311,703 research outputs found
Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition Codes
An optimal constant-composition or constant-weight code of weight has
linear size if and only if its distance is at least . When , the determination of the exact size of such a constant-composition or
constant-weight code is trivial, but the case of has been solved
previously only for binary and ternary constant-composition and constant-weight
codes, and for some sporadic instances.
This paper provides a construction for quasicyclic optimal
constant-composition and constant-weight codes of weight and distance
based on a new generalization of difference triangle sets. As a result,
the sizes of optimal constant-composition codes and optimal constant-weight
codes of weight and distance are determined for all such codes of
sufficiently large lengths. This solves an open problem of Etzion.
The sizes of optimal constant-composition codes of weight and distance
are also determined for all , except in two cases.Comment: 12 page
Exact Random Coding Secrecy Exponents for the Wiretap Channel
We analyze the exact exponential decay rate of the expected amount of
information leaked to the wiretapper in Wyner's wiretap channel setting using
wiretap channel codes constructed from both i.i.d. and constant-composition
random codes. Our analysis for those sampled from i.i.d. random coding ensemble
shows that the previously-known achievable secrecy exponent using this ensemble
is indeed the exact exponent for an average code in the ensemble. Furthermore,
our analysis on wiretap channel codes constructed from the ensemble of
constant-composition random codes leads to an exponent which, in addition to
being the exact exponent for an average code, is larger than the achievable
secrecy exponent that has been established so far in the literature for this
ensemble (which in turn was known to be smaller than that achievable by wiretap
channel codes sampled from i.i.d. random coding ensemble). We show examples
where the exact secrecy exponent for the wiretap channel codes constructed from
random constant-composition codes is larger than that of those constructed from
i.i.d. random codes and examples where the exact secrecy exponent for the
wiretap channel codes constructed from i.i.d. random codes is larger than that
of those constructed from constant-composition random codes. We, hence,
conclude that, unlike the error correction problem, there is no general
ordering between the two random coding ensembles in terms of their secrecy
exponent.Comment: 23 pages, 5 figures, submitted to IEEE Transactions on Information
Theor
Estimates on the Size of Symbol Weight Codes
The study of codes for powerlines communication has garnered much interest
over the past decade. Various types of codes such as permutation codes,
frequency permutation arrays, and constant composition codes have been proposed
over the years. In this work we study a type of code called the bounded symbol
weight codes which was first introduced by Versfeld et al. in 2005, and a
related family of codes that we term constant symbol weight codes. We provide
new upper and lower bounds on the size of bounded symbol weight and constant
symbol weight codes. We also give direct and recursive constructions of codes
for certain parameters.Comment: 14 pages, 4 figure
A Construction for Constant-Composition Codes
By employing the residue polynomials, a construction of constant-composition
codes is given. This construction generalizes the one proposed by Xing[16]. It
turns out that when d=3 this construction gives a lower bound of
constant-composition codes improving the one in [10]. Moreover, for d>3, we
give a lower bound on maximal size of constant-composition codes. In
particular, our bound for d=5 gives the best possible size of
constant-composition codes up to magnitude.Comment: 4 pages, submitted to IEEE Infromation Theor
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
On the Throughput of Channels that Wear Out
This work investigates the fundamental limits of communication over a noisy
discrete memoryless channel that wears out, in the sense of signal-dependent
catastrophic failure. In particular, we consider a channel that starts as a
memoryless binary-input channel and when the number of transmitted ones causes
a sufficient amount of damage, the channel ceases to convey signals. Constant
composition codes are adopted to obtain an achievability bound and the
left-concave right-convex inequality is then refined to obtain a converse bound
on the log-volume throughput for channels that wear out. Since infinite
blocklength codes will always wear out the channel for any finite threshold of
failure and therefore cannot convey information at positive rates, we analyze
the performance of finite blocklength codes to determine the maximum expected
transmission volume at a given level of average error probability. We show that
this maximization problem has a recursive form and can be solved by dynamic
programming. Numerical results demonstrate that a sequence of block codes is
preferred to a single block code for streaming sources.Comment: 23 pages, 1 table, 11 figures, submitted to IEEE Transactions on
Communication
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