Mismatched Exponents for Deterministic and Randomised Noise-Guessing Decoding

2026-06-25

AI Summary

This work investigates the trade-off between error exponent and computational complexity for mismatched noise guessing decoding over additive memoryless channels. It analyzes matched, α-tilted, and a proposed universal decoding metric based on the empirical entropy of noise sequences, under both deterministic and stochastic decoding frameworks. Theoretically, it is shown that under deterministic decoding, all considered metrics are equivalent and achieve optimal performance. In contrast, under stochastic decoding, the matched metric is not complexity-optimal; instead, optimality requires either tuning the α parameter according to the code rate or employing the proposed universal metric. Notably, this universal approach attains simultaneously optimal error and complexity exponents across all coding rates and channel conditions without requiring prior knowledge of the channel statistics.

Abstract

We study both the deterministic and randomised variants of noise-guessing decoding in additive memoryless channels. The error and complexity exponents of such decoding schemes are analysed under mismatched decoding metrics, and then specialised to matched, $α$-tilted, and universal decoding metrics. The $α$-tilted metric is proportional to the $α$-th power ($α>0$) of the true noise distribution. In deterministic decoding, the tilting operation does not affect the performance: all these metrics are equivalent to the matched one ($α=1$), and are optimal for both average error and complexity. On the other hand, in randomised decoding, the matched metric is not optimal for complexity exponents; we show that the decoder needs to tune the parameter~$α$ according to the code rate in order to simultaneously achieve both optimal exponents using a decoding metric in that family. Finally, a universal decoding metric based on the empirical entropy of the noise sequence achieves both optimal exponents, independently of the channel law and uniformly over code rates, for the deterministic and randomised variants.

Problem

• mismatched decoding
• noise-guessing decoding
• error exponent
• complexity exponent
• additive memoryless channels

Innovation

• mismatched decoding
• noise-guessing decoding
• error exponent
• complexity exponent
• universal decoding