Communicating Lists Over a Noisy Channel

TL;DR

This paper investigates the limits of communicating lists of messages over noisy channels, analyzing how list sizes and intersection thresholds affect reliable transmission beyond traditional single-message communication.

Contribution

It introduces a theoretical framework for list-based communication over noisy channels, deriving conditions for error-free transmission with list intersections.

Findings

Derived necessary and sufficient conditions for asymptotically error-free list communication.

Extended classical Shannon capacity to list-based communication scenarios.

Identified trade-offs between list sizes, intersection thresholds, and channel capacity.

Abstract

This work considers a communication scenario where the transmitter chooses a list of size K from a total of M messages to send over a noisy communication channel, the receiver generates a list of size L and communication is considered successful if the intersection of the lists at two terminals has cardinality greater than a threshold T. In traditional communication systems K=L=T=1. The fundamental limits of this setup in terms of K, L, T and the Shannon capacity of the channel between the terminals are examined. Specifically, necessary and/or sufficient conditions for asymptotically error free communication are provided.