Channel Input Adaptation via Natural Type Selection

TL;DR

This paper introduces a stochastic algorithm for adapting the input distribution in a communication system over a changing discrete memoryless channel, ensuring reliable transmission at a fixed rate with minimal feedback.

Contribution

It proposes a novel feedback-based adaptive algorithm that dynamically adjusts the input distribution to maintain reliable communication over slowly varying channels.

Findings

The algorithm converges to an input distribution that guarantees reliable communication below a certain threshold.

The method requires only one bit of feedback per transmitted block.

The approach is effective for channels with capacity above the threshold T.

Abstract

For the model of communication through a discrete memoryless channel using i.i.d. random block codes, where the channel is changing slowly from block to block, we propose a stochastic algorithm for adaptation of the generating distribution of the code in the process of continuous reliable communication. The purpose of the algorithm is to match the generating distribution $Q(x)$ to the changing channel $P(y\,|\,x)$, so that reliable communication is maintained at some constant rate $R$. This is achieved by a feedback of one bit per transmitted block. The feedback bit is determined by the joint type of the last transmitted codeword and the received block, a constant threshold $T>R$, and some conditional distribution $\Phi(x\,|\,y)$. Depending on the value of the feedback bit, the system parameters $Q(x)$ and $\Phi(x\,|\,y)$ are both updated according to the joint type of the last transmitted and received blocks, or remain unchanged. We show that, under certain technical conditions, the iterations of the algorithm lead to a distribution $Q(x)$, which guarantees reliable communication for all rates below the threshold $T$, provided that the discrete memoryless channel capacity of $P(y\,|\,x)$ stays above $T$.