Some Comments on the Strong Simplex Conjecture
Abstract
In the disproof of the Strong Simplex Conjecture presented in [Steiner, 1994], a counterexample signal set was found that has higher average probability of correct optimal decoding than the corresponding regular simplex signal set, when compared at small values of the signal-to-noise ratio. The latter was defined as the quotient of average signal energy and average noise power. In this paper, it is shown that this interpretation of the signal-to-noise ratio is inappropriate for a comparison of signal sets, since it leads to a contradiction with the Channel Coding Theorem. A modified counterexample signal set is proposed and examined using the classical interpretation of the signal-to-noise ratio, i.e., as the quotient of average signal energy and average noise energy. This signal set outperforms the regular simplex signal set for small signal-to-noise ratios without contradicting the Channel Coding Theorem, hence the Strong Simplex Conjecture remains proven false.
Keywords
Cite
@article{arxiv.1202.1081,
title = {Some Comments on the Strong Simplex Conjecture},
author = {Dejan E. Lazich and Christian Senger and Martin Bossert},
journal= {arXiv preprint arXiv:1202.1081},
year = {2012}
}
Comments
Submitted to the 2012 IEEE International Symposium on Information Theory, Cambridge, MA, USA, July 1 - 6, 2012. 5 pages, 6 figures