Research On Nonbinary Low-Density Parity-Check Codes

Low-Density Parity-Check (LDPC) codes are a class of capacity approaching codes. By using low complexity sum-product algorithm, LDPC codes can get near Shannon limit performance. For long code lengths, binary LDPC codes can even outperform Turbo codes. In terms of performance, binary LDPC codes start to show their weaknesses when the code size is small or moderate, and higher order modulation is used for transmission. For these cases, non-binary LDPC codes designed over higher order Galois fields GF(q) have shown great interest for its good performance.In this dissertation, the principles of decoding algorithm for non-binary LDPC codes and its application in high order modulation system are investigated. The main contents are as follows.1. The history and development of modern coding techniques are introduced, and the principles of decoding algorithm for binary LDPC codes are systematically summarized. Based on Normal graph, the equations for updating messages in sum-product algorithm (SPA)are also derived.2. Non-binary LDPC codes are also decoded with message passing algorithms as the sum-product decoder.A straightforward implementation has high complexity.A Fast Hadamard Transform (FHT) based implementation of the decoding algorithm is discussed, and a proof for its principles is also presented. A log-domain implementation of sum-product algorithm (Log-SPA) is also introduced. It has advantages over conventional SPA decoder in terms of implementation, computational complexity and numerical stability.Further, a modification of the log-domain implementation is proposed, yielding a lower computational complexity. A novel FHT-based Log-SPA decoding algorithm over low order field which has lower complexity and better numerical stability is also investigated.3. Both the random method and the algebraic method for constrcucting LDPC codes are introduced.An algebraic method for constrcucting binary and non binary QC-LDPC codes based on Reed-Solomon(RS) codes with two imformation symbols is presented. The application of nonbinary LDPC codes to high order modulation has been investigated Simulation result indicate that our code perform well at short block length.