Comparison of Channels: Criteria for Domination by a Symmetric Channel

This paper studies the basic question of whether a given channel $V$ can be dominated (in the precise sense of being more noisy) by a $q$-ary symmetric channel. The concept of "less noisy" relation between channels originated in network information theory (broadcast channels) and is defined in terms of mutual information or Kullback-Leibler divergence. We provide an equivalent characterization in terms of $\chi^2$-divergence. Furthermore, we develop a simple criterion for domination by a $q$-ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel $V$. The criterion is strengthened for the special case of additive noise channels over finite Abelian groups. Finally, it is shown that domination by a symmetric channel implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality for the original channel.Comment: 31 pages, 2 figures. Presented at 2017 IEEE International Symposium on Information Theory (ISIT

Error-and-Erasure Decoding for Block Codes with Feedback

Inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First an inner bound is derived using a two phase encoding scheme with communication and control phases together with the optimal decoding rule for the given encoding scheme, among decoding rules that can be represented in terms of pairwise comparisons between the messages. Then an outer bound is derived using a generalization of the straight-line bound to errors-and-erasures decoders and the optimal error exponent trade off of a feedback encoder with two messages. In addition upper and lower bounds are derived, for the optimal erasure exponent of error free block codes in terms of the rate. Finally we present a proof of the fact that the optimal trade off between error exponents of a two message code does not increase with feedback on DMCs.Comment: 33 pages, 1 figure

On contraction coefficients, partial orders and approximation of capacities for quantum channels

The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel. It is the centerpiece of many results in information theory and justifies the operational interpretation of most entropic quantities. In this work, we revisit the notion of contraction coefficients of quantum channels, which provide sharper and specialized versions of the data processing inequality. A concept closely related to data processing are partial orders on quantum channels. We discuss several quantum extensions of the well known less noisy ordering and then relate them to contraction coefficients. We further define approximate versions of the partial orders and show how they can give strengthened and conceptually simple proofs of several results on approximating capacities. Moreover, we investigate the relation to other partial orders in the literature and their properties, particularly with regards to tensorization. We then investigate further properties of contraction coefficients and their relation to other properties of quantum channels, such as hypercontractivity. Next, we extend the framework of contraction coefficients to general f-divergences and prove several structural results. Finally, we consider two important classes of quantum channels, namely Weyl-covariant and bosonic Gaussian channels. For those, we determine new contraction coefficients and relations for various partial orders.Comment: 47 pages, 2 figure

Deep Learning for Environmentally Robust Speech Recognition: An Overview of Recent Developments

Eliminating the negative effect of non-stationary environmental noise is a long-standing research topic for automatic speech recognition that stills remains an important challenge. Data-driven supervised approaches, including ones based on deep neural networks, have recently emerged as potential alternatives to traditional unsupervised approaches and with sufficient training, can alleviate the shortcomings of the unsupervised methods in various real-life acoustic environments. In this light, we review recently developed, representative deep learning approaches for tackling non-stationary additive and convolutional degradation of speech with the aim of providing guidelines for those involved in the development of environmentally robust speech recognition systems. We separately discuss single- and multi-channel techniques developed for the front-end and back-end of speech recognition systems, as well as joint front-end and back-end training frameworks