We examine-the implications of using a Low Density Parity Check Code (LDPCC) in place of the usual Goppa code in McEliece’s cryptosystem. Using a LDPCC allows for larger block lengths and the possibility of a combined error correction/encryption protocol.

| Binary Low Density Parity Check (LDPC) codes have been shown to have near Shannon limit performance when decoded using a probabilis-tic decoding algorithm. The analogous codes deened over nite elds GF (q) of order q > 2 show signii-cantly improved performance. We present the results of Monte Carlo simulations of the decoding of inn-nite LDPC Codes which can be used to obtain good construction...

The class of low-density parity-check (LDPC) codes was introduced by Gallager in his thesis in 1961 [2]. Until the invention of turbo codes, they were largely neglected, but received a lot of interest lately, due to the possibility of designing LDPC codes within 0.0045 dB of the Shannon limit. We review in this project techniques used to analyze the performance of LDPC codes under a message-pas...

We report the empirical performance of Gallager’s low density parity check codes on Gaussian channels. We show that performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed the performance is almost as close to the Shannon limit as that of Turbo codes. A linear code may be described in terms of a generator matrix G or in terms of a pari...

We introduce a new class of low-density parity-check (LDPC) codes constructed from a template called a protograph. The protograph serves as a blueprint for constructing LDPC codes of arbitrary size whose performance can be predicted by analyzing the protograph. We apply standard density evolution techniques to predict the performance of large protograph codes. Finally, we use a randomized searc...

Low-density parity-check codes are studied over Markov channels with time-varying gaussian or bit-flipping noise. The belief propagation decoding algorithm is extended to include channel estimation and the gains this extension produce are experimentally determined.

This paper presents a new approach to universal noiseless compression based on error correcting codes. The scheme is based on the concatenation of the Burrows-Wheeler block sorting transform (BWT) with the syndrome former of a Low-Density Parity-Check (LDPC) code. The proposed scheme has linear encoding and decoding times and uses a new closed-loop iterative doping algorithm that works in conju...

A novel soft-bit-domain decoding algorithm for low-density parity-check codes is derived as an alternative to belief propagation and min-sum algorithms. A simple approximation analogous to the min-sum approximation is also presented. Simulation results demonstrating the functionality of the algorithm are given both for floating and fixed point representations.

In this chapter, we treat code design and decoding for a family of error corWork supported by a CSIRO Telecommunications & Industrial Physics postgraduate scholarship and the Centre for Integrated Dynamics and Control (CIDAC). Work supported in part by Bell Laboratories Australia, Lucent Technologies, as well as the Australian Research Council under Linkage Project Grant LP0211210, and the Cent...