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Performance Bounds for Regular LDPC Codes for Asymmetric Channels

Authors:
Pål Ellingsen

Keywords: Asymmetric channel; Regular LDPC codes; Gallager's theorem

Abstract:
It is well known that it is not possible to achieve capacity on an asymmetric channel using an even input distribution. In recent literature, complex code constructions has been proposed that gives rise to uneven input distributions to the channel such that capacity in theory can be achieved. However, it is of interest to know how well we can do on these channels with ordinary, linear codes due to the other desirable properties of such codes. In this paper, density evolution for symbol dependent channels is used in combination with a classical theorem by Gallager to bound the performance of regular Low Density Parity Check (LDPC) codes by showing that the check node degree of the graph describing a regular LDPC code, must go to infinity if the code is to achieve capacity on the Z-channel. Based on this, performance bounds for different check node degrees are calculated, and it is also shown that this is only a problem for small error probabilities.

Pages: 7 to 11

Copyright: Copyright (c) IARIA, 2016

Publication date: February 21, 2016

Published in: conference

ISSN: 2308-4022

ISBN: 978-1-61208-455-8

Location: Lisbon, Portugal

Dates: from February 21, 2016 to February 25, 2016