Error Performance of Channel Coding in Random Access Communication

TL;DR

This paper analyzes the error performance of a novel channel coding scheme for random access communication, deriving bounds on error probabilities and error exponents for finite codeword lengths.

Contribution

It provides the first finite-length error bounds and error exponents for the proposed random access coding scheme, extending asymptotic results.

Findings

Derived achievable bounds on decoding error probability

Established bounds on collision miss detection probability

Obtained error exponents as codeword length increases

Abstract

A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the rate information among each other or with the receiver. The receiver will either decode the message or report a collision depending on whether reliable message recovery is possible. It was shown that, asymptotically as the codeword length goes to infinity, the set of communication rates supporting reliable message recovery can be characterized by an achievable region which equals Shannon's information rate region possibly without a convex hull operation. In this paper, we derive achievable bounds on error probabilities, including the decoding error probability and the collision miss detection probability, of random multiple access systems with a finite codeword length. Achievable error exponents are obtained by taking the codeword length to infinity.