Finite temperature error-correcting codes

Abstract

The correspondence between error-correcting convolution codes and gauge invariant spin-glass models is used to show that the optimal way to recover the original message is by decoding at a finite temperature ${\mathit{T}}_{\mathit{N}}$(p)>0, where p is the strength of the channel noise and ${\mathit{T}}_{\mathit{N}}$(p) the Nishimori temperature. This improves upon the retrieval performance of the T=0 maximal likelihood Viterbi decoding algorithm without increasing its computational complexity. Numerical simulations support the theory.