9,305 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
Universal Polar Codes for More Capable and Less Noisy Channels and Sources
We prove two results on the universality of polar codes for source coding and
channel communication. First, we show that for any polar code built for a
source there exists a slightly modified polar code - having the same
rate, the same encoding and decoding complexity and the same error rate - that
is universal for every source when using successive cancellation
decoding, at least when the channel is more capable than
and is such that it maximizes for the given channels
and . This result extends to channel coding for discrete
memoryless channels. Second, we prove that polar codes using successive
cancellation decoding are universal for less noisy discrete memoryless
channels.Comment: 10 pages, 3 figure
An Achievable Rate Region for the Broadcast Channel with Feedback
A single-letter achievable rate region is proposed for the two-receiver
discrete memoryless broadcast channel with generalized feedback. The coding
strategy involves block-Markov superposition coding, using Marton's coding
scheme for the broadcast channel without feedback as the starting point. If the
message rates in the Marton scheme are too high to be decoded at the end of a
block, each receiver is left with a list of messages compatible with its
output. Resolution information is sent in the following block to enable each
receiver to resolve its list. The key observation is that the resolution
information of the first receiver is correlated with that of the second. This
correlated information is efficiently transmitted via joint source-channel
coding, using ideas similar to the Han-Costa coding scheme. Using the result,
we obtain an achievable rate region for the stochastically degraded AWGN
broadcast channel with noisy feedback from only one receiver. It is shown that
this region is strictly larger than the no-feedback capacity region.Comment: To appear in IEEE Transactions on Information Theory. Contains
example of AWGN Broadcast Channel with noisy feedbac
Secrecy Through Synchronization Errors
In this paper, we propose a transmission scheme that achieves information
theoretic security, without making assumptions on the eavesdropper's channel.
This is achieved by a transmitter that deliberately introduces synchronization
errors (insertions and/or deletions) based on a shared source of randomness.
The intended receiver, having access to the same shared source of randomness as
the transmitter, can resynchronize the received sequence. On the other hand,
the eavesdropper's channel remains a synchronization error channel. We prove a
secrecy capacity theorem, provide a lower bound on the secrecy capacity, and
propose numerical methods to evaluate it.Comment: 5 pages, 6 figures, submitted to ISIT 201
Classical capacity of a qubit depolarizing channel with memory
The classical product state capacity of a noisy quantum channel with memory
is investigated. A forgetful noise-memory channel is constructed by Markov
switching between two depolarizing channels which introduces non-Markovian
noise correlations between successive channel uses. The computation of the
capacity is reduced to an entropy computation for a function of a Markov
process. A reformulation in terms of algebraic measures then enables its
calculation. The effects of the hidden-Markovian memory on the capacity are
explored. An increase in noise-correlations is found to increase the capacity
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