## Discrete denoising for channels with memory

Venue: | Communications in Information and Systems (CIS |

Citations: | 8 - 3 self |

### BibTeX

@INPROCEEDINGS{Zhang_discretedenoising,

author = {Rui Zhang and Tsachy Weissman},

title = {Discrete denoising for channels with memory},

booktitle = {Communications in Information and Systems (CIS},

year = {},

pages = {2005}

}

### OpenURL

### Abstract

Abstract. We consider the problem of estimating a discrete signal X n = (X1,..., Xn) based on its noise-corrupted observation signal Z n = (Z1,..., Zn). The noise-free, noisy, and reconstruc-tion signals are all assumed to have components taking values in the same finite M-ary alphabet {0,..., M − 1}. For concreteness we focus on the additive noise channel Zi = Xi + Ni, where ad-dition is modulo-M, and {Ni} is the noise process. The cumulative loss is measured by a given loss function. The distribution of the noise is assumed known, and may have memory restricted only to stationarity and a mild mixing condition. We develop a sequence of denoisers (indexed by the block length n) which we show to be asymptotically universal in both a semi-stochastic setting (where the noiseless signal is an individual sequence) and in a fully stochastic setting (where the noiseless signal is emitted from a stationary source). It is detailed how the problem formulation, denoising schemes, and performance guarantees carry over to non-additive channels, as well as to higher-dimensional data arrays. The proposed schemes are shown to be computationally implementable. We also discuss a variation on these schemes that is likely to do well on data of moderate size. We conclude with a report of experimental results for the binary burst noise channel, where the noise is a finite-state hidden Markov process (FS-HMP), and a finite-state hidden Markov random field (FS-HMRF), in the respective cases of one- and two-dimensional data. These support the theoretical predictions and show that, in practice, there is much to be gained by taking the channel memory into account. 1. Introduction. The