| This doctoral thesis presents new iterative decoding algorithms for low-density parity-check (LDPC) codes, and discusses the corresponding code design methods. We start by studying a class of hard-decision iterative decoding algorithms, referred to as majority-based (MB) algorithms, which are particularly attractive for their simple implementation. We show the great advantages that some MB decoding algorithms are capable of offering over such benchmarks as Gallager's decoding algorithm A ( GA ) and majority decoding algorithm. In particular, we demonstrate that while the asymptotic convergence speed of GA is exponential with iteration number, for other MB algorithms, it is super-exponential. Moreover, we shows that some MB algorithms outperform GA and majority decoding algorithm by a large margin, in terms of threshold values, and derive tight bounds on these thresholds. The fast convergence and the better performance offered by MB algorithms, suggest a serious role for them in future coding schemes. We then introduce hybrid decoding algorithms in a general framework. Hybrid algorithms combine existing iterative decoding algorithms in order to improve the decoding performance and/or speed of convergence. We propose a family of hybrid algorithms, called time-invariant hybrid. These algorithms use a specific blend of different algorithms in each iteration. The blend, however, does not change by iteration. We demonstrate, through various examples, that hybrid algorithms are capable of substantially improving error performance and convergence speed at the expense of a small increase in the complexity of the decoder's structure. We obtain optimized hybrid algorithms (jointly with the optimized code structures in the case of irregular codes). We also compare (optimized) time-invariant hybrid algorithms with better-known switch-type ones, and show that although switch-type hybrid algorithms outperform their time-invariant counterparts asymptotically, and when the channel parameter is perfectly known, the trend changes at finite block lengths and limited maximum number of iterations, or when a perfect knowledge of the channel is not available. This suggests that robust time-invariant hybrid algorithms could be practically more attractive than switch-type hybrid algorithm. |
