Timely Transmissions Using Optimized Variable Length Coding

TL;DR

This paper develops an analytical framework for optimizing variable-length codes in a status updating system employing HARQ, aiming to minimize the age-of-information by balancing codeword length and decoding delay.

Contribution

It introduces a sequential differential optimization method to derive optimal codeword lengths for timely message decoding in noisy channels.

Findings

Optimal codeword lengths are analytically derived.

The framework effectively balances decoding delay and message timeliness.

Applicable to systems with known feedback probability functions.

Abstract

A status updating system is considered in which a variable length code is used to transmit messages to a receiver over a noisy channel. The goal is to optimize the codewords lengths such that successfully-decoded messages are timely. That is, such that the age-of-information (AoI) at the receiver is minimized. A hybrid ARQ (HARQ) scheme is employed, in which variable-length incremental redundancy (IR) bits are added to the originally-transmitted codeword until decoding is successful. With each decoding attempt, a non-zero processing delay is incurred. The optimal codewords lengths are analytically derived utilizing a sequential differential optimization (SDO) framework. The framework is general in that it only requires knowledge of an analytical expression of the positive feedback (ACK) probability as a function of the codeword length.