Feedback Does Not Increase the Capacity of Approximately Memoryless Surjective POST Channels

TL;DR

This paper proves that for a broad class of POST channels, feedback does not increase capacity when the channels are approximately memoryless, extending classical results to more complex channel models.

Contribution

It establishes that feedback does not enhance capacity for approximately memoryless POST channels under certain conditions, generalizing Shannon's theorem.

Findings

Feedback capacity equals non-feedback capacity for these channels.

Almost all such channels with input size ≥ output size have no feedback capacity gain.

The result extends classical memoryless channel theorems to POST channels.

Abstract

We study a class of finite-state channels, known as POST channels, in which the previous channel output serves as the current state. A POST channel is deemed approximately memoryless when the state-dependent transition matrices are sufficiently close to one another. For this family of channels, under a surjectivity condition on the associated memoryless reference channel, we show that the feedback capacity coincides with the non-feedback capacity. Consequently, for almost all approximately memoryless POST channels whose input alphabet size is no smaller than the output alphabet size, feedback provides no capacity gain. This result extends Shannon's classical theorem on discrete memoryless channels and demonstrates that the phenomenon holds well beyond the strictly memoryless case.