This paper introduces a new and ubiquitous framework for establishing achievability results in network information theory (NIT) problems. The framework uses random binning arguments and is based on a duality between channel and source coding problems. Further, the framework uses pmf approximation arguments instead of counting and typicality. This allows for proving coordination and strong secrecy problems where certain statistical conditions on the distribution of random variables need to be satisfied. These statistical conditions include independence between messages and eavesdropper's observations in secrecy problems and closeness to a certain distribution (usually, i.i.d. distribution) in coordination problems. One important feature of the framework is to enable one to add an eavesdropper and obtain a result on the secrecy rates "for free."We make a case for generality of the framework by studying examples in the variety of settings containing channel coding, lossy source coding, joint source-channel coding, coordination, strong secrecy, feedback and relaying. In particular, by investigating the framework for the lossy source coding problem over broadcast channel, it is shown that the new framework provides a simple alternative scheme to hybrid coding scheme. Also, new results on secrecy rate region (under strong secrecy criterion) of wiretap broadcast channel and wiretap relay channel are derived. In a set of accompanied papers, we have shown the usefulness of the framework to establish achievability results for coordination problems including interactive channel simulation, coordination via relay and channel simulation via another channel.

This paper presents a new and ubiquitous framework for establishing achievability results in network information theory (NIT) problems. The framework is used to prove various new results. To express the main tool, consider a set of discrete memoryless correlated sources (DMCS). Assume that each source (except one, Z n ) is randomly binned at a finite rate. We find sufficient conditions on these rates such that the bin indices are nearly mutually independent of each other and of Z n . This is used in conjunction with the Slepian-Wolf (S-W) result to set up the framework. We begin by illustrating this method via examples from channel coding and rate-distortion (or covering problems). Next, we use the framework to prove a new result on the lossy transmission of a source over a broadcast channel. We also prove a new lower bound to a three receiver wiretap broadcast channel under a strong secrecy criterion. We observe that we can directly prove the strong notion of secrecy without resorting to the common techniques, e.g., the leftover hash lemma. We have also used our technique to solve the problem of two-node interactive channel simulation and the problem of coordination via a relay.

This paper proposes a novel technique to prove a one-shot version of achievability results in network information theory. The technique is not based on covering and packing lemmas. In this technique, we use an stochastic encoder and decoder with a particular structure for coding that resembles both the ML and the joint-typicality coders. Although stochastic encoders and decoders do not usually enhance the capacity region, their use simplifies the analysis. The Jensen inequality lies at the heart of error analysis, which enables us to deal with the expectation of many terms coming from stochastic encoders and decoders at once. The technique is illustrated via several examples: pointto-point channel coding, Gelfand-Pinsker, Broadcast channel (Marton), Berger-Tung, Heegard-Berger/Kaspi, Multiple description coding and Joint source-channel coding over a MAC. Most of our one-shot results are new. The asymptotic forms of these expressions is the same as that of classical results. Our one-shot bounds in conjunction with multidimensional Berry-Essen CLT imply new results in the finite blocklength regime. In particular applying the one-shot result for the memoryless broadcast channel in the asymptotic case, we get the entire region of Marton's inner bound without any need for time-sharing.March 5, 2013 DRAFT 3 Definition 2. For a pmf p X,Y,Z , the conditional information density ı(x; y|z) is defined byand for general r.v.'s it is defined byWhenever the underlying distribution is clear from the context, we drop the subscript p from ı p (x; y|z).Definition 3. Let X be a multi-dimensional normal variable with zero mean and covariance matrix V. The complementary multivariate Gaussian cumulative distribution region associated with V is defined byWe use M and J to denote size of alphabets of random variables M and J, respectively, i.e. M = |M| and J = |J |. All the logarithms are in base two throughout this paper. III. MULTI-TERMINAL CHANNEL CODING PROBLEMSTo illustrate the application of our technique to multi-terminal channel coding problems, we study the problems of point-to-point channel, Gelfand-Pinsker and Broadcast channels (Marton) in this section. A. Point-to-point channelWe begin our illustration of the one-shot achievability proof with the classical point-to-point channel. Consider a channel with the law q Y |X and an input distribution q X . Let C = {X(1), · · · , X(M)} be a random codebook where the elements X(i) are drawn independently from q X (each codeword X(i) is only a single rv). As usual, X(m) is the codeword used for transmission of the message m. For the decoding we use an stochastic variation of MAP decoding.Instead of declaring the messagem with maximal posterior probability as in MAP, the decoder randomly draws a messagem from the conditional pmf P M|Y , where P is the induced pmf by the code, P M,Y (m, y) = 1 M q(y|X(m)). 1 More specifically, P M|Y (m|y) = q(y|X(m)) m q(y|X(m)) = 2 ıq(y;X(m)) m 2 ıq(y;X(m)) .(1)The mutual information term ı q (y; X(m)) is computed using pmf q X q Y |X that has nothing...

In this paper, we study the problem of channel simulation via interactive communication, known as the coordination capacity, in a two-terminal network. We assume that two terminals observe i.i.d. copies of two random variables and would like to generate i.i.d. copies of two other random variables jointly distributed with the observed random variables. The terminals are provided with two-way communication links, and shared common randomness, all at limited rates. Two special cases of this problem are the interactive function computation studied by Ma and Ishwar, and the tradeoff curve between one-way communication and shared randomness studied by Cuff. The latter work had inspired Gohari and Anantharam to study the general problem of channel simulation via interactive communication stated above. However only inner and outer bounds for the special case of no shared randomness were obtained in their work. In this paper we settle this problem by providing an exact computable characterization of the multi-round problem. To show this we employ the technique of "output statistics of random binning" that has been recently developed by the authors.

In this correspondence, we focus on the performance analysis of the widely-used minimum description length (MDL) source enumeration technique in array processing. Unfortunately, available theoretical analysis exhibit deviation from the simulation results. We present an accurate and insightful performance analysis for the probability of missed detection. We also show that the statistical performance of the MDL is approximately the same under both deterministic and stochastic signal models. Simulation results show the superiority of the proposed analysis over available results. Index Terms-Minimum description length (MDL), source enumeration, performance analysis, deterministic signal. EDICS Category: SAM-PERF, SAM-SDET I. INTRODUCTION AND PRELIMINARIES MDL [1], is one of the most successful methods for determining the number of present signals in array processing and channel order detection [2]. MDL is a low complexity information theoretic criteria which does not need any subjective threshold setting usual in detection theoretic criteria. Other statistical properties, specially its asymptotic consistency [1], makes it a favorable choice for source enumeration. Unfortunately, only few approximate finite-sample performance analysis are available on the MDL method [3]-[8]. In [3], a simple asymptotic statistical model for the eigenvalues of the sample correlation matrix was used. Unfortunately, the theoretical results showed persistent bias from the simulation results [4].The next work [5], gives a computational approach for calculation of the probability of false alarm p f a . In calculating the probability of missed detection pm, the same inaccurate statistical model is used as in [3]. In [6], instead of exact performance estimation, theoretical bounds for performance were presented. A qualitative performance evaluation in terms of gap between noise and signal eigenvalues and also the dispersion of each group is given in [7]. In a recent work [8], a significantly different approach was used. Our simulation results show improved results of [8] in comparison with [3]. The performance analysis was generalized to the non-Gaussian signals while it was shown that the results reduce to the results of [5], [6] in Gaussian signals. We will show that the same modelling errors have degraded the analysis in [8] as in [3]- [6].In this correspondence, we use an approach very similar to [3]-[5] to estimate pm, including in the analysis the finite sample O(n −1 ) biases of the eigenvalues. The noise subspace eigenvalue spread is taken into account which prevents the signal subspace eigenvalues to approach σ 2 , the noise variance. The bias of the noise power estimator in MDL is calculated to get excellent match between theoretical and simulation results. We will not calculate p f a which is negligible.In the previous works, only the case of stochastic signal has been considered. Here, we use a perturbation analysis to calculate biases and variances of the eigenvalues under deterministic signal, too. Using these results, we show t...