14,191 research outputs found
Capacity of Binary State Symmetric Channel with and without Feedback and Transmission Cost
We consider a unit memory channel, called Binary State Symmetric Channel
(BSSC), in which the channel state is the modulo2 addition of the current
channel input and the previous channel output. We derive closed form
expressions for the capacity and corresponding channel input distribution, of
this BSSC with and without feedback and transmission cost. We also show that
the capacity of the BSSC is not increased by feedback, and it is achieved by a
first order symmetric Markov process
Sequential Necessary and Sufficient Conditions for Capacity Achieving Distributions of Channels with Memory and Feedback
We derive sequential necessary and sufficient conditions for any channel
input conditional distribution to maximize the
finite-time horizon directed information defined by for channel distributions
and
, where
and are the
channel input and output random processes, and is a finite nonnegative
integer.
\noi We apply the necessary and sufficient conditions to application examples
of time-varying channels with memory and we derive recursive closed form
expressions of the optimal distributions, which maximize the finite-time
horizon directed information. Further, we derive the feedback capacity from the
asymptotic properties of the optimal distributions by investigating the limit
without any \'a priori
assumptions, such as, stationarity, ergodicity or irreducibility of the channel
distribution. The necessary and sufficient conditions can be easily extended to
a variety of channels with memory, beyond the ones considered in this paper.Comment: 57 pages, 9 figures, part of the paper was accepted for publication
in the proceedings of the IEEE International Symposium on Information Theory
(ISIT), Barcelona, Spain 10-15 July, 2016 (Date of submission of the
conference paper: 25/1/2016
A Rate-Compatible Sphere-Packing Analysis of Feedback Coding with Limited Retransmissions
Recent work by Polyanskiy et al. and Chen et al. has excited new interest in
using feedback to approach capacity with low latency. Polyanskiy showed that
feedback identifying the first symbol at which decoding is successful allows
capacity to be approached with surprisingly low latency. This paper uses Chen's
rate-compatible sphere-packing (RCSP) analysis to study what happens when
symbols must be transmitted in packets, as with a traditional hybrid ARQ
system, and limited to relatively few (six or fewer) incremental transmissions.
Numerical optimizations find the series of progressively growing cumulative
block lengths that enable RCSP to approach capacity with the minimum possible
latency. RCSP analysis shows that five incremental transmissions are sufficient
to achieve 92% of capacity with an average block length of fewer than 101
symbols on the AWGN channel with SNR of 2.0 dB.
The RCSP analysis provides a decoding error trajectory that specifies the
decoding error rate for each cumulative block length. Though RCSP is an
idealization, an example tail-biting convolutional code matches the RCSP
decoding error trajectory and achieves 91% of capacity with an average block
length of 102 symbols on the AWGN channel with SNR of 2.0 dB. We also show how
RCSP analysis can be used in cases where packets have deadlines associated with
them (leading to an outage probability).Comment: To be published at the 2012 IEEE International Symposium on
Information Theory, Cambridge, MA, USA. Updated to incorporate reviewers'
comments and add new figure
A Simple Derivation of the Refined Sphere Packing Bound Under Certain Symmetry Hypotheses
A judicious application of the Berry-Esseen theorem via suitable Augustin
information measures is demonstrated to be sufficient for deriving the sphere
packing bound with a prefactor that is
for all codes on certain
families of channels -- including the Gaussian channels and the non-stationary
Renyi symmetric channels -- and for the constant composition codes on
stationary memoryless channels. The resulting non-asymptotic bounds have
definite approximation error terms. As a preliminary result that might be of
interest on its own, the trade-off between type I and type II error
probabilities in the hypothesis testing problem with (possibly non-stationary)
independent samples is determined up to some multiplicative constants, assuming
that the probabilities of both types of error are decaying exponentially with
the number of samples, using the Berry-Esseen theorem.Comment: 20 page
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