Etienne Perron

Using Three States for Binary Consensus on Complete Graphs

We consider the binary consensus problem where each node in the network initially observes one of two states and the goal for each node is to eventually decide which one of the two states was initially held by the majority of the nodes. Each node contacts other nodes and updates its current state based on the state communicated by the last contacted node. We assume that both signaling (the information exchanged at node contacts) and memory (computation state at each node) are limited and restrict our attention to systems where each node can contact any other node (i.e., complete graphs). It is well known that for systems with binary signaling and memory, the probability of reaching incorrect consensus is equal to the fraction of nodes that initially held the minority state. We show that extending both the signaling and memory by just one state dramatically improves the reliability and speed of reaching the correct consensus. Specifically, we show that the probability of error decays exponentially with the number of nodes N and the convergence time is logarithmic in N for large N. We also examine the case when the state is ternary and signaling is binary. The convergence of this system to consensus is again shown to be logarithmic in N for large N, and is therefore faster than purely binary systems. The type of distributed consensus problems that we study arises in the context of decentralized peer-to-peer networks, e.g. sensor networks and opinion formation in social networks - our results suggest that robust and efficient protocols can be built with rather limited signaling and memory.

Lossy source coding with Gaussian or erased side-information

In this paper we find properties that are shared between two seemingly unrelated lossy source coding setups with side-information. The first setup is when the source and side-information are jointly Gaussian and the distortion measure is quadratic. The second setup is when the side-information is an erased version of the source. We begin with the observation that in both these cases the Wyner-Ziv and conditional rate-distortion functions are equal. We further find that there is a continuum of optimal strategies for the conditional rate distortion problem in both these setups. Next, we consider the case when there are two decoders with access to different side-information sources. For the case when the encoder has access to the side-information we establish bounds on the rate-distortion function and a sufficient condition for tightness. Under this condition, we find a characterization of the rate-distortion function for physically degraded side-information. This characterization holds for both the Gaussian and erasure setups.

Cooperative Source Coding with Encoder Breakdown

This paper provides an inner bound to the rate- distortion region of a source coding setup in which two encoders are allowed some collaboration to describe a pair of discrete memoryless sources. We further require some robustness in case one of the encoders breaks down. This is modeled by having a second decoder, observing the messages from only one of the encoders. We prove the tightness of this inner bound for two special cases. In the first, one of the sources is required to be recovered losslessly if there is no encoder breakdown. In the second, the robustness requirement is dropped and only one of the sources is to be represented. For the second case, we explicitly compute the rate-distortion region for the quadratic Gaussian and binary Hamming problems.

On cooperative secrecy for discrete memoryless relay networks

In this paper we consider information-theoretically secure communication between two special nodes (“source” and “destination”) in a memoryless network with authenticated relays, where the secrecy is with respect to a class of eavesdroppers. We develop achievable secrecy rates when authenticated relays also help increase secrecy rate by inserting noise into the network.

On noise insertion strategies for wireless network secrecy

We provide lower and upper bounds on the optimal rate for reliable and secret transmission of a message from one node to another in an arbitrary wireless network with deterministic signal interaction. Certain relay nodes are allowed to insert noise into the transmission, i.e., to use a source of independent, random noise in their encoding functions. The secrecy is with respect to an eavesdropper whose channel statistics are known. The upper bound is also valid for noisy signal interaction. Our construction for the achievability relies on an auxiliary result of independent interest: an inner and an outer bound on the achievable rates for reliable transmission of multiple sources to a single destination in arbitrary deterministic networks without secrecy constraints.

On the Role of Encoder Side-Information in Source Coding for Multiple Decoders

We consider a lossy source coding problem where the description of a source is going to be used by two decoders, each having access to information correlated with the source. This side-information is also present at the encoder. We gave inner and outer bounds to the set of achievable rate and distortion triples. For the special case Gaussian sources wish degraded side-information and squared error distortions, the two bounds coincide and we obtain the true rate-distortion region. As a further specialization, we obtain the rate-distortion region of the Gaussian version of a problem previously solved by Kaspi for discrete memoryless sources. Using this resist we quantify bow much revealing the side-information to the encoder helps in such a Gaussian setup

The on-off fading channel

We introduce a simple on-off fading dis- crete memoryless multiple-access channel in which the multiplicative fading for each user is a Bernoulli ran- dom process. We find the capacity of this channel in the case that the receiver does not know the values of the channel gains.

The Interference-Multiple-Access Channel

We introduce the interference-multiple-access channel, which is a discrete memoryless channel with two transmitters and two receivers, similar to the interference channel. One receiver is required to decode the information encoded at one transmitter, the other receiver is required to decode the messages from both transmitters. We provide an inner bound on the capacity region of this channel, as well as an outer bound for a special class of such channels. For this class, we also quantify the gap between inner and outer bound and show that the bounds match for a semi-deterministic channel, providing a complete characterization. For the Gaussian case, we show that the gap is at most 1 bit, yielding an approximate characterization.

A multiple access approach for the compound wiretap channel

The compound wiretap channel generalizes the classical problem in broadcast information-theoretic secrecy by allowing a class of potential eavesdroppers. This represents uncertainty in the eavesdropper channel and the characterization of its secrecy capacity is an open question. In this paper we present a new coding scheme that generalizes known approaches to this problem. The scheme prefixes an artificial multiple access channel to the transmission scheme in order to design a structured transmit codebook. The idea is that such a structure can potentially increase the perfect secrecy rate for the legitimate users in the presence of the class of eavesdroppers. We develop the achievable secrecy rate of this scheme and provide examples where this scheme is optimal.

Wireless network secrecy with public feedback

In this paper we consider secret communication between two special nodes (ldquosourcerdquo and ldquodestinationrdquo) in a wireless network with authenticated relays: the message communicated to the destination is to be kept information-theoretically (unconditionally) secret from any eavesdropper within a class. A public feedback channel from the destination to all nodes may or may not be available. We focus on a one-relay network with a bottleneck link between the source and the relay to illustrate the ideas. For this particular network, we derive the rate-equivocation capacity region when the public feedback channel is absent, and an achievable secret key rate when public feedback is present.