Iterative decoding of product codes

• Iterative decoding of block codes is a rather old subjectthat regained much interest recently. The main idea behinditerative decoding is to break up the decoding problem into asequence of stages, iterations, such that each stage utilizesthe output from the previous stages to formulate its ownresult. In order for the iterative decoding algorithms to bepractically feasible, the complexity in each stage, in terms ofnumber of operations and hardware complexity, should be muchless than that for the original non-iterative decoding problem.At the same time, the performance should approach the optimum,maximum likelihood decoding performance in terms of bit errorrate.In this thesis, we study the problem of iterative decodingof product codes. We propose an iterative decoding algorithmthat best suits product codes but can be applied to other blockcodes of similar construction. The algorithm approaches maximumlikelihood performance. We also present another algorithm whichis suboptimal and can be viewed as a practical implementationof the rst algorithm on product codes. The performance of thesuboptimal algorithm is investigated both analytically and bycomputer simulations. The complexity is also investigated andcompared to the complexity of GMD and Viterbi decoding ofproduct codes.

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