HI,

I want to know how to implement the parallel syndrome for bch code.

Thanks in advance

Krupesh

If the bus width is 8 bits in your design. We will get the following
equation that will be iterated in the sydrome stage.
Sub(r[7:0]) = r[0]*a^0 + r[1]*a^1 + ... + r[7]*a^7
And then:
S1_clk0 = Sub(r[7:0])
S1_clk1 = Sub(r[7:0])*(a^8) + S1_clk0;
S1_clk2 = Sub(r[7:0])*(a^8) + S1_clk1;
...
S1_clkn = Sub(r[7:0])*(a^8) + S1_clk(n-1);
The S1_clkn will be the sydrome 1. And you can caculate other
syndromes in this way.
Good Luck.

Thank you very much for your reply.

From your reply I have designed the required syndromes.

I need one more favor from you.

I want to implement parallel chien search machine.Do you have any material for that? or can you guide me to implement that?

Again thank you very much for your reply.

Regards,

Krupesh

I just can list some tips because of some business constrain.
see the equation : 1+sigma_1*a^1+...+sigma_v*a^v=0,
you just need find the "a" with that the equation value is zero.
so if you need a 8 bits parrel chien search, 8 equation is needed.
sum[0] = 1+sigma_1*((a^1)^1)+...+sigma_v*((a^1)^v)
sum[1] = 1+sigma_1*((a^2)^1)+...+sigma_v*((a^2)^v)
...
sum[7] = 1+sigma_1*((a^8)^1)+...+sigma_v*((a^8)^v)
Any bits in the sum[7:0] is zero, the error location is found.

Again Thank you very much for your reply.

The solution you provided is really helpful.Now I am about to complete my work.

I want to ask you a last question regarding BCH decoder.My question is that How to find decoding failure?

I found some material in which it is mentioned that if the degree of lambda(error location polynomial) is greater then t(where t=no.of error correction bits) then it is a decoding failure.

Suppose after applying Chien Search algorithm,my lambda values are like this

lambda(0) = x^12+x^3+x+1
lambda(1) = x^3+x^2+x+1
lambda(2) = x^2+x+1
lambda[3] = x^4+x^3+x^2+x+1

From equation can we say that this is decoding failure because lambda(0) and lambda(3) are having a degree more then t(where t = 3).

Thanks in advance.

Again Thank you very much for your reply.

The solution you provided is really helpful.Now I am about to complete my work.

I want to ask you a last question regarding BCH decoder.My question is that How to find decoding failure?

I found some material in which it is mentioned that if the degree of lambda(error location polynomial) is greater then t(where t=no.of error correction bits) then it is a decoding failure.

Suppose after applying Chien Search algorithm,my lambda values are like this

lambda(0) = x^12+x^3+x+1
lambda(1) = x^3+x^2+x+1
lambda(2) = x^2+x+1
lambda[3] = x^4+x^3+x^2+x+1

From equation can we say that this is decoding failure because lambda(0) and lambda(3) are having a degree more then t(where t = 3).

Thanks in advance.