Variable-Length Feedback Codes under a Strict Delay Constraint

TL;DR

This paper investigates variable-length feedback codes under strict delay constraints in discrete memoryless channels, deriving bounds on their performance and showing they can outperform non-feedback codes, with results on how delay affects achievable rates.

Contribution

The study derives a lower bound on the maximum achievable average transmission rate for VLF codes under strict delay constraints and compares their performance to non-feedback codes, highlighting the impact of delay and decoding period.

Findings

VLF codes can outperform non-feedback codes with larger delay constraints.

The gap between VLF ATR and channel capacity scales at most as O(L^{-1}).

Achievable ATR increases as decoding period decreases.

Abstract

We study variable-length feedback (VLF) codes under a strict delay constraint to maximize their average transmission rate (ATR) in a discrete memoryless channel (DMC) while considering periodic decoding attempts. We first derive a lower bound on the maximum achievable ATR, and confirm that the VLF code can outperform non-feedback codes with a larger delay constraint. We show that for a given decoding period, as the strict delay constraint, L, increases, the gap between the ATR of the VLF code and the DMC capacity scales at most on the order of O(L^{-1}) instead of O(L^{-1/2}) for non-feedback codes as shown in Polyanskiy et al. ["Channel coding rate in the finite blocklengh regime," IEEE Trans. Inf. Theory, vol. 56, no. 5, pp. 2307-2359, May 2010.]. We also develop an approximation indicating that, for a given L, the achievable ATR increases as the decoding period decreases.