|
|
/* Convert lambda to index form and compute deg(lambda(x)) */
|
/* Convert lambda to index form and compute deg(lambda(x)) */
|
deg_lambda = 0;
|
deg_lambda = 0;
|
for(i=0;i<NN-KK+1;i++){
|
for(i=0;i<NN-KK+1;i++){
|
lambda[i] = Index_of[lambda[i]];
|
lambda[i] = Index_of[lambda[i]];
|
if(lambda[i] != A0)
|
if(lambda[i] != A0)
|
deg_lambda = i;
|
deg_lambda = i;
|
}
|
}
|
/*
|
/*
|
* Find roots of the error+erasure locator polynomial. By Chien
|
* Find roots of the error+erasure locator polynomial. By Chien
|
* Search
|
* Search
|
*/
|
*/
|
COPY(®[1],&lambda[1],NN-KK);
|
COPY(®[1],&lambda[1],NN-KK);
|
count = 0; /* Number of roots of lambda(x) */
|
count = 0; /* Number of roots of lambda(x) */
|
for (i = 1; i <= NN; i++) {
|
for (i = 1; i <= NN; i++) {
|
q = 1;
|
q = 1;
|
for (j = deg_lambda; j > 0; j--)
|
for (j = deg_lambda; j > 0; j--)
|
if (reg[j] != A0) {
|
if (reg[j] != A0) {
|
reg[j] = modnn(reg[j] + j);
|
reg[j] = modnn(reg[j] + j);
|
q ^= Alpha_to[reg[j]];
|
q ^= Alpha_to[reg[j]];
|
}
|
}
|
if (!q) {
|
if (!q) {
|
/* store root (index-form) and error location number */
|
/* store root (index-form) and error location number */
|
root[count] = i;
|
root[count] = i;
|
loc[count] = NN - i;
|
loc[count] = NN - i;
|
count++;
|
count++;
|
}
|
}
|
}
|
}
|
|
|
#ifdef DEBUG
|
#ifdef DEBUG
|
print("\n Final error positions:\t");
|
print("\n Final error positions:\t");
|
for (i = 0; i < count; i++)
|
for (i = 0; i < count; i++)
|
print_num(loc[i]);
|
print_num(loc[i]);
|
print("\n");
|
print("\n");
|
#endif
|
#endif
|
if (deg_lambda != count) {
|
if (deg_lambda != count) {
|
/*
|
/*
|
* deg(lambda) unequal to number of roots => uncorrectable
|
* deg(lambda) unequal to number of roots => uncorrectable
|
* error detected
|
* error detected
|
*/
|
*/
|
return -1;
|
return -1;
|
}
|
}
|
/*
|
/*
|
* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
|
* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
|
* x**(NN-KK)). in index form. Also find deg(omega).
|
* x**(NN-KK)). in index form. Also find deg(omega).
|
*/
|
*/
|
deg_omega = 0;
|
deg_omega = 0;
|
for (i = 0; i < NN-KK;i++){
|
for (i = 0; i < NN-KK;i++){
|
tmp = 0;
|
tmp = 0;
|
j = (deg_lambda < i) ? deg_lambda : i;
|
j = (deg_lambda < i) ? deg_lambda : i;
|
for(;j >= 0; j--){
|
for(;j >= 0; j--){
|
if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
|
if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
|
tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
|
tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
|
}
|
}
|
if(tmp != 0)
|
if(tmp != 0)
|
deg_omega = i;
|
deg_omega = i;
|
omega[i] = Index_of[tmp];
|
omega[i] = Index_of[tmp];
|
}
|
}
|
omega[NN-KK] = A0;
|
omega[NN-KK] = A0;
|
|
|
/*
|
/*
|
* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
|
* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
|
* inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
|
* inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
|
*/
|
*/
|
for (j = count-1; j >=0; j--) {
|
for (j = count-1; j >=0; j--) {
|
num1 = 0;
|
num1 = 0;
|
for (i = deg_omega; i >= 0; i--) {
|
for (i = deg_omega; i >= 0; i--) {
|
if (omega[i] != A0)
|
if (omega[i] != A0)
|
num1 ^= Alpha_to[modnn(omega[i] + i * root[j])];
|
num1 ^= Alpha_to[modnn(omega[i] + i * root[j])];
|
}
|
}
|
num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
|
num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
|
den = 0;
|
den = 0;
|
|
|
/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
|
/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
|
for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
|
for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
|
if(lambda[i+1] != A0)
|
if(lambda[i+1] != A0)
|
den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
|
den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
|
}
|
}
|
if (den == 0) {
|
if (den == 0) {
|
#ifdef DEBUG
|
#ifdef DEBUG
|
print("\n ERROR: denominator = 0\n");
|
print("\n ERROR: denominator = 0\n");
|
#endif
|
#endif
|
return -1;
|
return -1;
|
}
|
}
|
/* Apply error to data */
|
/* Apply error to data */
|
if (num1 != 0) {
|
if (num1 != 0) {
|
data[loc[j]] ^= Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
|
data[loc[j]] ^= Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
|
}
|
}
|
}
|
}
|
return count;
|
return count;
|
}
|
}
|
|
|
void
|
void
|
fill_eras(int eras_pos[],int n)
|
fill_eras(int eras_pos[],int n)
|
{
|
{
|
int i,j,t,work[NN];
|
int i,j,t,work[NN];
|
|
|
for(i=0;i<NN;i++)
|
for(i=0;i<NN;i++)
|
work[i] = i;
|
work[i] = i;
|
for(j=NN-1;j>0;j--){
|
for(j=NN-1;j>0;j--){
|
i = random() % j; /* not really uniform, I know */
|
i = random() % j; /* not really uniform, I know */
|
t = work[i];
|
t = work[i];
|
work[i] = work[j];
|
work[i] = work[j];
|
work[j] = t;
|
work[j] = t;
|
}
|
}
|
#ifdef notdef
|
#ifdef notdef
|
for(i=0;i<NN;i++)
|
for(i=0;i<NN;i++)
|
print_num(work[i]);
|
print_num(work[i]);
|
print("\n");
|
print("\n");
|
#endif
|
#endif
|
for(i=0;i<n;i++)
|
for(i=0;i<n;i++)
|
eras_pos[i] = work[i];
|
eras_pos[i] = work[i];
|
}
|
}
|
|
|
/* Return non-zero random number in range 0 - NN (NN power of 2 minus 1) */
|
/* Return non-zero random number in range 0 - NN (NN power of 2 minus 1) */
|
int
|
int
|
randomnz(void)
|
randomnz(void)
|
{
|
{
|
int i;
|
int i;
|
|
|
while((i = random() & NN) == 0)
|
while((i = random() & NN) == 0)
|
;
|
;
|
return i;
|
return i;
|
}
|
}
|
|
|
dtype data[NN];
|
dtype data[NN];
|
dtype tdata[NN];
|
dtype tdata[NN];
|
dtype ddata[NN];
|
dtype ddata[NN];
|
int eras_pos[NN];
|
int eras_pos[NN];
|
int
|
int
|
main(int argc,char *argv[])
|
main(int argc,char *argv[])
|
{
|
{
|
|
|
|
|
int i,trials;
|
int i,trials;
|
int nerrors,nerase,ntrials,verbose,timetest;
|
int nerrors,nerase,ntrials,verbose,timetest;
|
int detfails,fails;
|
int detfails,fails;
|
extern char *optarg;
|
extern char *optarg;
|
|
|
nerrors = nerase = 0;
|
nerrors = nerase = 0;
|
timetest = verbose = 0;
|
timetest = verbose = 0;
|
ntrials = 3;
|
ntrials = 3;
|
verbose = 1;
|
verbose = 1;
|
nerrors=11;
|
nerrors=11;
|
nerase=10;
|
nerase=10;
|
// while((i = getopt(argc,argv,"e:E:n:vt")) != EOF){
|
// while((i = getopt(argc,argv,"e:E:n:vt")) != EOF){
|
// switch(i){
|
// switch(i){
|
/// case 'e': /* Number of errors per block */
|
/// case 'e': /* Number of errors per block */
|
// nerrors = atoi(optarg);
|
// nerrors = atoi(optarg);
|
// break;
|
// break;
|
// case 'E': /* Number of erasures per block */
|
// case 'E': /* Number of erasures per block */
|
// nerase = atoi(optarg);
|
// nerase = atoi(optarg);
|
// break;
|
// break;
|
// case 'n': /* Number of trials */
|
// case 'n': /* Number of trials */
|
// ntrials = atoi(optarg);
|
// ntrials = atoi(optarg);
|
// break;
|
// break;
|
// case 'v': /* Be verbose */
|
// case 'v': /* Be verbose */
|
// verbose = 1;
|
// verbose = 1;
|
// break;
|
// break;
|
// case 't': /* Repeatedly decode the same block */
|
// case 't': /* Repeatedly decode the same block */
|
// timetest = 1;
|
// timetest = 1;
|
// break;
|
// break;
|
// default:
|
// default:
|
// printf("usage: %s [-v] [-t] [-e errors] [-E erasures] [-n ntrials]\n",argv[0]);
|
// printf("usage: %s [-v] [-t] [-e errors] [-E erasures] [-n ntrials]\n",argv[0]);
|
// exit(1);
|
// exit(1);
|
// }
|
// }
|
// }
|
// }
|
print("It takes very very long time for RTL Simulation.\n");
|
print("It takes very very long time for RTL Simulation.\n");
|
print("Reed-Solomon code is ");
|
print("Reed-Solomon code is ");
|
// for (i=3;i>0;i--){
|
// for (i=3;i>0;i--){
|
print_num(NN), print(" "); print_num(KK); print("over GF(");
|
print_num(NN), print(" "); print_num(KK); print("over GF(");
|
print_num(NN+1);print(")\n");
|
print_num(NN+1);print(")\n");
|
// print("i=");print_num(i);print("\n");
|
// print("i=");print_num(i);print("\n");
|
// }
|
// }
|
print("test erasures: ");print_num(nerase);print("errors ");print_num(nerrors);print("\n");
|
print("test erasures: ");print_num(nerase);print("errors ");print_num(nerrors);print("\n");
|
if(2*nerrors + nerase > NN-KK){
|
if(2*nerrors + nerase > NN-KK){
|
print("Warning: ");
|
print("Warning: ");
|
print_num(nerrors); print("errors and ");
|
print_num(nerrors); print("errors and ");
|
print_num(nerase); print("erasures exceeds the correction ability of the code\n");
|
print_num(nerase); print("erasures exceeds the correction ability of the code\n");
|
}
|
}
|
|
|
init_rs();
|
init_rs();
|
print("Init_RS Done");
|
print("Init_RS Done");
|
|
|
fails = detfails = 0;
|
fails = detfails = 0;
|
for(trials=0;trials < ntrials;trials++){
|
for(trials=0;trials < ntrials;trials++){
|
if(verbose){
|
if(verbose){
|
print(" Trial ");
|
print(" Trial ");
|
print_num(trials);
|
print_num(trials);
|
print("\n");
|
print("\n");
|
}
|
}
|
print("Making Encode Data");
|
print("Making Encode Data");
|
for(i=0;i<KK;i++)
|
for(i=0;i<KK;i++)
|
data[i] = random() & NN;
|
data[i] = random() & NN;
|
encode_rs(data,&data[KK]);
|
encode_rs(data,&data[KK]);
|
fill_eras(eras_pos,nerase+nerrors);
|
fill_eras(eras_pos,nerase+nerrors);
|
if(verbose && nerase){
|
if(verbose && nerase){
|
print("\n erasing:");
|
print("\n erasing:");
|
for(i=0;i<nerase;i++){
|
for(i=0;i<nerase;i++){
|
print(" ");print_num(eras_pos[i]);
|
print(" ");print_num(eras_pos[i]);
|
|
|
}
|
}
|
print("\n");
|
print("\n");
|
}
|
}
|
if(verbose && nerrors){
|
if(verbose && nerrors){
|
print(" erroring:");
|
print(" erroring:");
|
for(i=nerase;i<nerase+nerrors;i++){
|
for(i=nerase;i<nerase+nerrors;i++){
|
print(" ");print_num(eras_pos[i]);
|
print(" ");print_num(eras_pos[i]);
|
|
|
}
|
}
|
print("\n");
|
print("\n");
|
}
|
}
|
if(verbose){
|
if(verbose){
|
for(i=0;i<NN;i++){
|
for(i=0;i<NN;i++){
|
print_uchar(data[i]);
|
print_uchar(data[i]);
|
print(" ");
|
print(" ");
|
}
|
}
|
print("\n");
|
print("\n");
|
}
|
}
|
memcpy(ddata,data,sizeof(data));
|
memcpy(ddata,data,sizeof(data));
|
for(i=0;i<nerase+nerrors;i++)
|
for(i=0;i<nerase+nerrors;i++)
|
ddata[eras_pos[i]] ^= randomnz();
|
ddata[eras_pos[i]] ^= randomnz();
|
|
|
i = eras_dec_rs(ddata,eras_pos,nerase);
|
i = eras_dec_rs(ddata,eras_pos,nerase);
|
if(verbose){
|
if(verbose){
|
print("errs + erasures corrected: ");print_num(i);
|
print("errs + erasures corrected: ");print_num(i);
|
}
|
}
|
if(i == -1){
|
if(i == -1){
|
detfails++;
|
detfails++;
|
print("RS decoder detected failure\n");
|
print("RS decoder detected failure\n");
|
} else if(memcmp(ddata,data,NN) != 0){
|
} else if(memcmp(ddata,data,NN) != 0){
|
fails++;
|
fails++;
|
print(" Undetected decoding failure!\n");
|
print(" Undetected decoding failure!\n");
|
}
|
}
|
}
|
}
|
print(" \n\nTrials: ");
|
print(" \n\nTrials: ");
|
print_num(ntrials);
|
print_num(ntrials);
|
print(" decoding failures: ");
|
print(" decoding failures: ");
|
print_num(detfails); print(" not detected by decoder: ");
|
print_num(detfails); print(" not detected by decoder: ");
|
print_num(fails); print("\n");
|
print_num(fails); print("\n");
|
print("$finish");
|
print("$finish");
|
return 0;
|
return 0;
|
}
|
}
|
|
|
|
|