Coding with Encoding Uncertainty

TL;DR

This paper investigates the impact of encoding uncertainty on linear block codes, proposing worst-case and probabilistic models to determine code robustness and error correction capabilities.

Contribution

It introduces a novel framework modeling encoding errors as erasures and derives new code properties necessary for robustness against such uncertainties.

Findings

Maximum erasures tolerable for perfect correction

Conditions for vanishing error probability with increasing blocklength

New code properties required for robustness

Abstract

We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding uncertainty as erasures on the edges in the factor graph of the encoder generator matrix. We first take a worst-case approach and find the maximum tolerable number of erasures for perfect error correction. Next, we take a probabilistic approach and derive a sufficient condition on the rate of a set of codes, such that decoding error probability vanishes as blocklength tends to infinity. In both scenarios, due to the inherent asymmetry of the problem, we derive the results from first principles, which indicates that robustness to encoding errors requires new properties of codes different from classical properties.