Error Exponents of Low-Density Parity-Check Codes on the Binary Erasure Channel
Thierry Mora, Olivier Rivoire
TL;DR
This paper develops a thermodynamic formalism and uses the cavity method to analyze the error exponents of LDPC codes on the BEC, providing insights into their decoding performance.
Contribution
It introduces a novel thermodynamic approach and applies the cavity method to derive error exponents for LDPC codes on the BEC, advancing theoretical understanding.
Findings
Derived average and typical error exponents for LDPC codes
Applied statistical mechanics techniques to coding theory
Provided a new framework for analyzing error performance
Abstract
We introduce a thermodynamic (large deviation) formalism for computing error exponents in error-correcting codes. Within this framework, we apply the heuristic cavity method from statistical mechanics to derive the average and typical error exponents of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) under maximum-likelihood decoding.
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