Universal Decoding over Finite-State Additive Channels via Noise Guessing

TL;DR

This paper introduces noise-guessing universal decoders for finite-state additive channels, demonstrating they achieve optimal error exponents and outperform training-based methods through numerical examples.

Contribution

It proposes novel noise-guessing decoding strategies that are universal and low-complexity, with proven optimal error exponents for finite-state channels.

Findings

Both deterministic and randomized noise-guessing decoders are universal with optimal error exponents.

The proposed methods outperform training-based strategies in numerical simulations.

Upper bounds on decoder complexity are derived.

Abstract

We study universal decoding over unknown discrete additive channels determined by a finite-state (unifilar) random process. Aiming at low-complexity decoders, we study variants of noise-guessing decoders that use estimators for the probability of a noise sequence when the actual channel law is unknown. A deterministic version produces noise sequences in a fixed order, and a new randomised version draws them at random, until finding a sequence that, subtracted from the received sequence, results in a valid codeword. We show that both strategies are random-coding universal (i.e. have the same random-coding error exponent as the optimal maximum likelihood decoding), and derive upper bounds for their complexity. Numerical examples in additive Markov channels illustrate the proposed methods' performance, showing that they consistently outperform a more usual training-based strategy.