Mismatched Exponents for Deterministic and Randomised Noise-Guessing Decoding
Provides theoretical insights into the trade-offs between error and complexity in noise-guessing decoding, relevant for information theory and coding theory.
This paper analyzes error and complexity exponents of noise-guessing decoding under mismatched metrics. It shows that in deterministic decoding, all metrics are equivalent to the matched one, while in randomized decoding, tuning the α parameter is needed for optimal exponents; a universal metric achieves optimal exponents uniformly.
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.