Aslan Tchamkerten

Secure Broadcasting Over Fading Channels

We study a problem of broadcasting confidential messages to multiple receivers under an information-theoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are considered: parallel channels and fast-fading channels. For the case of reversely degraded parallel channels, one eavesdropper, and an arbitrary number of legitimate receivers, we determine the secrecy capacity for transmitting a common message, and the secrecy sum-capacity for transmitting independent messages. For the case of fast-fading channels, we assume that the channel state information of the legitimate receivers is known to all the terminals, while that of the eavesdropper is known only to itself. We show that, using a suitable binning strategy, a common message can be reliably and securely transmitted at a rate independent of the number of receivers. We also show that a simple opportunistic transmission strategy is optimal for the reliable and secure transmission of independent messages in the limit of large number of receivers.

An Efficient Distance Bounding RFID Authentication Protocol: Balancing False-Acceptance Rate and Memory Requirement

The Mafia fraud consists in an adversary transparently relaying the physical layer signal during an authentication process between a verifier and a remote legitimate prover. This attack is a major concern for certain RFID systems, especially for payment related applications. Previously proposed protocols that thwart the Mafia fraud treat relaying and non-relaying types of attacks equally: whether or not signal relaying is performed, the same probability of false-acceptance is achieved. Naturally, one would expect that non-relay type of attacks achieve a lower probability of false-acceptance. We propose a low complexity authentication protocol that achieves a probability of false-acceptance essentially equal to the best possible false-acceptance probability in the presence of Mafia frauds. This performance is achieved without degrading the performance of the protocol in the non-relay setting. As an additional feature, the verifier can make a rational decision to accept or to reject a proof of identity even if the protocol gets unexpectedly interrupted.

Variable length coding over an unknown channel

Burnashev in 1976 gave an exact expression for the reliability function of a discrete memoryless channel (DMC) with noiseless feedback. A coding scheme that achieves this exponent needs, in general, to know the statistics of the channel. Suppose now that the coding scheme is designed knowing only that the channel belongs to a family Q of DMCs. Is there a coding scheme with noiseless feedback that achieves Burnashevs exponent uniformly over Q at a nontrivial rate? We answer the question in the affirmative for two families of channels (binary symmetric, and Z). For these families we show that, for any given fraction, there is a feedback coding strategy such that for any member of the family: i) guarantees this fraction of its capacity as rate, and ii) guarantees the corresponding Burnashevs exponent. Therefore, for these families, in terms of delay and error probability, the knowledge of the channel becomes asymptotically irrelevant in feedback code design: there are blind schemes that perform as well as the best coding scheme designed with the foreknowledge of the channel under use. However, a converse result shows that, in general, even for families that consist of only two channels, such blind schemes do not exist.

On the discreteness of capacity-achieving distributions

We consider a scalar additive channel x /spl rarr/ x + N whose input is amplitude constrained. By extending Smiths (1969) argument, we derive a sufficient condition on noise probability density functions (pdf) that guarantee finite support for the associated capacity-achieving distribution(s).

Communication Under Strong Asynchronism

A formulation of the problem of asynchronous point-to-point communication is developed. In the system model of interest, the message codeword is transmitted over a channel starting at a randomly chosen time within a prescribed window. The length of the window scales exponentially with the codeword length, where the scaling parameter is referred to as the asynchronism exponent. The receiver knows the transmission window, but not the transmission time. Communication rate is defined as the ratio between the message size and the elapsed time between when transmission commences and when the decoder makes a decision. Under this model, several aspects of the achievable tradeoff between the rate of reliable communication and the asynchronism exponent are quantified. First, the use of generalized constant-composition codebooks and sequential decoding is shown to be sufficient for achieving reliable communication under strictly positive asynchronism exponents at all rates less than the capacity of the synchronized channel. Second, the largest asynchronism exponent under which reliable communication is possible, regardless of rate, is characterized. In contrast to traditional communication architectures, there is no separate synchronization phase in the coding scheme. Rather, synchronization and communication are implemented jointly. The results are relevant to a variety of sensor network and other applications in which intermittent communication is involved.

Optimal Sequential Frame Synchronization

We consider the ldquoone-shot frame synchronization problem,rdquo where a decoder wants to locate a sync pattern at the output of a memoryless channel on the basis of sequential observations. The sync pattern of length N starts being emitted at a random time within some interval of size A, where A characterizes the asynchronism level. We show that a sequential decoder can optimally locate the sync pattern, i.e., exactly, without delay, and with probability approaching one as N rarr infin, if the asynchronism level grows as O(eNalpha), with alpha below the synchronization threshold, a constant that admits a simple expression depending on the channel. If alpha exceeds the synchronization threshold, any decoder, sequential or nonsequential, locates the sync pattern with an error that tends to one as Nrarr infin. Hence, a sequential decoder can locate a sync pattern as well as the (nonsequential) maximum-likelihood decoder that operates on the basis of output sequences of maximum length A+N-1, but with far fewer observations.

Asynchronous Capacity per Unit Cost

The capacity per unit cost, or, equivalently, the minimum cost to transmit one bit, is a well-studied quantity under the assumption of full synchrony between the transmitter and the receiver. In many applications, such as sensor networks, transmissions are very bursty, with amounts of bits arriving infrequently at random times. In such scenarios, the cost of acquiring synchronization is significant and one is interested in the fundamental limits on communication without assuming a priori synchronization. In this paper, the minimum cost to transmit B bits of information asynchronously is shown to be equal to (B +H) ksync, where ksync is the synchronous minimum cost per bit and H is a measure of timing uncertainty equal to the entropy for most reasonable arrival time distributions. This result holds when the transmitter can stay idle at no cost and is a particular case of a general result which holds for arbitrary cost functions.

Asynchronous Communication: Capacity Bounds and Suboptimality of Training

Several aspects of the problem of asynchronous point-to-point communication without feedback are developed when the source is highly intermittent. In the system model of interest, the codeword is transmitted at a random time within a prescribed window whose length corresponds to the level of asynchronism between the transmitter and the receiver. The decoder operates sequentially and communication rate is defined as the ratio between the message size and the elapsed time between when transmission commences and when the decoder makes a decision. For such systems, general upper and lower bounds on capacity as a function of the level of asynchronism are established, and are shown to coincide in some nontrivial cases. From these bounds, several properties of this asynchronous capacity are derived. In addition, the performance of training-based schemes is investigated. It is shown that such schemes, which implement synchronization and information transmission on separate degrees of freedom in the encoding, cannot achieve the asynchronous capacity in general, and that the penalty is particularly significant in the high-rate regime.

A feedback strategy for binary symmetric channels

Communication over unknown binary symmetric channels with instantaneous and perfect feedback is considered. We describe a universal scheme based on a decision feedback strategy.

On cooperation in multi-terminal computation and rate distortion

A receiver wants to compute a function of two correlated sources separately observed by two transmitters. One of the transmitters is allowed to cooperate with the other transmitter by sending it some data before both transmitters convey information to the receiver. Assuming noiseless communication, what is the minimum number of bits that needs to be communicated by each transmitter to the receiver for a given number of cooperation bits? In this paper, first a general inner bound to the above three dimensional rate region is provided and shown to be tight in a number of interesting settings: the function is partially invertible, full cooperation, one-round point-to-point communication, two-round point-to-point communication, and cascade. Second, the related Kaspi-Berger rate distortion problem is investigated where the receiver now wants to recover the sources within some distortion. By using ideas developed for establishing the above inner bound, a new rate distortion inner bound is proposed. This bound always includes the time sharing of Kaspi-Bergers inner bounds and inclusion is strict in certain cases.