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-------------------------------------------------------------------------------
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-- Yahamm IP core
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--
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-- This file is part of the Yahamm project
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-- http://www.opencores.org/cores/yahamm
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--
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-- Description
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-- A hamming encoder and decoder with single-error correcting and
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-- double-error detecting capability. The message length can be configured
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-- through a generic. Both the code generator matrix and the parity-check
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-- matrix are computed in the VHDL itself.
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--
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-- Author:
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-- - Nicola De Simone, ndesimone@opencores.org
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--
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-------------------------------------------------------------------------------
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--
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-- Copyright (C) 2017 Authors and OPENCORES.ORG
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--
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-- This source file may be used and distributed without
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-- restriction provided that this copyright statement is not
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-- removed from the file and that any derivative work contains
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-- the original copyright notice and the associated disclaimer.
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--
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-- This source file is free software; you can redistribute it
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-- and/or modify it under the terms of the GNU Lesser General
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-- Public License as published by the Free Software Foundation;
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-- either version 2.1 of the License, or (at your option) any
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-- later version.
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--
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-- This source is distributed in the hope that it will be
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-- useful, but WITHOUT ANY WARRANTY; without even the implied
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-- warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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-- PURPOSE. See the GNU Lesser General Public License for more
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-- details.
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--
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--- You should have received a copy of the GNU Lesser General
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-- Public License along with this source; if not, download it
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-- from http://www.opencores.org/lgpl.shtml
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--
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-------------------------------------------------------------------------------
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2 |
ndesimone |
library ieee;
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use ieee.std_logic_1164.all;
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use ieee.math_real.all;
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use ieee.numeric_std.all;
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library yahamm;
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use yahamm.matrix_pkg.all;
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package yahamm_pkg is
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component yahamm_dec is
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generic (
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MESSAGE_LENGTH : natural;
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CORRECT : boolean;
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EXTRA_PARITY_BIT : natural range 0 to 1;
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ONE_PARITY_BIT : boolean;
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ERROR_LEN : natural;
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NPARITY_BITS : natural;
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BLOCK_LENGTH : natural);
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port (
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clk, rst : in std_logic;
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en : in std_logic;
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din : in std_logic_vector(MESSAGE_LENGTH - 1 downto 0);
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parity : in std_logic_vector(NPARITY_BITS + EXTRA_PARITY_BIT - 1 downto 0);
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dout : out std_logic_vector(MESSAGE_LENGTH - 1 downto 0);
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cnt_errors_corrected, cnt_errors_detected : out std_logic_vector(ERROR_LEN - 1 downto 0));
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end component yahamm_dec;
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component yahamm_enc is
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generic (
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MESSAGE_LENGTH : natural;
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EXTRA_PARITY_BIT : natural range 0 to 1;
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ONE_PARITY_BIT : boolean;
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NPARITY_BITS : natural;
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BLOCK_LENGTH : natural);
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port (
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clk, rst : in std_logic;
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en : in std_logic := '1';
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din : in std_logic_vector(MESSAGE_LENGTH - 1 downto 0);
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dout : out std_logic_vector(MESSAGE_LENGTH - 1 downto 0);
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parity : out std_logic_vector(NPARITY_BITS + EXTRA_PARITY_BIT - 1 downto 0));
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end component yahamm_enc;
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function get_parity_check_matrix (
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MESSAGE_LENGTH : natural;
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EXTRA_PARITY : natural range 0 to 1 := 1;
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ONE_PARITY_BIT : boolean := false)
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return matrix_t;
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function get_code_generator_matrix (
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MESSAGE_LENGTH : natural;
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4 |
ndesimone |
EXTRA_PARITY : natural range 0 to 1 := 1; -- number of data (non parity) bits
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2 |
ndesimone |
ONE_PARITY_BIT : boolean := false)
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return matrix_t;
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function calc_nparity_bits (
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4 |
ndesimone |
k : natural;
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2 |
ndesimone |
ONE_PARITY_BIT : boolean := false)
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return natural;
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function calc_block_length (
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4 |
ndesimone |
k : natural;
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2 |
ndesimone |
ONE_PARITY_BIT : boolean := false)
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return natural;
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procedure check_parameters (
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constant BLOCK_LENGTH : in natural;
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constant NPARITY_BITS : in natural;
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constant MESSAGE_LENGTH : in natural;
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constant EXTRA_PARITY_BIT : in natural;
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constant ONE_PARITY_BIT : in boolean;
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constant CORRECT : in boolean := false
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);
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4 |
ndesimone |
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2 |
ndesimone |
function xor_multiply (
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A : matrix_t;
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4 |
ndesimone |
B : matrix_t)
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2 |
ndesimone |
return matrix_t;
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function xor_multiply_vec (
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A : matrix_t;
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4 |
ndesimone |
x : bit_vector)
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2 |
ndesimone |
return bit_vector;
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function get_form_swap_matrix (
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MESSAGE_LENGTH : natural;
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EXTRA_PARITY : natural;
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ONE_PARITY_BIT : boolean := false)
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return matrix_t;
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end package yahamm_pkg;
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package body yahamm_pkg is
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4 |
ndesimone |
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2 |
ndesimone |
-- purpose: Return a matrix S that can be used to tranform a parity
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-- check matrix or a code generator matrix M from non-systematic
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-- form to systematic form MS and viceversa (because S = S
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-- transposed = S^-1). Use as as MS = M x S.
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-- Also works for M with extra parity bit: set EXTRA_PARITY to 1 and
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-- the swap matrix increases of one extra column and one extra row
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-- (as the parity check matrix) and the extra column is not swapped.
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function get_form_swap_matrix (
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MESSAGE_LENGTH : natural;
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4 |
ndesimone |
EXTRA_PARITY : natural;
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2 |
ndesimone |
ONE_PARITY_BIT : boolean := false)
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return matrix_t is
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constant BLOCK_LENGTH : natural := calc_block_length(MESSAGE_LENGTH, ONE_PARITY_BIT);
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constant NPARITY_BITS : natural := calc_nparity_bits(MESSAGE_LENGTH, ONE_PARITY_BIT);
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variable idmatrix : matrix_t(0 to BLOCK_LENGTH + EXTRA_PARITY - 1, 0 to BLOCK_LENGTH + EXTRA_PARITY - 1) := (others => (others => '0'));
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variable swap_matrix : matrix_t(0 to BLOCK_LENGTH + EXTRA_PARITY - 1, 0 to BLOCK_LENGTH + EXTRA_PARITY - 1); -- output
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begin -- function get_systematic_swap_matrix
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-- Fill up the identity matrix idmatrix. It's initialized to zeros, so
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-- just write ones on the diagonal.
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for irow in idmatrix'range(1) loop
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for icol in idmatrix'range(2) loop
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if irow = icol then
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idmatrix(irow, icol) := '1';
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end if;
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end loop;
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end loop;
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-- Swap columns corresponding to parity bits position in the
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-- parity check matrix (0, 1, 3, 7 etc...) with the right-most
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-- columns (starting with inner possibile rightmost). E.g. let's
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-- say that, with the given message length, BLOCK_LENGTH is 7 and
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-- the parity bits are in positions 0, 1 and 3. The swap will be:
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-- 0 <-> 5
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-- 1 <-> 6
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-- 3 <-> 7
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--
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-- Note: if EXTRA_PARITY is set, last colum is ignored because is not to be
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-- swapped.
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swap_matrix := idmatrix;
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for np in 0 to NPARITY_BITS-1 loop
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swap_cols(swap_matrix, 2**np - 1, BLOCK_LENGTH - NPARITY_BITS + np);
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end loop; -- np
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return swap_matrix;
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end function get_form_swap_matrix;
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-- purpose: Return the result of the matrix M x vector v product. Internal sums are
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-- replaced by xor operations. E.g.:
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-- [1 1; 0 1] * [a; b] = [a xor b; b]
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-- [1 1; 0 1] * [1 1; 1 0] = [0 1; 1 0]
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function xor_multiply (
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A : matrix_t;
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B : matrix_t)
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return matrix_t is
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--variable y : bit_vector(A'reverse_range(1));
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variable y : matrix_t(A'range(1), B'range(2));
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variable element : bit;
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begin -- function matrix_multiply
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--report "xor_multiply: Matrix A sized "
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-- & integer'image(A'length(1)) & "x" & integer'image(A'length(2))
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-- & ". Matrix B sized "
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-- & integer'image(B'length(1)) & "x" & integer'image(B'length(2)) & "."
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-- severity note;
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assert A'length(2) = B'length(1)
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report "Cannot multiply matrix A sized "
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& integer'image(A'length(1)) & "x" & integer'image(A'length(2))
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& " with matrix B sized "
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& integer'image(B'length(1)) & "x" & integer'image(B'length(2)) & "."
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severity error;
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for Arow in A'range(1) loop
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for Bcol in B'range(2) loop
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element := '0';
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for Acol in A'range(2) loop
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element := element xor (A(Arow, Acol) and B(Acol, Bcol));
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end loop; -- i
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y(Arow, Bcol) := element;
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--report
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-- "(" & integer'image(Arow) & ", " & integer'image(Bcol) & "): " &
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-- "y(Arow, Bcol) := " & bit'image(element)
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-- severity note;
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end loop; -- Bcol
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--assert false report "y(" & integer'image(y'length-Arow-1) & ") := " & bit'image(y(y'length-Arow-1)) severity note;
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end loop;
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236 |
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--pretty_print_matrix(A);
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--pretty_print_matrix(B);
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--pretty_print_matrix(y);
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240 |
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return y;
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242 |
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end function xor_multiply;
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243 |
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244 |
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245 |
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-- purpose: Return the result of the matrix operation y = A*x using
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246 |
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-- xor_multiply function. See xor_multiply comment for details.
|
247 |
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function xor_multiply_vec (
|
248 |
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A : matrix_t;
|
249 |
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x : bit_vector)
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250 |
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return bit_vector is
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251 |
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252 |
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variable B : matrix_t(x'range, 0 to 0);
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253 |
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variable C : matrix_t(A'range(1), 0 to 0);
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254 |
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255 |
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variable y : bit_vector(A'reverse_range(1)); -- output
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256 |
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|
257 |
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begin -- function matrix_multiply
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258 |
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259 |
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assert A'length(2) = x'length
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260 |
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report "Cannot multiply matrix A sized "
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261 |
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& integer'image(A'length(1)) & "x" & integer'image(A'length(2))
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262 |
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& " with vector x of length "
|
263 |
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& integer'image(x'length) & "."
|
264 |
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severity error;
|
265 |
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266 |
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-- Transform bit_vector x into a 1-column matrix_t.
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267 |
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for i in x'range loop
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268 |
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B(i, 0) := x(i);
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269 |
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end loop; -- i
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270 |
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271 |
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C := xor_multiply(A, B);
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272 |
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273 |
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-- Transform the 1-column matrix_t C into a bit_vector.
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274 |
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for i in C'range(1) loop
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275 |
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y(i) := C(i, 0);
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276 |
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end loop; -- i
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277 |
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|
278 |
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--report "xor_multiply_vec: Matrix A sized "
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279 |
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-- & integer'image(A'length(1)) & "x" & integer'image(A'length(2))
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280 |
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-- & ". Matrix B sized "
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281 |
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-- & integer'image(B'length(1)) & "x" & integer'image(B'length(2)) & "."
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282 |
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-- severity note;
|
283 |
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|
284 |
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--pretty_print_matrix(A);
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285 |
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--pretty_print_matrix(B);
|
286 |
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--pretty_print_matrix(C);
|
287 |
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--pretty_print_vector(y);
|
288 |
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|
289 |
|
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return y;
|
290 |
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|
291 |
|
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end function xor_multiply_vec;
|
292 |
|
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|
293 |
|
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-- purpose: Generate the parity check matrix for a given message length. The
|
294 |
|
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-- matrix is in non-systematic form.
|
295 |
|
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function get_parity_check_matrix (
|
296 |
|
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MESSAGE_LENGTH : natural;
|
297 |
|
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EXTRA_PARITY : natural range 0 to 1 := 1; -- increase hamming distance to 4
|
298 |
|
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ONE_PARITY_BIT : boolean := false)
|
299 |
|
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return matrix_t is
|
300 |
|
|
|
301 |
|
|
constant NPARITY_BITS : natural := calc_nparity_bits(MESSAGE_LENGTH, ONE_PARITY_BIT);
|
302 |
|
|
constant BLOCK_LENGTH : natural := calc_block_length(MESSAGE_LENGTH, ONE_PARITY_BIT);
|
303 |
|
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|
304 |
|
|
variable m : matrix_t(0 to NPARITY_BITS-1, 0 to BLOCK_LENGTH-1);
|
305 |
|
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variable parity, bit_pos : natural;
|
306 |
|
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variable ubit_pos : unsigned(BLOCK_LENGTH - 1 downto 0);
|
307 |
|
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|
308 |
|
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-- add 1 row and 1 column respect to m to build a parity check
|
309 |
|
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-- matrix with extra parity bit.
|
310 |
|
|
variable m_extra : matrix_t(0 to m'length(1), 0 to m'length(2));
|
311 |
|
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variable hecol : bit_vector(m_extra'range(1));
|
312 |
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|
313 |
|
|
begin -- function get_parity_check_matrix
|
314 |
|
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|
315 |
|
|
if ONE_PARITY_BIT then
|
316 |
|
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m := (0 => (others => '1'));
|
317 |
|
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return m;
|
318 |
|
|
end if;
|
319 |
|
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|
320 |
|
|
for iparity in m'range(1) loop
|
321 |
|
|
parity := 2**iparity;
|
322 |
|
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|
323 |
|
|
if parity >= 2 then
|
324 |
|
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for bit_pos in 0 to parity-2 loop
|
325 |
|
|
m(iparity, bit_pos) := '0';
|
326 |
|
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end loop;
|
327 |
|
|
end if;
|
328 |
|
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|
329 |
|
|
for bit_pos in parity-1 to m'length(2)-1 loop
|
330 |
|
|
ubit_pos := to_unsigned(bit_pos+1, BLOCK_LENGTH);
|
331 |
|
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|
332 |
|
|
m(iparity, bit_pos) := to_bit(ubit_pos(iparity));
|
333 |
|
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|
334 |
|
|
end loop; -- bit_pos
|
335 |
|
|
end loop; -- iparity
|
336 |
|
|
|
337 |
|
|
if EXTRA_PARITY = 0 then
|
338 |
|
|
return m;
|
339 |
|
|
else
|
340 |
|
|
-- m_extra is the parity check matrix with extra parity bits.
|
341 |
|
|
-- It is constructed from m in 2 steps. m_extra has an extra
|
342 |
|
|
-- row and extra column respect to m.
|
343 |
|
|
|
344 |
|
|
-- 1. copy m in m_extra.
|
345 |
|
|
for irow in m'range(1) loop
|
346 |
|
|
for icol in m'range(2) loop
|
347 |
|
|
m_extra(irow, icol) := m(irow, icol);
|
348 |
|
|
end loop;
|
349 |
|
|
end loop;
|
350 |
|
|
|
351 |
|
|
-- 2. Add extra row with '1'.
|
352 |
|
|
for icol in m_extra'range(2) loop
|
353 |
|
|
m_extra(m_extra'high(1), icol) := '1';
|
354 |
|
|
end loop;
|
355 |
|
|
|
356 |
|
|
return m_extra;
|
357 |
|
|
end if;
|
358 |
|
|
|
359 |
|
|
end function get_parity_check_matrix;
|
360 |
|
|
|
361 |
|
|
-- purpose: Create the code generator matrix in systematic form.
|
362 |
|
|
function get_code_generator_matrix (
|
363 |
|
|
MESSAGE_LENGTH : natural;
|
364 |
|
|
EXTRA_PARITY : natural range 0 to 1 := 1; -- increase hamming ndistance to 4
|
365 |
|
|
ONE_PARITY_BIT : boolean := false)
|
366 |
|
|
|
367 |
|
|
return matrix_t is
|
368 |
|
|
|
369 |
|
|
constant BLOCK_LENGTH : natural := calc_block_length(MESSAGE_LENGTH, ONE_PARITY_BIT);
|
370 |
|
|
constant NPARITY_BITS : natural := calc_nparity_bits(MESSAGE_LENGTH, ONE_PARITY_BIT);
|
371 |
|
|
|
372 |
|
|
-- The only reason the code generator matrix is systematic is because H
|
373 |
|
|
-- returned from get_code_generator_matrix is systematic (see
|
374 |
|
|
-- make_systematic in code_generator_matrix).
|
375 |
|
|
variable H : matrix_t(0 to NPARITY_BITS + EXTRA_PARITY - 1,
|
376 |
|
|
|
377 |
|
|
EXTRA_PARITY,
|
378 |
|
|
ONE_PARITY_BIT);
|
379 |
|
|
|
380 |
|
|
-- G is the code generator matrix.
|
381 |
|
|
variable G : matrix_t(0 to BLOCK_LENGTH - NPARITY_BITS - 1, 0 to BLOCK_LENGTH + EXTRA_PARITY - 1);
|
382 |
|
|
-- GT is G transposed.
|
383 |
|
|
variable GT : matrix_t(G'range(2), G'range(1));
|
384 |
|
|
|
385 |
|
|
variable gcol : bit_vector(H'range(2)); -- G matrix column
|
386 |
|
|
variable hcol : bit_vector(H'range(1)); -- H matrix column
|
387 |
|
|
|
388 |
|
|
variable swap_matrix : matrix_t(0 to BLOCK_LENGTH + EXTRA_PARITY - 1, 0 to BLOCK_LENGTH + EXTRA_PARITY - 1);
|
389 |
|
|
|
390 |
|
|
begin -- function get_code_generator_matrix
|
391 |
4 |
ndesimone |
|
392 |
2 |
ndesimone |
-- Identity submatrix on the left (I_k)
|
393 |
|
|
for col in 0 to BLOCK_LENGTH - NPARITY_BITS - 1 loop
|
394 |
|
|
gcol := (others => '0');
|
395 |
|
|
gcol(col) := '1';
|
396 |
|
|
set_col(G, col, gcol);
|
397 |
|
|
end loop; -- col
|
398 |
|
|
|
399 |
|
|
-- transform H in systematic form
|
400 |
|
|
swap_matrix := get_form_swap_matrix(MESSAGE_LENGTH, EXTRA_PARITY, ONE_PARITY_BIT);
|
401 |
|
|
H := xor_multiply(H, swap_matrix);
|
402 |
|
|
|
403 |
|
|
if EXTRA_PARITY = 1 then
|
404 |
|
|
-- This is a trick that avoids a very tedious row reduction.
|
405 |
|
|
|
406 |
|
|
for icol in H'range(2) loop
|
407 |
|
|
hcol := get_col(H, icol);
|
408 |
4 |
ndesimone |
if xor_reduce(hcol) = '0' then
|
409 |
2 |
ndesimone |
H(H'high(1), icol) := '0';
|
410 |
|
|
end if;
|
411 |
|
|
end loop; -- icol
|
412 |
|
|
|
413 |
|
|
end if;
|
414 |
|
|
|
415 |
|
|
--pretty_print_matrix(H);
|
416 |
|
|
--pretty_print_matrix(xor_multiply(H, swap_matrix));
|
417 |
|
|
|
418 |
|
|
-- Submatrix A transposed.
|
419 |
|
|
for col in BLOCK_LENGTH - NPARITY_BITS to BLOCK_LENGTH + EXTRA_PARITY - 1 loop
|
420 |
|
|
for row in 0 to BLOCK_LENGTH - NPARITY_BITS - 1 loop
|
421 |
|
|
G(row, col) := H(col-(BLOCK_LENGTH-NPARITY_BITS), row);
|
422 |
|
|
end loop;
|
423 |
|
|
end loop;
|
424 |
|
|
|
425 |
|
|
-- transpose G
|
426 |
|
|
for irow in G'range(1) loop
|
427 |
|
|
for icol in G'range(2) loop
|
428 |
|
|
GT(icol, irow) := G(irow, icol);
|
429 |
|
|
end loop;
|
430 |
|
|
end loop;
|
431 |
|
|
|
432 |
|
|
return GT;
|
433 |
|
|
|
434 |
|
|
end function get_code_generator_matrix;
|
435 |
|
|
|
436 |
|
|
-- purpose: Calculate the number of parity bits (r) needed for the
|
437 |
8 |
ndesimone |
-- specified message length (k). The code has k = 2^r - r - 1 for r >= 2.
|
438 |
2 |
ndesimone |
function calc_nparity_bits (
|
439 |
|
|
k : natural;
|
440 |
|
|
ONE_PARITY_BIT : boolean := false)
|
441 |
|
|
return natural is
|
442 |
|
|
variable r : natural := 0;
|
443 |
|
|
begin -- function calc_nparity_bits
|
444 |
|
|
|
445 |
|
|
-- assert k > 0 report "Code construction not implement for message length 0." severity failure;
|
446 |
|
|
|
447 |
|
|
if ONE_PARITY_BIT then
|
448 |
|
|
return 1;
|
449 |
|
|
end if;
|
450 |
|
|
|
451 |
|
|
r := 0;
|
452 |
|
|
while true loop
|
453 |
|
|
if 2**r - r - 1 >= k then
|
454 |
|
|
return r;
|
455 |
|
|
end if;
|
456 |
|
|
|
457 |
|
|
r := r + 1;
|
458 |
|
|
end loop;
|
459 |
|
|
|
460 |
|
|
report "This should never happen." severity failure;
|
461 |
|
|
return 0;
|
462 |
|
|
|
463 |
|
|
end function calc_nparity_bits;
|
464 |
|
|
|
465 |
|
|
-- purpose: Calculate the code block length n for the specified
|
466 |
|
|
-- message length (k). The code has n = 2^r - 1 for r >= 2.
|
467 |
|
|
function calc_block_length (
|
468 |
4 |
ndesimone |
k : natural;
|
469 |
2 |
ndesimone |
ONE_PARITY_BIT : boolean := false)
|
470 |
|
|
return natural is
|
471 |
|
|
variable r : natural := 0;
|
472 |
|
|
begin -- function calc_nparity_bits
|
473 |
|
|
|
474 |
|
|
-- assert k > 0 report "Code construction not implement for message length 0." severity failure;
|
475 |
|
|
|
476 |
|
|
if ONE_PARITY_BIT then
|
477 |
|
|
return k + 1;
|
478 |
|
|
end if;
|
479 |
|
|
|
480 |
|
|
r := calc_nparity_bits(k);
|
481 |
|
|
|
482 |
|
|
return 2**r - 1;
|
483 |
|
|
|
484 |
|
|
end function calc_block_length;
|
485 |
|
|
|
486 |
|
|
procedure check_parameters (
|
487 |
|
|
constant BLOCK_LENGTH : in natural;
|
488 |
|
|
constant NPARITY_BITS : in natural;
|
489 |
|
|
constant MESSAGE_LENGTH : in natural;
|
490 |
|
|
constant EXTRA_PARITY_BIT : in natural;
|
491 |
|
|
constant ONE_PARITY_BIT : in boolean;
|
492 |
|
|
constant CORRECT : in boolean := false) is
|
493 |
|
|
begin
|
494 |
|
|
assert BLOCK_LENGTH = calc_block_length(MESSAGE_LENGTH, ONE_PARITY_BIT) report "Invalid parameter value BLOCK_LENGTH := " & natural'image(BLOCK_LENGTH) severity failure;
|
495 |
|
|
assert NPARITY_BITS = calc_nparity_bits(MESSAGE_LENGTH, ONE_PARITY_BIT) report "Invalid parameter value NPARITY_BITS := " & natural'image(NPARITY_BITS) severity failure;
|
496 |
|
|
|
497 |
|
|
if ONE_PARITY_BIT then
|
498 |
|
|
assert EXTRA_PARITY_BIT = 0 report "EXTRA_PARITY_BIT 1 is not compatible with ONE_PARITY_BIT true." severity failure;
|
499 |
|
|
assert CORRECT = false report "CORRECT true is not compatible with ONE_PARITY_BIT true." severity failure;
|
500 |
|
|
end if;
|
501 |
|
|
|
502 |
|
|
end procedure check_parameters;
|
503 |
|
|
|
504 |
|
|
end package body yahamm_pkg;
|