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We investigate the asymptotic rates of length-n binary codes with VC-dimension at most dn and minimum distance at least δn. Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a shortening approach combining Sauer-Shelah lemma and the linear programming bound. Two lower bounds are given using Gilbert-Varshamov type arguments over constant-weight and Markov-type...
The problem of modulating the value of a parameter onto a band-limited signal to be transmitted over a continuous-time, additive white Gaussian noise (AWGN) channel, and estimating this parameter at the receiver, is considered. The performance is measured by the mean power-α error (MPαE), which is defined as the worst-case αth order moment of the absolute estimation error. The optimal exponential...
Suppose Y n is obtained by observing a uniform Bernoulli random vector Xn through a binary symmetric channel. Courtade and Kumar asked how large the mutual information between Y n and a Boolean function b(Xn) could be, and conjectured that the maximum is attained by the dictator function. An equivalent formulation of this conjecture is that dictator minimizes the prediction cost in sequentially predicting...
A Shannon cipher system for memoryless sources is considered, in which distortion is allowed at the legitimate decoder. The source is compressed using a rate distortion code secured by a shared key, which satisfies a constraint on the compression rate, as well as a constraint on the exponential rate of the excess-distortion probability at the legitimate decoder. Secrecy is measured by the exponential...
We analyze the optimal trade-off between the error exponent and the excess-rate exponent for variable-rate Slepian-Wolf codes. We first derive upper (converse) bounds on the optimal error and excess-rate exponents, and then lower (achievable) bounds, via a simple class of variable-rate codes which assign the same rate to all source blocks of the same type class. The resulting Slepian-Wolf codes bridge...
We consider the problem of erasure/list decoding using certain classes of simplified decoders. Specifically, we assume a class of erasure/list decoders, such that a codeword is in the list if its likelihood is larger than a threshold. This class of decoders both approximates the optimal decoder of Forney, and also includes the following simplified subclasses of decoding rules: The first is a function...
We study the problem of universal decoding for unknown discrete memoryless channels in the presence of erasure/list option at the decoder, in the random coding regime. Specifically, we harness a universal version of Forney's classical erasure/list decoder developed in earlier studies, which is based on the competitive minimax methodology, and guarantees universal achievability of a certain fraction...
We analyze the asymptotic performance of ensembles of random binning Slepian-Wolf codes, where each type class of the source might have a different coding rate. In particular, we first provide the exact encoder excess rate exponent as well as the decoder error exponent. Then, using the error exponent expression, we determine the optimal rate function, namely, the minimal rate for each type class needed...
We consider the problem of slotted asynchronous ccoded communication, where in each time frame (slot), the ctransmitter is either silent or transmits a codeword from a given c(randomly selected) codebook. The task of the decoder is to decide cwhether transmission has taken place, and if so, to decode the cmessage. We derive the optimum detection/decoding rule in the csense of the best trade-off among...
In a previous work, a universal decoder in a competitive minimax sense was developed for unknown block fading linear white Gaussian channels. For a given codebook (with finite blocklength), a high SNR optimal metric for the decoder was found, whose direct calculation requires solving a non-convex optimization problem and may be formidable. In this paper, the metric calculation problem is facilitated...
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