1,003 research outputs found
Arithmetic coding for finite-state noiseless channels
Includes bibliographical references (p. 19-20).Supported by AT&T Bell Laboratories GRPW Fellowship and a Vinton Hayes Fellowship. Supported by the NSF. 8802991-NCRSerap A. Savari, Robert G. Gallager
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
About adaptive coding on countable alphabets
This paper sheds light on universal coding with respect to classes of
memoryless sources over a countable alphabet defined by an envelope function
with finite and non-decreasing hazard rate. We prove that the auto-censuring AC
code introduced by Bontemps (2011) is adaptive with respect to the collection
of such classes. The analysis builds on the tight characterization of universal
redundancy rate in terms of metric entropy % of small source classes by Opper
and Haussler (1997) and on a careful analysis of the performance of the
AC-coding algorithm. The latter relies on non-asymptotic bounds for maxima of
samples from discrete distributions with finite and non-decreasing hazard rate
Universal Source Polarization and an Application to a Multi-User Problem
We propose a scheme that universally achieves the smallest possible
compression rate for a class of sources with side information, and develop an
application of this result for a joint source channel coding problem over a
broadcast channel.Comment: to be presented at Allerton 201
Analytical tools for optimizing the error correction performance of arithmetic codes
International audienceIn joint source-channel arithmetic coding (JSCAC) schemes, additional redundancy may be introduced into an arithmetic source code in order to be more robust against transmission errors. The purpose of this work is to provide analytical tools to predict and evaluate the effectiveness of that redundancy. Integer binary Arithmetic Coding (AC) is modeled by a reduced-state automaton in order to obtain a bit-clock trellis describing the encoding process. Considering AC as a trellis code, distance spectra are then derived. In particular, an algorithm to compute the free distance of an arithmetic code is proposed. The obtained code properties allow to compute upper bounds on both bit error and symbol error probabilities and thus provide an objective criterion to analyze the behavior of JSCAC schemes when used on noisy channels. This criterion is then exploited to design efficient error-correcting arithmetic codes. Simulation results highlight the validity of the theoretical error bounds and show that for equivalent rate and complexity, a simple optimization yields JSCACs that outperform classical tandem schemes at low to medium SNR
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