On The Reliability Function of Discrete Memoryless Multiple-Access Channel with Feedback

TL;DR

This paper establishes bounds on the reliability function of discrete memoryless multiple-access channels with feedback, using novel coding schemes and extending point-to-point techniques to multi-user scenarios.

Contribution

It introduces a new coding scheme with data and confirmation stages for MACs and derives bounds that match for certain channel classes, extending feedback reliability analysis.

Findings

Bounds increase linearly with Euclidean distance to capacity boundary

Lower and upper bounds match for specific MAC classes

Proposed coding scheme improves error exponent analysis

Abstract

We derive a lower and upper bound on the reliability function of discrete memoryless multiple-access channel (MAC) with noiseless feedback and variable-length codes (VLCs). For the upper-bound, we use proof techniques of Burnashev for the point-to-point case. Also, we adopt the techniques used to prove the converse for the feedback-capacity of MAC. For the lower-bound on the error exponent, we present a coding scheme consisting of a data and a confirmation stage. In the data stage, any arbitrary feedback capacity-achieving code is used. In the confirmation stage, each transmitter sends one bit of information to the receiver using a pair of codebooks of size two, one for each transmitter. The codewords at this stage are selected randomly according to an appropriately optimized joint probability distribution. The bounds increase linearly with respect to a specific Euclidean distance measure defined between the transmission rate pair and the capacity boundary. The lower and upper bounds match for a class of MACs.