On the Reliability Function for a BSC with Noiseless Feedback at Zero Rate

TL;DR

This paper determines the reliability function at zero rate for a binary symmetric channel with noiseless feedback by establishing matching upper and lower bounds on the decoding error exponent.

Contribution

It provides the exact reliability function at zero rate for BSCs with noiseless feedback, filling a gap in understanding channel performance at low rates.

Findings

Derived an upper bound for the decoding error exponent.

Matched bounds to find the exact reliability function at zero rate.

Enhanced understanding of BSC performance with noiseless feedback.

Abstract

We consider the transmission of nonexponentially many messages through a binary symmetric channel with noiseless feedback. We obtain an upper bound for the best decoding error exponent. Combined with the corresponding known lower bound, this allows to find the reliability function for this channel at zero rate.