Channel Detection in Coded Communication

TL;DR

This paper addresses channel set detection in block-coded communication, deriving optimal and sub-optimal detection rules, bounds on error exponents, and demonstrating a universal detector's asymptotic optimality, with detailed analysis for binary symmetric channels.

Contribution

It introduces the optimal detection/decoding rule for channel set detection, derives error exponent bounds, and proposes a universal detector that performs asymptotically as well as the optimal.

Findings

Optimal detection/decoding rule derived for singleton channel sets.

Exact single-letter characterization of random coding error exponents.

Universal detector performs asymptotically as well as the optimal detector.

Abstract

We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to detect the set which contains the prevailing channel. We begin with the simplified case where each of the sets is a singleton. For any given code, we derive the optimum detection/decoding rule in the sense of the best trade-off among the probabilities of decoding error, false alarm, and misdetection, and also introduce sub-optimal detection/decoding rules which are simpler to implement. Then, various achievable bounds on the error exponents are derived, including the exact single-letter characterization of the random coding exponents for the optimal detector/decoder. We then extend the random coding analysis to general sets of channels, and show that there exists a universal detector/decoder which performs asymptotically as well as the optimal detector/decoder, when tuned to detect a channel from a specific pair of channels. The case of a pair of binary symmetric channels is discussed in detail.