Research And Design Of The Structure Of The Ra Code And Ra Code Interleaver

LDPC codes and Turbo codes are two kinds of typical codes in channel error control coding, they have the excellent performance of closing to the Shannon limit. RA codes are simultaneously a class of simple"turbo-like"codes and a class of low-density parity-check (LDPC) codes. This dual representation of RA codes allows the flexibility to use a Turbo code representation for encoding and an LDPC code representation for the decoding, thereby gaining the benefits of both schemes. The results show that RA codes are also the"near Shannon limit"codes.Some researches show the interleaver is very significant for the coder of the systematic repeat accumulate (RA) codes based on the belief propagation algorithms. If we can find the better parametor of the interleaver, we can get the RA codes achieving excellent performance without small-cycles in the parity check matrix. In this paper we have presented straightforward two kinds of deterministic construction methods for practical RA interleavers including L-interleaver and new interleaver based on the thoughts of linear congruence and prime number. These interleavers are shown to give excellent decoding performances for RA codes over a wide range of code lengths and rates. The deterministic nature of the interleaver gives improved performance over random interleavers for short codes, where structure is required to avoid codes with bad Tanner graphs, without hindering their performance in very long codes. Thus the new interleavers represent an excellent choice over both existing simple interleavers, which they outperform, and randomly constructed interleavers which they perform at least as well as, but with the added advantage of a deterministic description.Especially, the latter new interleaver does the better than L-interleaver in practice. It resolves the problem on the limit of the length of the information and chooses parameters flexibly. The most important, it's proved that there are no 4-cycles and 6-cycles in the parity check matrix when RA codes consisting of the latter inteleaver, as only no 4-cycles when L-interleaver. Results have shown that the latter make the RA codes having lower error floor with the decoder of belief propagation algorithms.We also apply these interleavers to extending the RA codes, and propose two simple extended codes including RmD codes and DRA codes. RmD codes can be constructed by transforming the accumulator of the encoder. DRA codes are made up by two concatenated RA codes. The two codes designed jointly not only break the 4-cycles or the 6-cycles but also increase the flexibility in choosing degree distributions. Degree distribution is optimized based on EXIT chart technology for the improved codes. Simulation result shows that the RmD codes have more benefit than RA codes, and the DRA codes of middle length have lower error floor relative to ARA codes with the the same interleaver and the decoder of BP algorithms.