1,515 research outputs found
Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems
Stabilization of non-stationary linear systems over noisy communication
channels is considered. Stochastically stable sources, and unstable but
noise-free or bounded-noise systems have been extensively studied in
information theory and control theory literature since 1970s, with a renewed
interest in the past decade. There have also been studies on non-causal and
causal coding of unstable/non-stationary linear Gaussian sources. In this
paper, tight necessary and sufficient conditions for stochastic stabilizability
of unstable (non-stationary) possibly multi-dimensional linear systems driven
by Gaussian noise over discrete channels (possibly with memory and feedback)
are presented. Stochastic stability notions include recurrence, asymptotic mean
stationarity and sample path ergodicity, and the existence of finite second
moments. Our constructive proof uses random-time state-dependent stochastic
drift criteria for stabilization of Markov chains. For asymptotic mean
stationarity (and thus sample path ergodicity), it is sufficient that the
capacity of a channel is (strictly) greater than the sum of the logarithms of
the unstable pole magnitudes for memoryless channels and a class of channels
with memory. This condition is also necessary under a mild technical condition.
Sufficient conditions for the existence of finite average second moments for
such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor
A Simple Converse of Burnashev's Reliability
In a remarkable paper published in 1976, Burnashev determined the reliability
function of variable-length block codes over discrete memoryless channels with
feedback. Subsequently, an alternative achievability proof was obtained by
Yamamoto and Itoh via a particularly simple and instructive scheme. Their idea
is to alternate between a communication and a confirmation phase until the
receiver detects the codeword used by the sender to acknowledge that the
message is correct. We provide a converse that parallels the Yamamoto-Itoh
achievability construction. Besides being simpler than the original, the
proposed converse suggests that a communication and a confirmation phase are
implicit in any scheme for which the probability of error decreases with the
largest possible exponent. The proposed converse also makes it intuitively
clear why the terms that appear in Burnashev's exponent are necessary.Comment: 10 pages, 1 figure, updated missing referenc
Feedback Capacity of the Compound Channel
In this work we find the capacity of a compound finite-state channel with
time-invariant deterministic feedback. The model we consider involves the use
of fixed length block codes. Our achievability result includes a proof of the
existence of a universal decoder for the family of finite-state channels with
feedback. As a consequence of our capacity result, we show that feedback does
not increase the capacity of the compound Gilbert-Elliot channel. Additionally,
we show that for a stationary and uniformly ergodic Markovian channel, if the
compound channel capacity is zero without feedback then it is zero with
feedback. Finally, we use our result on the finite-state channel to show that
the feedback capacity of the memoryless compound channel is given by
.Comment: 34 pages, 2 figures, submitted to IEEE Transactions on Information
Theor
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