BCH codes
in [DSP]
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From: javi on 14 Sep 2005 08:37 Hi all, I need to implement a BCH encoder in c++. I already have the code generator polinomial, and know k (the information block length) and n( the codeword length). Does anybody know where I can find some info about how to implement it? Or maybe some freely available code which performs this encoding in c++? If I got it right, the redundant bits are the reminder of dividing (modulo-2)the information bits by the generator polinomial. But, should I add zeros to the information bits before performing the division? I say this because somewhere I read that I should add as many zeros as the degree of the code generator polinomial. And the other issue is, how to implement this modulo-2 division in c++? Is there any available source that performs this operation? This message was sent using the Comp.DSP web interface on www.DSPRelated.com
From: jaco.versfeld on 14 Sep 2005 15:59 Hi Javi, > If I got it right, the redundant bits are the reminder of dividing > (modulo-2)the information bits by the generator polinomial. But, should I > add zeros to the information bits before performing the division? I say > this because somewhere I read that I should add as many zeros as the > degree of the code generator polinomial. Yes, c(x) = x^{n-k}*p(x) + [x^{n-k}*p(x)] mod g(x). Thus, you shift your data bits (represented by the polynomial p(x)) left and add the remainder of the shifted polynomial divided by g(x). This gives you a systematic encoding. Another way is to construct the Generator matrix G, and to multiply your data by G. If you do not need a systematic encoding, you can simply multiply your data polynomial p(x) by g(x). > And the other issue is, how to implement this modulo-2 division in c++? Is > there any available source that performs this operation? I used Matlab for my coding simulations (very fast implementation, not too fast when running the simulations). Otherwise, if you want to fast track yourself without re-inventing the wheel using C++, try the NTL library: http://www.shoup.net/ntl/ . I also did some simulations (Reed-Solomon codes, a subclass of BCH codes) using Java. I adapted the code from http://jeans.studentenweb.org/study/tai/galois/galois.html to do my Java simulations. Hope this helps, Jaco Versfeld
From: javi on 19 Sep 2005 10:16 >Hi Javi, > >> If I got it right, the redundant bits are the reminder of dividing >> (modulo-2)the information bits by the generator polinomial. But, should I >> add zeros to the information bits before performing the division? I say >> this because somewhere I read that I should add as many zeros as the >> degree of the code generator polinomial. > >Yes, c(x) = x^{n-k}*p(x) + [x^{n-k}*p(x)] mod g(x). Thus, you shift >your data bits (represented by the polynomial p(x)) left and add the >remainder of the shifted polynomial divided by g(x). This gives you a >systematic encoding. > >Another way is to construct the Generator matrix G, and to multiply >your data by G. > >If you do not need a systematic encoding, you can simply multiply your >data polynomial p(x) by g(x). > >> And the other issue is, how to implement this modulo-2 division in c++? Is >> there any available source that performs this operation? > >I used Matlab for my coding simulations (very fast implementation, not >too fast when running the simulations). Otherwise, if you want to fast >track yourself without re-inventing the wheel using C++, try the NTL >library: http://www.shoup.net/ntl/ . > >I also did some simulations (Reed-Solomon codes, a subclass of BCH >codes) using Java. I adapted the code from >http://jeans.studentenweb.org/study/tai/galois/galois.html to do my >Java simulations. > >Hope this helps, >Jaco Versfeld > > Thank you very much for your information,Jaco, I found it very helpful for my work. Best regards, Javi This message was sent using the Comp.DSP web interface on www.DSPRelated.com
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