A Technique for Deriving One-Shot Achievability Results in Network Information Theory

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: point-to-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 multi-dimensional 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 Martons inner bound without any need for time-sharing.

Non-Asymptotic Output Statistics of Random Binning and Its Applications

In this paper we develop a finite blocklength version of the Output Statistics of Random Binning (OSRB) framework. The framework is shown to be optimal in the point-to-point case. New second order regions for broadcast channel and wiretap channel with strong secrecy criterion are derived.

Channel simulation via interactive communications

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.

Coordination via a relay

In this paper, we study the problem of coordinating two nodes which can only exchange information via a relay at limited rates. The nodes are allowed to do a two-round interactive two-way communication with the relay, after which they should be able to generate i.i.d. copies of two random variables with a given joint distribution within a vanishing total variation distance. We prove inner and outer bounds on the coordination capacity region for this problem. Our inner bound is proved using the technique of output statistics of random binning that has recently been developed by Yassaee, et al.

Achievability proof via output statistics of random binning

This paper introduces a new and ubiquitous framework for establishing achievability results in emph{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 emph{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 eavesdroppers 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 emph{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.

Slepian-Wolf Coding Over Cooperative Relay Networks

This paper deals with the problem of multicasting a set of discrete memoryless correlated sources (DMCS) over a cooperative relay network. Necessary conditions with cut-set interpretation are presented. A emph{Joint source-Wyner-Ziv encoding/sliding window decoding} scheme is proposed, in which decoding at each receiver is done with respect to an ordered partition of other nodes. For each ordered partition a set of feasibility constraints is derived. Then, utilizing the sub-modular property of the entropy function and a novel geometrical approach, the results of different ordered partitions are consolidated, which lead to sufficient conditions for our problem. The proposed scheme achieves operational separation between source coding and channel coding. It is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks, namely, Aref network and finite-field deterministic network. Also, in Gaussian cooperative networks, it is shown that reliable transmission of all DMCS whose Slepian-Wolf region intersects the cut-set bound region within a constant number of bits, is feasible. In particular, all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two-way relay networks.

Slepian-Wolf Coding over Cooperative Networks

We present sufficient conditions for multicasting a set of correlated sources over cooperative networks. We propose joint source-Wyner-Ziv encoding/sliding-window decoding scheme, in which each receiver considers an ordered partition of other nodes. Subject to this scheme, we obtain a set of feasibility constraints for each ordered partition. We consolidate the results of different ordered partitions by utilizing a result of geometrical approach to obtain the sufficient conditions. We observe that these sufficient conditions are indeed necessary conditions for Aref networks. As a consequence of the main result, we obtain an achievable rate region for networks with multicast demands. Also, we deduce an achievability result for two-way relay networks, in which two nodes want to communicate over a relay network.