4 research outputs found
Simplified Erasure/List Decoding
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 of the output vector only, but not the codebook
(which is most suitable for high rates), and the second is a scaled version of
the maximum likelihood decoder (which is most suitable for low rates). We
provide single-letter expressions for the exact random coding exponents of any
decoder in these classes, operating over a discrete memoryless channel. For
each class of decoders, we find the optimal decoder within the class, in the
sense that it maximizes the erasure/list exponent, under a given constraint on
the error exponent. We establish the optimality of the simplified decoders of
the first and second kind for low and high rates, respectively.Comment: Submitted to IEEE Transactions on Information Theor
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