36,680 research outputs found
On the Capacity Region for Secure Index Coding
We study the index coding problem in the presence of an eavesdropper, where
the aim is to communicate without allowing the eavesdropper to learn any single
message aside from the messages it may already know as side information. We
establish an outer bound on the underlying secure capacity region of the index
coding problem, which includes polymatroidal and security constraints, as well
as the set of additional decoding constraints for legitimate receivers. We then
propose a secure variant of the composite coding scheme, which yields an inner
bound on the secure capacity region of the index coding problem. For the
achievability of secure composite coding, a secret key with vanishingly small
rate may be needed to ensure that each legitimate receiver who wants the same
message as the eavesdropper, knows at least two more messages than the
eavesdropper. For all securely feasible index coding problems with four or
fewer messages, our numerical results establish the secure index coding
capacity region
Channel Detection in Coded Communication
We consider the problem of block-coded communication, where in each block,
the channel law belongs to one of two disjoint sets. The decoder is aimed to
decode only messages that have undergone a channel from one of the sets, and
thus has to detect the set which contains the prevailing channel. We begin with
the simplified case where each of the sets is a singleton. For any given code,
we derive the optimum detection/decoding rule in the sense of the best
trade-off among the probabilities of decoding error, false alarm, and
misdetection, and also introduce sub-optimal detection/decoding rules which are
simpler to implement. Then, various achievable bounds on the error exponents
are derived, including the exact single-letter characterization of the random
coding exponents for the optimal detector/decoder. We then extend the random
coding analysis to general sets of channels, and show that there exists a
universal detector/decoder which performs asymptotically as well as the optimal
detector/decoder, when tuned to detect a channel from a specific pair of
channels. The case of a pair of binary symmetric channels is discussed in
detail.Comment: Submitted to IEEE Transactions on Information Theor
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