Tighter Decoding Reliability Bound for Gallager's Error-Correcting Code

Abstract

Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored.

11 pages, 1 figure

References in corpus (4)

• Typical Performance of Gallager-type Error-Correcting Codes
• The Statistical Physics of Regular Low-Density Parity-Check Error-Correcting Codes
• The statistical mechanics of turbo codes
• Turbo codes: the phase transition

Cited by in corpus (14)

• The glassy phase of Gallager codes
• The Dynamic Phase Transition for Decoding Algorithms
• Average and reliability error exponents in low-density parity-check codes
• Statistical mechanics of typical set decoding
• Critical Noise Levels for LDPC decoding
• The Generalized Random Energy Model and its Application to the Statistical Physics of Ensembles of Hierarchical Codes
• Thermodynamic Construction of an One-Step Replica-Symmetry-Breaking Solution in Finite Connectivity Spin Glasses
• The random energy model in a magnetic field and joint source-channel coding
• Analyticity of the energy in an Ising spin glass with correlated disorder
• How could the replica method improve accuracy of performance assessment of channel coding?
• Weight vs Magnetization Enumerator for Gallager Codes
• Statistical mechanical analysis of a hierarchical random code ensemble in signal processing
• Relations between random coding exponents and the statistical physics of random codes
• An identity of Chernoff bounds with an interpretation in statistical physics and applications in information theory