Variable-Length Codes with Bursty Feedback

TL;DR

This paper introduces variable-length bursty-feedback (VLBF) codes for discrete memoryless channels with bursty feedback, demonstrating their advantages over traditional feedback schemes at short blocklengths through non-asymptotic bounds and numerical evaluations.

Contribution

The paper presents a novel non-asymptotic achievability bound for VLBF codes with bursty feedback, showing their superiority over existing variable-length stop-feedback codes in short blocklength regimes.

Findings

VLBF codes outperform VLSF codes at short blocklengths.

Richer bursty feedback improves performance significantly.

VLBF codes with limited bursts outperform bounds for infinite feedback.

Abstract

We study variable-length codes for point-to-point discrete memoryless channels with noiseless unlimited-rate feedback that occurs in $L$ bursts. We term such codes variable-length bursty-feedback (VLBF) codes. Unlike classical codes with feedback after each transmitted code symbol, bursty feedback fits better with protocols that employ sparse feedback after a packet is sent and also with half-duplex end devices that cannot transmit and listen to the channel at the same time. We present a novel non-asymptotic achievability bound for VLBF codes with $L$ bursts of feedback over any discrete memoryless channel. We numerically evaluate the bound over the binary symmetric channel (BSC). We perform optimization over the time instances at which feedback occurs for both our own bound and Yavas et al.'s non-asymptotic achievability bound for variable-length stop-feedback (VLSF) codes, where only a single bit is sent at each feedback instance. Our results demonstrate the advantages of richer feedback: VLBF codes significantly outperform VLSF codes at short blocklengths, especially as the error probability $\epsilon$ decreases. Remarkably, for BSC(0.11) and error probability $10^{-10}$, our VLBF code with $L=5$ and expected decoding time $N\leq 400$ outperforms the achievability bound given by Polyanskiy et al. for VLSF codes with $L=\infty$, and our VLBF code with $L=3$.