On Universal Decoding over Discrete Additive Channels by Noise Guessing (2501.12971v1)

Abstract: We study universal decoding over parametric discrete additive channels. Our decoders are 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 randomised one draws them at random; noise sequences are then queried whether they result in a valid codeword when subtracted from the received sequence. In all cases, we give sufficient conditions on the family of parametric channels for the decoding strategies to be random-coding strongly universal, and we derive non-asymptotic upper bounds for the complexity of such strategies. We give examples of families in which our results hold, and a numerical example illustrates this performance.