142 research outputs found
On the calculation of the minimax-converse of the channel coding problem
A minimax-converse has been suggested for the general channel coding problem
by Polyanskiy etal. This converse comes in two flavors. The first flavor is
generally used for the analysis of the coding problem with non-vanishing error
probability and provides an upper bound on the rate given the error
probability. The second flavor fixes the rate and provides a lower bound on the
error probability. Both converses are given as a min-max optimization problem
of an appropriate binary hypothesis testing problem. The properties of the
first converse were studies by Polyanskiy and a saddle point was proved. In
this paper we study the properties of the second form and prove that it also
admits a saddle point. Moreover, an algorithm for the computation of the saddle
point, and hence the bound, is developed. In the DMC case, the algorithm runs
in a polynomial time.Comment: Extended version of a submission to ISIT 201
On the Diversity-Multiplexing Tradeoff of Unconstrained Multiple-Access Channels
In this work the optimal diversity-multiplexing tradeoff (DMT) is
investigated for the multiple-input multiple-output fading multiple-access
channels with no power constraints (infinite constellations). For K users
(K>1), M transmit antennas for each user, and N receive antennas, infinite
constellations in general and lattices in particular are shown to attain the
optimal DMT of finite constellations for the case N equals or greater than
(K+1)M-1, i.e., user limited regime. On the other hand for N<(K+1)M-1 it is
shown that infinite constellations can not attain the optimal DMT. This is in
contrast to the point-to-point case in which infinite constellations are DMT
optimal for any M and N. In general, this work shows that when the network is
heavily loaded, i.e. K>max(1,(N-M+1)/M), taking into account the shaping region
in the decoding process plays a crucial role in pursuing the optimal DMT. By
investigating the cases where infinite constellations are optimal and
suboptimal, this work also gives a geometrical interpretation to the DMT of
infinite constellations in multiple-access channels
A Universal Decoder Relative to a Given Family of Metrics
Consider the following framework of universal decoding suggested in
[MerhavUniversal]. Given a family of decoding metrics and random coding
distribution (prior), a single, universal, decoder is optimal if for any
possible channel the average error probability when using this decoder is
better than the error probability attained by the best decoder in the family up
to a subexponential multiplicative factor. We describe a general universal
decoder in this framework. The penalty for using this universal decoder is
computed. The universal metric is constructed as follows. For each metric, a
canonical metric is defined and conditions for the given prior to be normal are
given. A sub-exponential set of canonical metrics of normal prior can be merged
to a single universal optimal metric. We provide an example where this decoder
is optimal while the decoder of [MerhavUniversal] is not.Comment: Accepted to ISIT 201
Optimal Feedback Communication via Posterior Matching
In this paper we introduce a fundamental principle for optimal communication
over general memoryless channels in the presence of noiseless feedback, termed
posterior matching. Using this principle, we devise a (simple, sequential)
generic feedback transmission scheme suitable for a large class of memoryless
channels and input distributions, achieving any rate below the corresponding
mutual information. This provides a unified framework for optimal feedback
communication in which the Horstein scheme (BSC) and the Schalkwijk-Kailath
scheme (AWGN channel) are special cases. Thus, as a corollary, we prove that
the Horstein scheme indeed attains the BSC capacity, settling a longstanding
conjecture. We further provide closed form expressions for the error
probability of the scheme over a range of rates, and derive the achievable
rates in a mismatch setting where the scheme is designed according to the wrong
channel model. Several illustrative examples of the posterior matching scheme
for specific channels are given, and the corresponding error probability
expressions are evaluated. The proof techniques employed utilize novel
relations between information rates and contraction properties of iterated
function systems.Comment: IEEE Transactions on Information Theor
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