Optimization of Sparse VLSF Codes for Short-Packet Transmission via Saddlepoint Methods

TL;DR

This paper introduces an optimization framework for sparse VLSF codes using saddlepoint approximation, enabling efficient parameter tuning for short-packet transmission over common channels.

Contribution

It develops a saddlepoint-based optimization method for sparse VLSF codes and proposes a refined decoding rule for improved bounds.

Findings

Achieves near-optimal decoding configurations with low computational cost.

Refined decoding rule tightens achievability bounds.

Demonstrates effectiveness over multiple memoryless channels.

Abstract

In this work, we present an optimization framework for sparse variable-length stop-feedback (VLSF) codes based on a saddlepoint approximation, which jointly optimizes the decoding configuration parameters. Thanks to the analytical tractability of the saddlepoint approximation, the framework enables efficient gradient-based optimization of such parameters for common memoryless channels, including the additive white Gaussian noise, binary symmetric, and binary erasure channels. We further propose a refined decoding rule that extends the conventional fixed-threshold rule and leads to a tighter achievability bound. Numerical results demonstrate that our framework provides near-optimal decoding configurations at low computational cost. Moreover, the results from our refined rule demonstrate that the fixed-threshold decoding rule is restrictive and that achievability bounds can be further tightened.