MMSE of "Bad" Codes
Abstract
We examine codes, over the additive Gaussian noise channel, designed for reliable communication at some specific signal-to-noise ratio (SNR) and constrained by the permitted minimum mean-square error (MMSE) at lower SNRs. The maximum possible rate is below point-to-point capacity, and hence these are non-optimal codes (alternatively referred to as "bad" codes). We show that the maximum possible rate is the one attained by superposition codebooks. Moreover, the MMSE and mutual information behavior as a function of SNR, for any code attaining the maximum rate under the MMSE constraint, is known for all SNR. We also provide a lower bound on the MMSE for finite length codes, as a function of the error probability of the code.
Cite
@article{arxiv.1106.1017,
title = {MMSE of "Bad" Codes},
author = {Ronit Bustin and Shlomo Shamai},
journal= {arXiv preprint arXiv:1106.1017},
year = {2012}
}
Comments
8 pages, 2 figures, submitted to the IEEE Transactions on Information Theory