Research Encoding And Decoding Of RS Codes And The Application Of Soft-Decision Decoding

The technology of error correction is an important part of information theory. Both theory and practice should be known by the people who research on error-correcting codes. Being an important linear block code in error control field, the Reed-Solomon (RS) code has very strong capability of correcting random and burst errors, which is widely used in various modern communication systems to satisfy the requirement of channel reliability. Addition to the method of encoding and decoding RS codes, an algorithm of soft decision decoding is presented in the thesis.The algebraic decoding algorithms are researched, and such as the common algorithm for the codes whose error correction ability is low, and the iterative algorithm for those whose error correction ability is great. Programs are implemented for (27, 9) RS and (54, 18) RS. Just like the theoretical analyses, results demonstrate that the two codes can correct nine errors and eighteen errors respectively. The bit error rates have been improved correspondingly. Furthermore, the encoding and decoding methods of (16, 12) RS are simply discussed.The method of soft-decision decoding of RS code is researched. Soft-decision decoding can make full use of the output information, and substantial coding gain can be gotten, which has been observed early. Since soft-decision decoding needs much more computation, it is so complex as to be infeasible in many applications. Though some soft-decision algorithms for binary finite field have existed, non-binary finite field is seldom concerned. An algorithm for soft-decision decoding (15, 11) RS is presented, which refers to the Chase algorithm. Simulation result shows that four errors can be corrected at most. This algorithm can improve error-correction ability and coding gain.