Theory and Performance of ML Decoding for LDPC Codes Using Genetic Algorithm

• Main Authors: Meng-Lin Wu, 吳孟霖
• Other Authors: Da-Shan Shiu
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/64317738328812502720

碩士 === 國立臺灣大學 === 電信工程學研究所 === 97 === Low-density parity-check (LDPC) codes drawn large attention lately due to their exceptional performance. Typical decoders operate based on the belief-propagation principle. Although these decoding algorithms work remarkably well, it is generally suspected that they do not achieve the performance of ML decoding. The ML performance of LDPC codes remains unknown because efficient ML decoders have not been discovered. Although it has been proved that for various appropriately chosen ensembles of LDPC codes, low error probability and reliable communication is possible up to channel capacity, we still want to know the actual limit for one specific code. Thus, in this thesis, our goal is to establish the ML performance. At a word error probability (WEP) of 10^{-5} or lower, we find that perturbed decoding can effectively achieve the ML performance at reasonable complexity. In higher error probability regime, the complexity of PD becomes prohibitive. In light of this, we propose the use of gifts. Proper gifts can induce high likelihood decoded codewords. We investigate the feasibility of using gifts in detail and discover that the complexity is dominated by the effort to identify small gifts that can pass the trigger criterion. A greedy concept is proposed to maximize the probability for a receiver to produce such a gift. Here we also apply the concept of gift into the genetic algorithm to find the ML bounds of LDPC codes. In genetic decoding algorithm (GDA), chromosomes are amount of gift sequence with some known gift bits. A conventional SPA decoder is used to assign fitness values for the chromosomes in the population. After evolution in many generations, chromosomes that correspond to decoded codewords of very high likelihood emerge. We also propose a parallel genetic decoding algorithm (P-GDA) based on the greedy concept and feasibility research of gifts. The most important aspect of GDA, in our opinion, is that one can utilize the ML bounding technique and GDA to empirically determine an effective lower bound on the error probability with ML decoding. Our results show that GDA and P-GDA outperform conventional decoder by 0.1 ~ 0.13 dB and the two bounds converge at a WEP of $10^{-5}$. Our results also indicate that, for a practical block size of thousands of bits, the SNR-error probability relationship of LDPC codes trends smoothly in the same fashion as the sphere packing bound. The abrupt cliff-like error probability curve is actually an artifact due to the ineffectiveness of iterative decoding. If additional complexity is allowed, our methods can be applied to improve on the typical decoders.