Coding with Encoding Uncertainty
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.
Cite
@article{arxiv.1305.3733,
title = {Coding with Encoding Uncertainty},
author = {Jad Hachem and I-Hsiang Wang and Christina Fragouli and Suhas Diggavi},
journal= {arXiv preprint arXiv:1305.3733},
year = {2013}
}
Comments
12 pages; a shorter version of this work will appear in the proceedings of ISIT 2013