New Bounds and Constructions for Variable Packet-Error Coding

TL;DR

This paper investigates variable packet-error coding in network communications, establishing bounds on rate-distortion trade-offs and proposing two new coding schemes that improve or optimize these trade-offs under different conditions.

Contribution

It provides new theoretical bounds and two explicit coding constructions, one using MDS codes and another based on repetition codes, enhancing the understanding of error correction in variable error scenarios.

Findings

The first construction improves the rate--distortion trade-off over existing methods.

The second construction achieves an optimal rate--distortion trade-off in certain regimes.

New bounds on the rate--distortion trade-off for variable packet-error coding.

Abstract

In this paper, we consider the problem of variable packet-error coding, which emerges in network communication scenarios where a source transmits information to a destination through multiple disjoint paths. The objective is to design codes with dynamic error-correcting capabilities that adapt to varying numbers of errors. Specifically, we first provide several bounds on the rate--distortion trade-off for general variable packet-error coding schemes. Then, we present two explicit constructions of variable packet-error coding schemes. The first construction uses higher-order MDS codes and provides a coding scheme that achieves a better rate--distortion trade-off compared to known results for general parameter regimes. The second construction is based on a variant of the repetition code and yields a coding scheme with an optimal rate--distortion trade-off, with respect to our bound, for certain parameter regimes.