Research On Finite Alphabet Iteratiye Decoding Algorithm Of LDPC Codes

Low-Density Parity-check (LDPC) codes are a kind of error correction codeswhich have low complexity and strong error-correction capacity. By using the beliefpropagation (BP) iterative decoding algorithm, LDPC codes can approach Shannontheoretical limits of channel capacity. However, this capacity approaching propertyholds only in the asymptotic limit of code length, while codes of practical lengths sufferthe error floor phenomenon. How to design the approximate iterative decodingalgorithm to reduce the error floor phenomenon has become one of the researchhotspots.Based on the research of the error floor in LDPC codes and the finite alphabetiterative decoding algorithm, we study the greedy algorithm that selects candidateFAIDs and the3-bit iterative decoding algorithm in detail. Main works in this paper aresummarized as follows:1. The basic principle of LDPC codes and its Tanner graph description are brieflyexpounded, and analyze the belief propagation (BP) iterative decoding algorithm basedon soft decision in detail. Combining with the decoding performance figure of LDPCcodes the error floor is analyzed and the concept of trapping set is given.2. The basic framework of the existing FAID algorithm is analyzed in detail.Research the noisy trapping set and two important evaluation parameters, noisy criticalnumber vector and decoder domination. Using the above notion as the core, theimplementation of the greedy algorithm on the selection of finite alphabet is provided,which outputs a set of potentially good FAIDs. The comparing simulation verifies theeffectiveness of this algorithm.3. Based on adding two bits which are chosen to reflect the local neighborhood of aparticular node in the graph on the original conveyed message of Gallager-A algorithmand making use of the derived finite alphabet which has good performance, a kind of3-bits iterative algorithm implementation is provided. This algorithm has lowercomplexity and outperforms BP in the error floor region. The result of the comparingsimulation indicates the algorithm is simple and effective.