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 Burnashev's 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 Burnashev's 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.     

Sequential estimation of a threshold crossing time for a Gaussian random walk through correlated observations

Given a Gaussian random walk X with drift, we consider the problem of estimating its first-passage time ?? _A for a given level A from an observation process Y correlated to X. Estimators may be any stopping times ?? with respect to the observation process Y. Two cases of the process Y are considered: a noisy version of X and a process X with delay d. For a given loss function f(x), in both cases we find exact asymptotics of the minimal possible risk E f((?? ? ?? _A )/r) as A, d ?? ??, where r is a normalizing coefficient. The results are extended to the corresponding continuous-time setting where X and Y are Brownian motions with drift.     

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.     

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 Smith's (1969) argument, we derive a sufficient condition on noise probability density functions (pdf) that guarantee finite support for the associated capacity-achieving distribution(s).     

On the universality of Burnashev's error exponent

We consider communication over a time-invariant discrete memoryless channel (DMC) with noiseless and instantaneous feedback. We assume that the transmitter and the receiver are not aware of the underlying channel, however, they know that it belongs to some specific family of DMCs. Recent results show that for certain families (e.g., binary-symmetric channels and Z channels) there exist coding schemes that universally achieve any rate below capacity while attaining Burnashev's error exponent. We show that this is not the case in general by deriving an upper bound to the universally achievable error exponent.     

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.