Typical performance of low-density parity-check codes over general symmetric channels

Abstract

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Theoretical framework for dealing with general symmetric channels is provided, based on which Gallager and MacKay-Neal codes are studied as examples of LDPC codes. It has been shown that the basic properties of these codes known for particular channels, including the property to potentially saturate Shannon's limit, hold for general symmetric channels. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.

10 pages, 4 figures, RevTeX4; an error in reference corrected

References in corpus (5)

• Radiative corrections to K_{l3} decays
• The glassy phase of Gallager codes
• The Dynamic Phase Transition for Decoding Algorithms
• Critical Noise Levels for LDPC decoding
• Magnetization enumerator of real-valued symmetric channels in Gallager error-correcting codes

Cited by in corpus (7)

• Finite-Connectivity Spin-Glass Phase Diagrams and Low Density Parity Check Codes
• Gallager error correcting codes for binary asymmetric channels
• Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes
• Spatially Coupled LDPC Codes for Decode-and-Forward in Erasure Relay Channel
• Code optimization, frozen glassy phase and improved decoding algorithms for low-density parity-check codes
• Statistical mechanics of LDPC codes on channels with memory
• Spatially-Coupled Binary MacKay-Neal Codes for Channels with Non-Binary Inputs and Affine Subspace Outputs