9,577 research outputs found
Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications
Motivated by a recent surge of interest in convex optimization techniques,
convexity/concavity properties of error rates of the maximum likelihood
detector operating in the AWGN channel are studied and extended to
frequency-flat slow-fading channels. Generic conditions are identified under
which the symbol error rate (SER) is convex/concave for arbitrary
multi-dimensional constellations. In particular, the SER is convex in SNR for
any one- and two-dimensional constellation, and also in higher dimensions at
high SNR. Pairwise error probability and bit error rate are shown to be convex
at high SNR, for arbitrary constellations and bit mapping. Universal bounds for
the SER 1st and 2nd derivatives are obtained, which hold for arbitrary
constellations and are tight for some of them. Applications of the results are
discussed, which include optimum power allocation in spatial multiplexing
systems, optimum power/time sharing to decrease or increase (jamming problem)
error rate, an implication for fading channels ("fading is never good in low
dimensions") and optimization of a unitary-precoded OFDM system. For example,
the error rate bounds of a unitary-precoded OFDM system with QPSK modulation,
which reveal the best and worst precoding, are extended to arbitrary
constellations, which may also include coding. The reported results also apply
to the interference channel under Gaussian approximation, to the bit error rate
when it can be expressed or approximated as a non-negative linear combination
of individual symbol error rates, and to coded systems.Comment: accepted by IEEE IT Transaction
Capacity of a Nonlinear Optical Channel with Finite Memory
The channel capacity of a nonlinear, dispersive fiber-optic link is
revisited. To this end, the popular Gaussian noise (GN) model is extended with
a parameter to account for the finite memory of realistic fiber channels. This
finite-memory model is harder to analyze mathematically but, in contrast to
previous models, it is valid also for nonstationary or heavy-tailed input
signals. For uncoded transmission and standard modulation formats, the new
model gives the same results as the regular GN model when the memory of the
channel is about 10 symbols or more. These results confirm previous results
that the GN model is accurate for uncoded transmission. However, when coding is
considered, the results obtained using the finite-memory model are very
different from those obtained by previous models, even when the channel memory
is large. In particular, the peaky behavior of the channel capacity, which has
been reported for numerous nonlinear channel models, appears to be an artifact
of applying models derived for independent input in a coded (i.e., dependent)
scenario
Push sum with transmission failures
The push-sum algorithm allows distributed computing of the average on a
directed graph, and is particularly relevant when one is restricted to one-way
and/or asynchronous communications. We investigate its behavior in the presence
of unreliable communication channels where messages can be lost. We show that
exponential convergence still holds and deduce fundamental properties that
implicitly describe the distribution of the final value obtained. We analyze
the error of the final common value we get for the essential case of two nodes,
both theoretically and numerically. We provide performance comparison with a
standard consensus algorithm
Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
We deal with zero-delay source coding of a vector-valued Gauss-Markov source
subject to a mean-squared error (MSE) fidelity criterion characterized by the
operational zero-delay vector-valued Gaussian rate distortion function (RDF).
We address this problem by considering the nonanticipative RDF (NRDF) which is
a lower bound to the causal optimal performance theoretically attainable (OPTA)
function and operational zero-delay RDF. We recall the realization that
corresponds to the optimal "test-channel" of the Gaussian NRDF, when
considering a vector Gauss-Markov source subject to a MSE distortion in the
finite time horizon. Then, we introduce sufficient conditions to show existence
of solution for this problem in the infinite time horizon. For the asymptotic
regime, we use the asymptotic characterization of the Gaussian NRDF to provide
a new equivalent realization scheme with feedback which is characterized by a
resource allocation (reverse-waterfilling) problem across the dimension of the
vector source. We leverage the new realization to derive a predictive coding
scheme via lattice quantization with subtractive dither and joint memoryless
entropy coding. This coding scheme offers an upper bound to the operational
zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then
for "r" active dimensions of the vector Gauss-Markov source the gap between the
obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1
bits/vector. We further show that it is possible when we use vector
quantization, and assume infinite dimensional Gauss-Markov sources to make the
previous gap to be negligible, i.e., Gaussian NRDF approximates the operational
zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian
sources of any finite memory under mild conditions. Our theoretical framework
is demonstrated with illustrative numerical experiments.Comment: 32 pages, 9 figures, published in IEEE Journal of Selected Topics in
Signal Processin
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