The Shannon capacity of a graphG is defined as c(G) = supd≥1(α(G )) 1 d , where α(G) is the independence number of G. The Shannon capacity of the cycle C5 on 5 vertices was determined by Lovász in 1979, but the Shannon capacity of a cycle Cp for general odd p remains one of the most notorious open problems in information theory. By prescribing stabilizers for the independent sets in C p and usi...

We study and compare the Shannon capacity region and the stable throughput region for a random access system in which source nodes multicast their messages to multiple destination nodes. Under an erasure channel model which accounts for interference and allows for multipacket reception, we first characterize the Shannon capacity region. We then consider a queueing-theoretic formulation and char...

Towards understanding energy requirements for computation with noisy elements, we consider the computation of an arbitrary k-input, k-output binary invertible function. In our model, not all gates need to be noisy. However, the input nodes on the computation graph must be separated from the output nodes by a noisy cut. For this setup, we show that for the “information-friction” model proposed r...

Transmit diversity techniques provide attractive solutions for increasing downlink capacity in 3G systems within low–mobility environments, and open–loop and closed–loop transmit diversity modes with two transmit antennas have already been included into 3GPP WCDMA specification. In this paper we study the optimality of the closed–loop schemes with respect to Shannon capacity.

This paper studies index coding with two senders. In this setup, source messages are distributed among the senders (possibly with overlapping of messages). In addition, there are multiple receivers, where each receiver having some messages a priori, known as side-information, is requesting one unique message such that each message is requested by only one receiver. Index coding in this setup is...

Reliable communication imposes an upper limit on the achievable rate, namely the Shannon capacity. Wyner’s wiretap coding, which ensures a security constraint also, in addition to reliability, results in decrease of the achievable rate. To mitigate the loss in the secrecy rate, we propose a coding scheme where we use sufficiently old messages as key and for this scheme prove that multiple messa...

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given.