Single and joint iterative decoding for higher order modulation schemes

Abstract

The research project described in this thesis concentrates on the study, and application of specific channel coding techniques, in particular, low-density parity-check (LDPC) codes, iterative decoding on Tanner graphs, and their application on joint iterative receivers based on the turbo principle, previously proposed. The construction of random LDPC codes that fulfil certain desirable characteristics, such as large girth, specific p and -y values, and acceptable BER and FER performance for short code lengths, traditionally requires a high degree of processing power (i. e. CPU cycles) to run stochastic routines that firstly search within all the possible combinations for those ones that match the desired characteristics of the LDPC matrix, and secondly determines the bit-error rate (BER) and frame-error rate (FER) performance. The construction of well structured LDPC codes by means of algebraic methods has provided LDPC codes that achieve excellent performance, with desirable structure on their LDPC matrices. However, from the universe of LDPC matrices, those ones created through well structured procedures are a small group. Multiple procedures to modify their characteristics such as length and rate have assisted to increase the pool of LDPC codes based on well structured procedures. This thesis study the problem of constructing random LDPC codes with particular length, girth, and column weight as design parameters, with reduced processing power, while providing, at the same time, a desirable structure to allow efficient use of the memory and of the parallel processing capacity to reduce delay through efficient encoding and decoding. Based on previous studies that analysed the same problem, an algorithm is introduced to construct the Girth-Partition and Shift (GPS) LDPC codes, which are half-rate quasi-cyclic (QC) LDPC codes. Several GPS constructions are analysed over the AWGN channel and the flat-fading channel. The effect on the BER and FER performance from variations on their design parameters, is included in this study. This work also includes the BER and FER performance of the concatenation in parallel of different LDPC codes, some of which are based on well structured procedures, such as Euclidean Geometries (EG) and Projective Geomtries (PG), and Margulis constructions based on the Cayley graph, while the rest are based on random procedures, such as Graphical Models (GM) and GPS-LDPC codes. The aim of the analysis of this scheme, combined with the referred LDPC code constructions, include the improvement of the BER and FER performance for short code lengths and the reduction of the encoding complexity. The BER and FER performance achieved by the parallel concatenation of the previously mentioned LDPC codes, is further analysed in a joint demapping, parallel channel decoding and source decoding system. The impact of each component on the overall system performance is also examined