High-throughput VLSI Implementations of Iterative Decoders and Related Code Construction Problems
Journal of VLSI Signal Processing Systems
Structured LDPC codes over integer residue rings
EURASIP Journal on Wireless Communications and Networking - Advances in Error Control Coding Techniques
Large girth quasi-cyclic LDPC codes based on the Chinese remainder theorem
IEEE Communications Letters
Shortening for irregular QC-LDPC codes
IEEE Communications Letters
On the stopping distance of array code parity-check matrices
IEEE Transactions on Information Theory
Cooperative relay channel with LDPC codes constructed from array codes
WTS'09 Proceedings of the 2009 conference on Wireless Telecommunications Symposium
Quasi-cyclic LDPC codes: an algebraic construction, rank analysis, and codes on Latin squares
IEEE Transactions on Communications
Hi-index | 754.90 |
One approach to designing structured low-density parity-check (LDPC) codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity-check matrix contain all the variables involved in short cycles. This approach is especially effective if the parity-check matrix of a code is a matrix composed of blocks of circulant permutation matrices, as is the case for the class of codes known as array codes. We show how to shorten array codes by deleting certain columns of their parity-check matrices so as to increase their girth. The shortening approach is based on the observation that for array codes, and in fact for a slightly more general class of LDPC codes, the cycles in the corresponding Tanner graph are governed by certain homogeneous linear equations with integer coefficients. Consequently, we can selectively eliminate cycles from an array code by only retaining those columns from the parity-check matrix of the original code that are indexed by integer sequences that do not contain solutions to the equations governing those cycles. We provide Ramsey-theoretic estimates for the maximum number of columns that can be retained from the original parity-check matrix with the property that the sequence of their indices avoid solutions to various types of cycle-governing equations. This translates to estimates of the rate penalty incurred in shortening a code to eliminate cycles. Simulation results show that for the codes considered, shortening them to increase the girth can lead to significant gains in signal-to-noise ratio (SNR) in the case of communication over an additive white Gaussian noise (AWGN) channel