On the construction of some capacity-approaching coding schemes
On the construction of some capacity-approaching coding schemes
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
IEEE Transactions on Information Theory
LDPC Codes Over Rings for PSK Modulation
IEEE Transactions on Information Theory
Density evolution for asymmetric memoryless channels
IEEE Transactions on Information Theory
Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels
IEEE Transactions on Information Theory
IEEE Journal on Selected Areas in Communications
Design and analysis of non-binary LDPC and IRA modulation codes
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
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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 = 2p. 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).