70,584 research outputs found
Second-order rate region of constant-composition codes for the multiple-access channel
This paper studies the second-order asymptotics of coding rates for the
discrete memoryless multiple-access channel with a fixed target error
probability. Using constant-composition random coding, coded time-sharing, and
a variant of Hoeffding's combinatorial central limit theorem, an inner bound on
the set of locally achievable second-order coding rates is given for each point
on the boundary of the capacity region. It is shown that the inner bound for
constant-composition random coding includes that recovered by i.i.d. random
coding, and that the inclusion may be strict. The inner bound is extended to
the Gaussian multiple-access channel via an increasingly fine quantization of
the inputs.Comment: (v2) Results/proofs given in matrix notation, det(V)=0 handled more
rigorously, Berry-Esseen derivation given. (v3) Gaussian case added (v4)
Significant change of presentation; added local dispersion results; added new
method to obtain non-standard tangent vector terms using coded time-sharing;
(v5) Final version (IEEE Transactions on Information Theory
Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities
This monograph presents a unified treatment of single- and multi-user
problems in Shannon's information theory where we depart from the requirement
that the error probability decays asymptotically in the blocklength. Instead,
the error probabilities for various problems are bounded above by a
non-vanishing constant and the spotlight is shone on achievable coding rates as
functions of the growing blocklengths. This represents the study of asymptotic
estimates with non-vanishing error probabilities.
In Part I, after reviewing the fundamentals of information theory, we discuss
Strassen's seminal result for binary hypothesis testing where the type-I error
probability is non-vanishing and the rate of decay of the type-II error
probability with growing number of independent observations is characterized.
In Part II, we use this basic hypothesis testing result to develop second- and
sometimes, even third-order asymptotic expansions for point-to-point
communication. Finally in Part III, we consider network information theory
problems for which the second-order asymptotics are known. These problems
include some classes of channels with random state, the multiple-encoder
distributed lossless source coding (Slepian-Wolf) problem and special cases of
the Gaussian interference and multiple-access channels. Finally, we discuss
avenues for further research.Comment: Further comments welcom
Second-Order Asymptotics for the Discrete Memoryless MAC with Degraded Message Sets
This paper studies the second-order asymptotics of the discrete memoryless
multiple-access channel with degraded message sets. For a fixed average error
probability and an arbitrary point on the boundary of the
capacity region, we characterize the speed of convergence of rate pairs that
converge to that point for codes that have asymptotic error probability no
larger than , thus complementing an analogous result given previously
for the Gaussian setting.Comment: 5 Pages, 1 Figure. Follow-up paper of http://arxiv.org/abs/1310.1197.
Accepted to ISIT 201
Random Access Channel Coding in the Finite Blocklength Regime
Consider a random access communication scenario over a channel whose
operation is defined for any number of possible transmitters. Inspired by the
model recently introduced by Polyanskiy for the Multiple Access Channel (MAC)
with a fixed, known number of transmitters, we assume that the channel is
invariant to permutations on its inputs, and that all active transmitters
employ identical encoders. Unlike Polyanskiy, we consider a scenario where
neither the transmitters nor the receiver know which transmitters are active.
We refer to this agnostic communication setup as the Random Access Channel, or
RAC. Scheduled feedback of a finite number of bits is used to synchronize the
transmitters. The decoder is tasked with determining from the channel output
the number of active transmitters () and their messages but not which
transmitter sent which message. The decoding procedure occurs at a time
depending on the decoder's estimate of the number of active transmitters,
, thereby achieving a rate that varies with the number of active
transmitters. Single-bit feedback at each time , enables all
transmitters to determine the end of one coding epoch and the start of the
next. The central result of this work demonstrates the achievability on a RAC
of performance that is first-order optimal for the MAC in operation during each
coding epoch. While prior multiple access schemes for a fixed number of
transmitters require simultaneous threshold rules, the proposed
scheme uses a single threshold rule and achieves the same dispersion.Comment: Presented at ISIT18', submitted to IEEE Transactions on Information
Theor
- β¦