NDLI: Density Evolution for Nonbinary LDPC Codes Under Gaussian Approximation

Content Provider	IEEE Xplore Digital Library
Author	Ge Li Fair, I.J. Krzymien, W.A.
Copyright Year	1963
Abstract	This paper extends the work on density evolution for binary low-density parity-check (LDPC) codes with Gaussian approximation to LDPC codes over GF(q) . We first generalize the definition of channel symmetry for nonbinary inputs to include q-ary phase-shift keying (PSK) modulated channels for prime q and binary-modulated channels for q that is a power of 2. For the well-defined q-ary-input symmetric-output channel, we prove that under the Gaussian assumption, the density distribution for messages undergoing decoding is fully characterized by (q-1) quantities. Assuming uniform edge weights, we further show that the density of messages computed by the check node decoder (CND) is fully defined by a single number. We then present the approximate density evolution for regular and irregular LDPC codes, and show that the (q-1) -dimensional integration involved can be simplified using a dimensionality reduction algorithm for the important case of q=2^p. Through application of approximate density evolution and linear programming, we optimize the degree distribution of LDPC codes over GF(3) and GF(4). The optimized irregular LDPC codes demonstrate performance close to the Shannon capacity for long codewords. We also design GF(q) codes for high-order modulation by using the idea of a channel adapter. We find that codes designed in this fashion outperform those optimized specifically for the binary additive white Gaussian noise (AWGN) channel for a short codewords and a spectral efficiency of 2 bits per channel use (b/cu).
Sponsorship	IEEE Information Theory Society
Starting Page	997
Ending Page	1015
Page Count	19
File Size	1219133
File Format	PDF
ISSN	00189448
Volume Number	55
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Parity check codes Gaussian approximation AWGN Phase shift keying Decoding Phase modulation Linear programming Modulation coding Design optimization Additive white noise low-density parity-check (LDPC) codes density evolution
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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