Research On Decoding Performance Of RS Codes Based On Normalized Min-sum And Sphere Decoding

Reed-Solomon (RS) code is a kind of nonbinary cyclic code, which can correct not only random errors, but also the burst errors with strong capability. So it is widely used in mobile communication, satellite communication, magnetic recording media, digital audio and video transmission etc. The HDD algorithm and the coding method of RS code are considered as perfect combination of the algebraic theory and the engineering realization. However, there is a lot of decoding gain loss because the HDD doesn’t fully use the soft information. Hence, researches on soft decision decoding of RS codes do have great value not only in theory, but also in engineering.This thesis is mainly on the soft decision decoding of RS codes, especially on adaptive belief propagation (ABP) algorithm. Based on the Normalized Min-Sum and Sphere Decoding, the improved algorithm of ABP is proposed. Some results are obtained and summarized as follow:1. The principle of encoding for RS codes in time domain and frequency domain coding principle is surveyed, the RS binary pattern mapping method is presented, and the error probability of bounded distance decoding and the performance of hard decoding are investigated.2. Based on the analysis of RS codes’traditional decoding algorithm, a detailed discussion of ABP is given, and the decoding complexity of ABP is also investigated. The types of improved algorithm of ABP are summarized following. Using Normalized Min-Sum Algorithm, the computational formula of extrinsic information in Bit-level reliabilities updates is optimized, and a new improved method is given.3. The structure of concatenated decoding algorithm based on ABP is analyzed deeply, and ABP-OSD algorithm, BIAS-BMA algorithm, ALLR-ABP-OSD algorithm are discussed in detail, which provide better decoding performance. Inspired by those concatenated decoding algorithm, combined with the advantages of ABP in decoding performance and SD in decoding complexity, a new concatenated decoding method is proposed. Simulation results of the proposed method reveal that is efficient and has a lower decoding complexity.