Spatially-coupled LDCP coding for the correlated erasure channel

Abstract

In this thesis, spatially-coupled low density parity-check (LDPC) codes, which have been shown to exhibit the threshold saturation phenomenon over the binary erasure channel (BEC), are considered and a low-delay iterative decoding scheme, called window decoding, is explained. Code ensembles with minimal coupling are enumerated and by using density evolution analysis, code ensembles with the best performance over the BEC are determined and some practical design criteria for construction an e cient ensemble are presented. It has been shown that the performance of these codes decreases drastically over correlated erasure channels where burst of high-probable erasures may hit the transmitted codeword. In the literature, this challenge is faced by presenting additional code design rules to build a robust ensemble against bursts. However, this approach results in more constraints on the code, which can be contradictory to some other properties of the code ensemble. In this thesis, we try to confront the transmission over correlated erasure channel by designing a communication system employing a convolutional interleaver. Asymptotic and practical performances of such a system over the correlated erasure channel have been studied and it has been shown that using a convolutional interleaver results in considerable improvement in the performance of the code compared to non-interleaving schemes which are purely based on code design criteria. All in one, major contributions of this thesis are deriving some practical design criteria for constructing a good code ensemble and also introducing the convolutional interleaver based spatially-coupled coding scheme which not only considerably mitigates the e ect of burst degradations, but also in contrast to its block counterpart, introduces a negligible amount of delay, which makes this system a very suitable candidate for next-generation wireless communication standards.