Universal communication part II: channels with memory

TL;DR

This paper demonstrates that for channels with fading memory, a universal communication system with feedback and common randomness can asymptotically achieve the optimal rate without prior channel knowledge, extending previous results to more general models.

Contribution

It generalizes the concept of capacity to channels with memory that fade over time, showing achievable rates with feedback and common randomness without knowing the channel.

Findings

Achievability of a generalized capacity for fading memory channels.

Weaker capacity results for non-fading memory channels.

Extension of previous results to more complex channel models.

Abstract

Consider communication over a channel whose probabilistic model is completely unknown vector-wise and is not assumed to be stationary. Communication over such channels is challenging because knowing the past does not indicate anything about the future. The existence of reliable feedback and common randomness is assumed. In a previous paper it was shown that the Shannon capacity cannot be attained, in general, if the channel is not known. An alternative notion of "capacity" was defined, as the maximum rate of reliable communication by any block-coding system used over consecutive blocks. This rate was shown to be achievable for the modulo-additive channel with an individual, unknown noise sequence, and not achievable for some channels with memory. In this paper this "capacity" is shown to be achievable for general channel models possibly including memory, as long as this memory fades with time. In other words, there exists a system with feedback and common randomness that, without knowledge of the channel, asymptotically performs as well as any block code, which may be designed knowing the channel. For non-fading memory channels a weaker type of "capacity" is shown to be achievable.