First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources with General Mixture

The first- and second-order optimum achievable exponents in the simple hypothesis testing problem are investigated. The optimum achievable exponent for type II error probability, under the constraint that the type I error probability is allowed asymptotically up to epsilon, is called the epsilon-optimum exponent. In this paper, we first give the second-order epsilon-exponent in the case where the null hypothesis and the alternative hypothesis are a mixed memoryless source and a stationary memoryless source, respectively. We next generalize this setting to the case where the alternative hypothesis is also a mixed memoryless source. We address the first-order epsilon-optimum exponent in this setting. In addition, an extension of our results to more general setting such as the hypothesis testing with mixed general source and the relationship with the general compound hypothesis testing problem are also discussed.Comment: 23 page

Second-Order Coding Rates for Channels with State

We study the performance limits of state-dependent discrete memoryless channels with a discrete state available at both the encoder and the decoder. We establish the epsilon-capacity as well as necessary and sufficient conditions for the strong converse property for such channels when the sequence of channel states is not necessarily stationary, memoryless or ergodic. We then seek a finer characterization of these capacities in terms of second-order coding rates. The general results are supplemented by several examples including i.i.d. and Markov states and mixed channels

A Formula for the Capacity of the General Gel'fand-Pinsker Channel

We consider the Gel'fand-Pinsker problem in which the channel and state are general, i.e., possibly non-stationary, non-memoryless and non-ergodic. Using the information spectrum method and a non-trivial modification of the piggyback coding lemma by Wyner, we prove that the capacity can be expressed as an optimization over the difference of a spectral inf- and a spectral sup-mutual information rate. We consider various specializations including the case where the channel and state are memoryless but not necessarily stationary.Comment: Accepted to the IEEE Transactions on Communication

Quantum channels and their entropic characteristics

One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing system. This development resulted in an elaborated structural theory and was accompanied by the discovery of a whole spectrum of entropic quantities, notably the channel capacities, characterizing information-processing performance of the channels. This paper gives a survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite dimensional quantum systems. We also touch upon the "continuous-variables" case, which provides an arena for quantum Gaussian systems. Most of the practical realizations of quantum information processing were implemented in such systems, in particular based on principles of quantum optics. Several important entropic quantities are introduced and used to describe the basic channel capacity formulas. The remarkable role of the specific quantum correlations - entanglement - as a novel communication resource, is stressed.Comment: review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys. (in press

Second-Order Asymptotics of Visible Mixed Quantum Source Coding via Universal Codes

This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TIT.2016.2571662The simplest example of a quantum information source with memory is a mixed source which emits signals entirely from one of two memoryless quantum sources with given a priori probabilities. Considering a mixed source consisting of a general one-parameter family of memoryless sources, we derive the second order asymptotic rate for fixed-length visible source coding. Furthermore, we specialize our main result to a mixed source consisting of two memoryless sources. Our results provide the first example of second order asymptotics for a quantum information-processing task employing a resource with memory. For the case of a classical mixed source (using a finite alphabet), our results reduce to those obtained by Nomura and Han [IEEE Trans. on Inf. Th. 59.1 (2013), pp. 1-16]. To prove the achievability part of our main result, we introduce universal quantum source codes achieving second order asymptotic rates. These are obtained by an extension of Hayashi's construction [IEEE Trans. on Inf. Th. 54.10 (2008), pp. 4619-4637] of their classical counterparts