Enhancements to Low Density Parity Check (LDPC)

Abstract

LDPC Codes are considered serious competitors to turbo codes in terms of performance and complexity. They are also based on a similar philosophy, which is of constrained random code ensembles and iterative decoding algorithms. They are specified by a sparse parity check matrix containing mostly O's and relatively few 1 's.

In this thesis we study LDPC codes carefully and evaluate their performance in several coding structures. We also apply them to a practical system, that is the IEEE802.16 WiMAX system, and propose ways to enhance the LDPC codes proposed for such a

system.

First, we use high rate LDPC codes in a concatenated coding structure as an outer code, with convolutional codes as an inner code. We compare the performance of such a concatenated code with the commonly used one utilizing Reed-Solomon codes, and show better performance. We used a soft output MAP decoder for the convolutional codes, rather than the hard output Viterbi decoder typically used in these structures. Since it is relatively easy to make a competitive LDPC code with almost any rate and block size, we compare the concatenated code proposed for the IEEE802.16 standard, with an RS outer code, with the proposed concatenated code with an LDPC code having the same rate as the RS code. We also evaluated the performance of our concatenated code using the LDPC code proposed for the OFDMA version of the IEEE802.16 standard. We show that concatenated coding schemes proposed in this thesis achieve higher performance over both AWGN and SUI-3 channel models.

Next, we use the binary parity check matrix proposed in the IEEE802.16 standard, and propose a novel parity check matrix for an LDPC codes over GF(4). We show that our