1,783 research outputs found
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
Asymptotic Behavior of Error Exponents in the Wideband Regime
In this paper, we complement Verd\'{u}'s work on spectral efficiency in the
wideband regime by investigating the fundamental tradeoff between rate and
bandwidth when a constraint is imposed on the error exponent. Specifically, we
consider both AWGN and Rayleigh-fading channels. For the AWGN channel model,
the optimal values of and are calculated, where
is the maximum rate at which information can be transmitted over a
channel with bandwidth when the error-exponent is constrained to be
greater than or equal to Based on this calculation, we say that a sequence
of input distributions is near optimal if both and are
achieved. We show that QPSK, a widely-used signaling scheme, is near-optimal
within a large class of input distributions for the AWGN channel. Similar
results are also established for a fading channel where full CSI is available
at the receiver.Comment: 59 pages, 6 figure
The Sphere Packing Bound For Memoryless Channels
Sphere packing bounds (SPBs) ---with prefactors that are polynomial in the
block length--- are derived for codes on two families of memoryless channels
using Augustin's method: (possibly non-stationary) memoryless channels with
(possibly multiple) additive cost constraints and stationary memoryless
channels with convex constraints on the composition (i.e. empirical
distribution, type) of the input codewords. A variant of Gallager's bound is
derived in order to show that these sphere packing bounds are tight in terms of
the exponential decay rate of the error probability with the block length under
mild hypotheses.Comment: 29 page
The Sphere Packing Bound for DSPCs with Feedback a la Augustin
Establishing the sphere packing bound for block codes on the discrete
stationary product channels with feedback ---which are commonly called the
discrete memoryless channels with feedback--- was considered to be an open
problem until recently, notwithstanding the proof sketch provided by Augustin
in 1978. A complete proof following Augustin's proof sketch is presented, to
demonstrate its adequacy and to draw attention to two novel ideas it employs.
These novel ideas (i.e., the Augustin's averaging and the use of subblocks) are
likely to be applicable in other communication problems for establishing
impossibility results.Comment: 12 pages, 2 figure
Error Probability Bounds for Gaussian Channels under Maximal and Average Power Constraints
This paper studies the performance of block coding on an additive white
Gaussian noise channel under different power limitations at the transmitter.
Lower bounds are presented for the minimum error probability of codes
satisfying maximal and average power constraints. These bounds are tighter than
previous results in the finite blocklength regime, and yield a better
understanding on the structure of good codes under an average power limitation.
Evaluation of these bounds for short and moderate blocklengths is also
discussed.Comment: Submitted to the IEEE Transactions on Information Theory. This
article was presented in part at the 2019 IEEE International Symposium on
Information Theory, Paris, France (ISIT 2019) and at the 2020 International
Z\"urich Seminar on Communication and Information, Z\"urich, Switzerland (IZS
2020
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