A Generalized Channel Coding Theory for Distributed Communication

TL;DR

This paper develops a generalized channel coding framework for distributed communication systems, characterizing performance limits and error probabilities when multiple transmitters choose codes independently in time-slotted environments.

Contribution

It introduces a novel theoretical model that accounts for arbitrary code choices and defines achievable regions and error bounds in distributed communication.

Findings

Achievable regions for reliable decoding are characterized.

Tradeoffs between operation region and error performance are established.

Reliable collision detection is possible outside the achievable region.

Abstract

This paper presents generalized channel coding theorems for a time-slotted distributed communication system where a transmitter-receiver pair is communicating in parallel with other transmitters. Assume that the channel code of each transmitter is chosen arbitrarily in each time slot. The coding choice of a transmitter is denoted by a code index parameter, which is known neither to other transmitters nor to the receiver. Fundamental performance limitation of the system is characterized using an achievable region defined in the space of the code index vectors. As the codeword length is taken to infinity, for all code index vectors inside the region, the receiver will decode the message reliably, while for all code index vectors outside the region, the receiver will report a collision reliably. A generalized system error performance measure is defined as the weighted sum of probabilities of different types of communication error events. Assume that the receiver chooses an "operation region" and intends to decode the message if the code index vector is inside the operation region. Achievable bounds on the tradeoff between the operation region and the generalize error performance measure are obtained under the assumption of a finite codeword length.