Research On The Construction Of Non-binary Low Density Parity Check Codes

Low-Density Parity-Check Code is a good error code near the Shannon limit. If the code length is long enough, the LDPC codes'decoding performance can even surpass the Turbo code. The binary LDPC codes'encoding technique is proficient now and it has been used in many fields. As have a medium or short code length, the non-binary LDPC codes perform an excellent decoding performance either. But the non-binary LDPC code's encoding and decoding complexity has restricted its development very much. As a result, the research in the field that how to construct the non-binary LDPC code with low complexity is very popular.This paper is mainly about the research of the non-binary LDPC codes'construction. First we analyze several common constructing methods. Based on the research of the finite geometries encoding theory, we used an encoding algorithm to construct the binary LDPC matrix with large girth based on the cage module. This algorithm can construct excellent error codes in low encoding complexity. Using the propsed binary matrix as a base matrix, we can transform it to a non-binary matrix with a random replacing algorithm based on the primitive polynomial. Encoding non-binary LDPC codes by this method only need very low complexity. At last we will simulate the error checking performance of the non-binary LDPC codes.The simulation results show that the proposed binary LDPC codes have better error checking performance, lower encoding complexity and larger girth than the PEG codes in given code length and code rate. The proposed non-binary LDPC codes have a similar error checking performance with the binary LDPC codes in the low SNR field, but it converges faster, and will perform better in the high SNR field. And the low complexity of this encoding algorithm let it have a good application prospect.