Here I post the same message I've posted in another forum, where I've not yet received an answer. I've a basic question about encoding with Reed Solomon code. Suppose that C is a RS-code of length n = q-1 over the field F_q, designed distance d and dimension k. Let b a primitive element in F_q. The generator of the code is g(x) = (x-b) (x-b^2)...(x-b^(d-1)). Now, if I want to encode an element p(x) in F_q [x] of degree less or equal to k-1, I must multiply g(x) p(x). The result is an element of C. Is it correct to encode in this way? (I suppose the answer is affermative). However I have read about a systematic encoding. This method seems different. And the result of encoding too. So, if a choose a fixed RS-code C, with a generator g(x), using the first method and the systematic encoding I have two different result. Can you confirm this?

# Reed Solomon encoding

Started by ●June 10, 2006

Reply by ●June 10, 20062006-06-10

sugolini@gmail.com said the following on 10/06/2006 22:51: > I've a basic question about encoding with Reed Solomon code. Suppose> that C is a RS-code of length n = q-1 over the field F_q, designed > distance d and dimension k. Let b a primitive element in F_q. The > generator of the code is g(x) = (x-b) (x-b^2)...(x-b^(d-1)). Now, if I > want to encode an element p(x) in F_q [x] of degree less or equal to > k-1, I must multiply g(x) p(x). The result is an element of C. Is it > correct to encode in this way? (I suppose the answer is affermative). > However I have read about a systematic encoding. This method seems > different. And the result of encoding too. So, if a choose a fixed > RS-code C, with a generator g(x), using the first method and the > systematic encoding I have two different result. Can you confirm this?The systematic form of any coding scheme (not just RS) maintains the same codeword set, but does not maintain the mapping between the set of possible inputs and this codeword set. So yes, you will get a different output if you adopt a systematic encoder. However, as the codeword set is the same, your Hamming and Euclidean distance spectra will be the same as for the non-systematic form, so there is no change to the effectiveness of the code. -- Oli

Reply by ●June 11, 20062006-06-11

Oli Filth wrote:> The systematic form of any coding scheme (not just RS) maintains the > same codeword set, but does not maintain the mapping between the set of > possible inputs and this codeword set. > > So yes, you will get a different output if you adopt a systematic > encoder. However, as the codeword set is the same, your Hamming and > Euclidean distance spectra will be the same as for the non-systematic > form, so there is no change to the effectiveness of the code. > > > > -- > OliThank you a lot.