55,778 research outputs found
Coding with Encoding Uncertainty
We study the channel coding problem when errors and uncertainty occur in the
encoding process. For simplicity we assume the channel between the encoder and
the decoder is perfect. Focusing on linear block codes, we model the encoding
uncertainty as erasures on the edges in the factor graph of the encoder
generator matrix. We first take a worst-case approach and find the maximum
tolerable number of erasures for perfect error correction. Next, we take a
probabilistic approach and derive a sufficient condition on the rate of a set
of codes, such that decoding error probability vanishes as blocklength tends to
infinity. In both scenarios, due to the inherent asymmetry of the problem, we
derive the results from first principles, which indicates that robustness to
encoding errors requires new properties of codes different from classical
properties.Comment: 12 pages; a shorter version of this work will appear in the
proceedings of ISIT 201
On Multistage Successive Refinement for Wyner-Ziv Source Coding with Degraded Side Informations
We provide a complete characterization of the rate-distortion region for the
multistage successive refinement of the Wyner-Ziv source coding problem with
degraded side informations at the decoder. Necessary and sufficient conditions
for a source to be successively refinable along a distortion vector are
subsequently derived. A source-channel separation theorem is provided when the
descriptions are sent over independent channels for the multistage case.
Furthermore, we introduce the notion of generalized successive refinability
with multiple degraded side informations. This notion captures whether
progressive encoding to satisfy multiple distortion constraints for different
side informations is as good as encoding without progressive requirement.
Necessary and sufficient conditions for generalized successive refinability are
given. It is shown that the following two sources are generalized successively
refinable: (1) the Gaussian source with degraded Gaussian side informations,
(2) the doubly symmetric binary source when the worse side information is a
constant. Thus for both cases, the failure of being successively refinable is
only due to the inherent uncertainty on which side information will occur at
the decoder, but not the progressive encoding requirement.Comment: Submitted to IEEE Trans. Information Theory Apr. 200
Extrinsic Jensen-Shannon Divergence: Applications to Variable-Length Coding
This paper considers the problem of variable-length coding over a discrete
memoryless channel (DMC) with noiseless feedback. The paper provides a
stochastic control view of the problem whose solution is analyzed via a newly
proposed symmetrized divergence, termed extrinsic Jensen-Shannon (EJS)
divergence. It is shown that strictly positive lower bounds on EJS divergence
provide non-asymptotic upper bounds on the expected code length. The paper
presents strictly positive lower bounds on EJS divergence, and hence
non-asymptotic upper bounds on the expected code length, for the following two
coding schemes: variable-length posterior matching and MaxEJS coding scheme
which is based on a greedy maximization of the EJS divergence.
As an asymptotic corollary of the main results, this paper also provides a
rate-reliability test. Variable-length coding schemes that satisfy the
condition(s) of the test for parameters and , are guaranteed to achieve
rate and error exponent . The results are specialized for posterior
matching and MaxEJS to obtain deterministic one-phase coding schemes achieving
capacity and optimal error exponent. For the special case of symmetric
binary-input channels, simpler deterministic schemes of optimal performance are
proposed and analyzed.Comment: 17 pages (two-column), 4 figures, to appear in IEEE Transactions on
Information Theor
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