| The concatenated codes are a mirror in the realization of long codes and hold the outstanding correction capability for random error and burst correction. The concatenated codes have mostly three sort ways: they can be sorted to concatenated linear block codes and concatenated convolution codes in term of the style of component codes, the component codes of concatenated linear block codes choice extended BCH codes and RS codes that have short or middling code length and high code rate, the component codes of concatenated convolution codes are Recursive Systematic Convolution; they can be sorted to serially concatenated codes and parallel concatenated codes by the mode of concatenation, the component codes of parallel concatenated codes are linear block codes and convolution codes, but the component codes of serially concatenated codes are only linear block codes; they can be sorted to two dimensional concatenated codes and multidimensional concatenated codes by the number of concatenation, the component codes of multidimensional product codes have commonly short code length and high code rate. It can gain very excellent error-correcting capability when a concatenated code performs decoding with the method of turbo codes based on SISO iterative decoding. The classical iterative decoding algorithm of BTC bases on computing Logarithm Likelihood Ratio, the strongpoint of algorithm is it can gain excellent error-correcting capability and out of Error floor, the defect is the decoder has a relatively big complexity. The classical iterative decoding algorithm of CTC has two sorts as follows: one is MAP algorithm and its improved algorithm, it can obtain near-Shannon capacity, but at one time there will appear big time delay and computational complexity; the other is SOVA algorithm and its improved algorithm, its time delay and computational complexity are smaller than MAP algorithm, but the correction capability is lower.This content of paper is described in two parts as follows:1) A new iterative decoding algorithm based on linear combination feedback is advanced for the extended BCH product codes, the iterative process is make up of the design of component decoder, the acquisition way of soft output and the feedback model: ?the Chase decoder of LLR algorithm may usually produce sixteen candidate code words when p=4. However we can get different p by improving on the Chase decoder, and analyze the complexity and performance of decoder in each p.(2)to get the soft output, the LLR algorithm needs find out the corresponding competing code words,when the decoder cannot search the competing code words the soft output will be replaced by a constant "β". There is a bright spot that two simple methods have taken over the complicated compute of LLR about the algorithm based on linear combination feedback, one is the output of Chase decoder is mapped from (0, 1) to (+1,-1), the other is output of Chase decoder is added a correlation operation before the mapping, either can advance the performance of decoder, ③the classical turbo codes get feedback by the direct overlap of the soft output and receipt information. However, to get effective feedback, we defined a new term "a (m)"that can control the depth of feedback, so the soft output and receipt information possess the obvious characteristic of linear combination, a important assignment of the paper is how to find out a good sequence for a (m).2 ) We will extend the new algorithm to two dimensional serially concatenated RS codes, two dimensional parallel concatenated eBCH code, multidimensional concatenated eBCH codes, two dimensional parallel concatenated convolution codes and so on. The interleaver object of concatenated RS codes includes bit and symbol; The distinguish of serially and parallel concatenated codes is the parity bit of parallel concatenated codes don't take part in the interleaver and the compute of SISO; the iteration principle of multidimensional concatenated codes is very similar with the two dimensional concatenated codes; the concatenated convolution codes have cancelled correlation operation and added a new variable "β(m)". The code rate, complexity, time delay, correction capability and application range of different style concatenated codes are analyzed in detail by setting up their Matlab model.
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