Coordination in State-Dependent Distributed Networks: The Two-Agent Case

This paper addresses a coordination problem between two agents (Agents $1$ and $2$) in the presence of a noisy communication channel which depends on an external system state $\{x_{0,t}\}$. The channel takes as inputs both agents' actions, $\{x_{1,t}\}$ and $\{x_{2,t}\}$ and produces outputs that are observed strictly causally at Agent $2$ but not at Agent $1$. The system state is available either causally or non-causally at Agent $1$ but unknown at Agent $2$. Necessary and sufficient conditions on a joint distribution $\bar{Q}(x_0,x_1,x_2)$ to be implementable asymptotically (i.e, when the number of taken actions grows large) are provided for both causal and non-causal state information at Agent $1$. Since the coordination degree between the agents' actions, $x_{1,t}$ and $x_{2,t}$, and the system state $x_{0,t}$ is measured in terms of an average payoff function, feasible payoffs are fully characterized by implementable joint distributions. In this sense, our results allow us to derive the performance of optimal power control policies on an interference channel and to assess the gain provided by non-causal knowledge of the system state at Agent $1$. The derived proofs readily yield new results also for the problem of state-amplification under a causality constraint at the decoder.Comment: Published in 2015 IEEE International Symposium on Information Theor

Extrinsic Jensen-Shannon Divergence: Applications to Variable-Length Coding

This paper considers the problem of variable-length coding over a discrete memoryless channel (DMC) with noiseless feedback. The paper provides a stochastic control view of the problem whose solution is analyzed via a newly proposed symmetrized divergence, termed extrinsic Jensen-Shannon (EJS) divergence. It is shown that strictly positive lower bounds on EJS divergence provide non-asymptotic upper bounds on the expected code length. The paper presents strictly positive lower bounds on EJS divergence, and hence non-asymptotic upper bounds on the expected code length, for the following two coding schemes: variable-length posterior matching and MaxEJS coding scheme which is based on a greedy maximization of the EJS divergence. As an asymptotic corollary of the main results, this paper also provides a rate-reliability test. Variable-length coding schemes that satisfy the condition(s) of the test for parameters $R$ and $E$, are guaranteed to achieve rate $R$ and error exponent $E$. The results are specialized for posterior matching and MaxEJS to obtain deterministic one-phase coding schemes achieving capacity and optimal error exponent. For the special case of symmetric binary-input channels, simpler deterministic schemes of optimal performance are proposed and analyzed.Comment: 17 pages (two-column), 4 figures, to appear in IEEE Transactions on Information Theor

Complete Interference Mitigation Through Receiver-Caching in Wyner's Networks

We present upper and lower bounds on the per-user multiplexing gain (MG) of Wyner's circular soft-handoff model and Wyner's circular full model with cognitive transmitters and receivers with cache memories. The bounds are tight for cache memories with prelog $\mu\geq 2/3D$ in the soft-handoff model and for $\mu \geq D$ in the full model, where $D$ denotes the number of possibly demanded files. In these cases the per-user MG of the two models is $1+\mu/D$, the same as for non-interfering point-to-point links with caches at the receivers. Large receiver cache-memories thus allow to completely mitigate interference in these networks.Comment: Submitted to ITW 2016 in Cambridg

Source Coding Problems with Conditionally Less Noisy Side Information

A computable expression for the rate-distortion (RD) function proposed by Heegard and Berger has eluded information theory for nearly three decades. Heegard and Berger's single-letter achievability bound is well known to be optimal for \emph{physically degraded} side information; however, it is not known whether the bound is optimal for arbitrarily correlated side information (general discrete memoryless sources). In this paper, we consider a new setup in which the side information at one receiver is \emph{conditionally less noisy} than the side information at the other. The new setup includes degraded side information as a special case, and it is motivated by the literature on degraded and less noisy broadcast channels. Our key contribution is a converse proving the optimality of Heegard and Berger's achievability bound in a new setting. The converse rests upon a certain \emph{single-letterization} lemma, which we prove using an information theoretic telescoping identity {recently presented by Kramer}. We also generalise the above ideas to two different successive-refinement problems