Study On Channel Coding With Crossover Structure

Channel coding which guarantees reliable information transmission is an in-dispensable part of digital communication systems. Over recent years, modern channel coding has been the major concern in the research area of channel cod-ing. Turbo codes, low-density parity-check (LDPC) codes and generalized LDPC (GLDPC) codes all belong to typical modern channel coding techniques. Combin-ing the research results and analysis methods of the existing modern channel cod-ing techniques, this dissertation investigates some new channel codes which have low encoding/decoding complexity and good bit error rate (BER) performance. The main work and results obtained are summarized as follows.1. Simulation experiments have been carried out to determine the performance of Crossover Product Accumulate (CPA) codes, and an efficient iterative de-coding stop criterion is proposed for CPA codes. Extrinsic Information Trans-fer (EXIT) Chart is used to predict the convergence thresholds of CPA codes and Product Accumulate (PA) codes, and the analysis results show that the two codes have almost the same convergence threshold. To design channel codes with lower convergence thresholds, Generalized Crossover Product Accumulate (GCPA) codes are proposed by extending the crossover struc-ture in the outer code of CPA codes. EXIT charts are used to search GCPA codes with low convergence thresholds. One class of obtained codes has a threshold about 0.22dB away to the Shannon limit.2. A new class of codes, termed Multiple Crossover-Parallel-Concatenated Single Parity-Check (M-CPC-SPC) codes, is proposed by introducing a crossover structure among the parallel component codes of Multiple Parallel-Concatenated Single Parity-Check (M-PC-SPC) codes. An iterative decoding algorithm based on local decoding is proposed according to the character-istics of M-CPC-SPC encoders. We focus on a kind of M-CPC-SPC codes with accumulated-crossover structures, which is called Multiple Accumulated-Crossover-Parallel-Concatenated SPC (M-ACPC-SPC) codes. M-ACPC-SPC codes have low coding/decoding complexity, and the local decoding can be implemented by the sum-product algorithm (SPA). With the help of union bounds analysis, an upper bound to the Bit Error Probability (BEP) is given to evaluate the average BER performance of M-ACPC-SPC codes with dif-ferent random interleavers. The interleavers of M-ACPC-SPC codes are also designed to improve the decoding performance. Analysis and simulation re-sults show that M-ACPC-SPC codes with dimension 5 have a lower error floor than (37,21) Turbo codes. Simulations also show that the designed inter-leavers can decrease the error floors of M-ACPC-SPC codes, and M-ACPC-SPC codes with dimension 5 can provide BER performance comparable to the irregular LDPC codes and better than (3,6) LDPC codes for short code length.3. The check bits of M-ACPC-SPC codes are grouped, and then Rate Compati-ble M-ACPC-SPC (RC-M-ACPC-SPC) codes can be constructed by punctur-ing check bits in group. The puncturing priority for each group is determined by density evolution using the Gaussian approximation. Analysis and simu-lation results show that RC-M-ACPC-SPC codes have a simple puncturing pattern and good BER performance.4. On the basis of low-density generator matrix codes, a class of systematic GLDPC codes with zigzag codes as component codes, termed Zigzag-based Systematic GLDPC (ZS-GLDPC) codes, is proposed. ZS-GLDPC codes have linear encoding complexity, and can be decoded by the SPA iteratively. Union bound analysis and density evolution using the Gaussian approximation are used to analyze the upper bounds to BEP and convergence thresholds of ZS-GLDPC codes respectively. Analysis shows that there is a tradeoff between the error floors and convergence thresholds for ZS-GLDPC codes with differ-ent parameters. Simulation results show that ZS-GLDPC codes with proper parameters have good BER performance for short code length.