CONTROLLED GIRTH, STRUCTURED LDPC CODES

Abstract

Low Density Parity Check (LDPC) codes have stimulated a. lot of interest in recent years due to their capacity approaching performance and availability of fast decoding algorithms. LDPC codes can be represented by bipartite graphs known as Tanner graphs. The girth of the graph is the length of the shortest cycle of the graph. It is well known that iterative decoding on LDPC codes performs well when the underlying Tanner graph has high girth. Therefore the design of LDPC codes having high girth is desirable. An elementary Turbo Structured Tanner graph construction for a family of regular LDPC codes attaining desired high girth is designed and obtained in this dissertation. The design studied in the dissertation provides flexibility in choice of parameters like column weight (j ~ 2), row weight k and arbitrary girth g. Turbo Structured low density parity check (TS-LDPC) codes are regular codes whose Tanner graph is composed of two trees connected by an interleaver. TS-LDPC codes with good girth properties are easy to construct. Careful design of the interleaver component prevents short cycles of any desired length in its Tanner graph. Simulation results demonstrates that the bit error rate (BER) performance at low signal to noise ratio ( SNR) is competitive with error performance of Random LDPC codes of same size, with better error performance at high SNR. - The issue of complexity of construction of codes is also addressed in the dissertation. Here a linear encoding algorithm- for a type of Turbo structured LDPC codes. This encoding can be developed with few restrictions and alterations in Tanner graph of TS LDPC codes.