Adaptation is Useless for Two Discrete Additive-Noise Two-Way Channels

TL;DR

This paper demonstrates that for certain two-way discrete channels, including the modulo additive-noise channel with memory and the multiple access/degraded broadcast channel, adaptive coding strategies do not increase the capacity region beyond standard methods.

Contribution

It proves that adaptation is ineffective for enlarging capacity in two specific classes of two-way discrete channels, clarifying the limits of adaptive coding.

Findings

Adaptation does not improve capacity for the modulo additive-noise channel with memory.

Adaptation does not improve capacity for the multiple access/degraded broadcast channel.

Standard coding methods are optimal for these channel classes.

Abstract

In two-way channels, each user transmits and receives at the same time. This allows each encoder to interactively adapt the current input to its own message and all previously received signals. Such coding approach can introduce correlation between inputs of different users, since all the users' outputs are correlated by the nature of the channel. However, for some channels, such adaptation in the coding scheme and its induced correlation among users are useless in the sense that they do not help enlarge the capacity region with respect to the standard coding method (where each user encodes only based on its own message). In this paper, it is shown that adaptation is not helpful for enlarging the capacity region of two classes of two-way discrete channels: the modulo additive-noise channel with memory and the multiple access/degraded broadcast channel.