Core Concepts
Generalized low-density parity-check (GLDPC) codes under the a posteriori probability (APP) decoder can reduce the gap to capacity compared to their original LDPC counterparts over the binary erasure channel and binary-input additive white Gaussian noise channel when an appropriate proportion of generalized constraint nodes is used.
Abstract
The paper analyzes the performance of generalized low-density parity-check (GLDPC) codes under the a posteriori probability (APP) decoder. It explores the concentration, symmetry, and monotonicity properties of GLDPC codes under the APP decoder, extending the applicability of density evolution to GLDPC codes.
The key highlights and insights are:
GLDPC codes can reduce the original gap to capacity compared to their original LDPC counterparts over the binary erasure channel (BEC) and binary-input additive white Gaussian noise (BI-AWGN) channel when an appropriate proportion of generalized constraint (GC) nodes is used.
On the BI-AWGN channel, the paper adopts Gaussian mixture distributions to approximate the message distributions from variable nodes and Gaussian distributions for those from constraint nodes. This approximation technique significantly enhances the precision of the channel parameter threshold compared to traditional Gaussian approximations while maintaining low computational complexity.
Simulation experiments provide empirical evidence that GLDPC codes, when decoded with the APP decoder and equipped with the right fraction of GC nodes, can achieve substantial performance improvements compared to low-density parity-check (LDPC) codes.
The paper identifies a class of error-correcting block codes, referred to as message-invariant subcodes, that can simplify the performance analysis and practical decoding of GLDPC codes under the APP decoder.
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