Design and analysis of communication systems with high error correction capability through optimization

Abstract

Channel coding is the term used for the collection of techniques that are employed in order to minimize errors which occur during the transmission of digital information from one place to another. Low–density parity–check (LDPC) code family takes at tention with its channel capacity–approaching error correction capability and sparse parity–check matrix representation. Sparsity property of the matrix gives rise to the development of heuristic iterative decoding algorithms with low complexity. Ease of the application of iterative decoding algorithms brings the advantage of low decod ing latency. In spite of these benefits of LDPC codes, receiver can obtain erroneous information because of both structural properties of LDPC codes and non–optimal decoders. In the first part of this thesis, we develop optimization–based LDPC decoding algorithms for a communication system with high error performance and we compare its performance with the existing methods in the literature. Error performance of a communication system can still be improved by determining and eliminating small cycles in LDPC codes that cause iterative decoding algorithms to halt or terminate without a conclusive result during the decoding process. At the second place, we implement heuristic and optimization–based approaches for efficiently designing high quality LDPC codes of practically relevant dimensions. We carry out extensive com putational experiments to assess the efficiency of proposed methods.