Evangelos S. Eleftheriou

On the computation of the minimum distance of low-density parity-check codes

Low-density parity-check (LDPC) codes in their broader-sense definition are linear codes whose parity-check matrices have fewer 1s than 0s. Finding their minimum distance is therefore in general an NP-hard problem. We propose a randomized algorithm called nearest nonzero codeword search (NNCS) approach to tackle this problem for iteratively decodable LDPC codes. The principle of the NNCS approach is to search codewords locally around the all-zero codeword perturbed by minimal noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum-Hamming- weight codeword whose Hamming weight is equal to the minimum distance of the linear code. This approach has its roots in Berrou et al.s error-impulse method and a form of Fossoriers list decoding for LDPC codes.

Performance analysis of magnetic recording systems

Approximations to the union bound performance of sequence detection in the presence of colored noise and an algorithm to compute bit error and error event probabilities are presented and compared to bit-by-bit simulation results. These computations, which are very accurate at bit error probabilities /spl les/10/sup -3/, are then used to analyze the performance of standard and reverse concatenated Reed-Solomon(RS)/modulation coding schemes for generalized partial-response channels corrupted by colored noise. The analysis is used to determine the optimum RS code rate for recording systems that are of current interest.

Approximate algorithms for computing the minimum distance of low-density parity-check codes

We propose a family of randomized approximate algorithms, called nearest nonzero codewords search (NNCS), for computing the minimum distance of low-density parity-check (LDPC) codes, including Gallager-type and finite-geometry-type codes.