Weight Spectrum Based Optimal RCPT Code Design And The Performance Analysis Of Turbo Codes

Considerable attention has been paid to Turbo codes due to its impressive performance close to Shannon limit, and it is regarded as a milestone in the history of channel coding theory. At present, Turbo codes have been widely utilized by different wireless communication systems. Although the theoretical basis of Turbo codes has gradually been formulated, some investigations of Turbo codes are still insufficient, such as the weight spectrum calculations, performance analysis of the waterfall region and the convergence characteristics of iterative decoding. With the rapid development of wireless communication technology, future mobile communication systems will have higher requirements on the performance and throughput of Turbo codes. Therefore, the optimal design and performance analysis of Turbo codes is very necessary.Firstly, the structure of Turbo encoder is addressed to highlight the problem in determining the weight spectrum. It is shown that, exact weight spectrum will be the basis for the optimal design and performance analysis of Turbo codes. Constrained subcode algorithm is effective in determining the weight spectrum of Turbo codes, albeit its complexity is still high. In this thesis, it is validated that the merging calculation of multiple continuous inputs into one step calculation, as well as the enhanced bounds with additional input weight constraints could be employed to improve the calculation efficiency of the constrained subcode algorithm. It is disclosed that the enhanced bounds with additional input weight constraints proposed by Rosnes and Ytrehus will miss some of the weight terms.Secondly, the puncturing pattern design criteria for rate-compatible punctured Turbo (RCPT) codes are investigated. And the optimized weight spectrum sequence (OWSS) is applied to devise the optimal periodic puncturing pattern for both the systematic RCPT (S-RCPT) codes and the partially-systematic RCPT (PS-RCPT) codes. Simulation results are presented to validate the OWSS criterion in determining the optimal puncturing patterns. Moreover, it is shown that the periodic puncturing with large enough puncturing period will be sufficient to approximate the performance by RCPT codes with aperiodic puncturing pattern. For a given code rate, the optimal PS-RCPT codes outperform the RCPT codes with pseudo-random puncturing pattern. Meanwhile, rate-1/2 PS-RCPT codes may achieve better error floor performance than their rate-1/3 mother codes. It is shown that the optimal RCPT codes and the optimal PS-RCPT codes will be attractive in adaptive error control coding applications.Thirdly, the scaling law model, the curve fitting model and the exponential model are addressed for enabling waterfall region performance estimate for Turbo codes. At first, the estimate accuracy of the above three models are verified. It is unveiled that the exponential model is able to offer a simple but effective method to estimate the performance for Turbo codes with different code rates within the waterfall region over diverse channels. By combining the exponential model and the union bound, a new hybrid model is presented to approximate both the bit error ratio and frame error ratio of Turbo codes within the whole signal to noise ratio region.Finally, this thesis briefly reviews the principle and calculation method of the extrinsic information transfer (EXIT) chart, then utilizes it to reveal the convergence behavior of the parallel Turbo coding scheme base on frame split and trellis terminating (FSTT). The EXIT chart shows that the parallel Turbo coding scheme with FSTT exhibits excellent decoding convergence. Meanwhile, the simulation results further disclose that the parallel Turbo coding scheme with FSTT is able to achieve a reasonable decoding convergence performance while achieving the reliability close to the regular serial Turbo decoding, especially when either the sub-block number is small or the code rate is high. Thus, the parallel Turbo coding scheme with FSTT provides an attractive alternative in implementing the high speed parallel Turbo coding in practical applications.