7 research outputs found
The Third-Order Term in the Normal Approximation for the AWGN Channel
This paper shows that, under the average error probability formalism, the
third-order term in the normal approximation for the additive white Gaussian
noise channel with a maximal or equal power constraint is at least . This matches the upper bound derived by
Polyanskiy-Poor-Verd\'{u} (2010).Comment: 13 pages, 1 figur
Refined Strong Converse for the Constant Composition Codes
A strong converse bound for constant composition codes of the form
is
established using the Berry-Esseen theorem through the concepts of Augustin
information and Augustin mean, where is a constant determined by the
channel , the composition , and the rate , i.e., does not depend
on the block length .Comment: 7 page
Sphere-packing bound for symmetric classical-quantum channels
Β© 2017 IEEE. "To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award." We provide a sphere-packing lower bound for the optimal error probability in finite blocklengths when coding over a symmetric classical-quantum channel. Our result shows that the pre-factor can be significantly improved from the order of the subexponential to the polynomial, This established pre-factor is arguably optimal because it matches the best known random coding upper bound in the classical case. Our approaches rely on a sharp concentration inequality in strong large deviation theory and crucial properties of the error-exponent function
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
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 via Augustin's Method
A sphere packing bound (SPB) with a prefactor that is polynomial in the block
length is established for codes on a length product channel
assuming that the maximum order Renyi capacity among the component
channels, i.e. , is . The
reliability function of the discrete stationary product channels with feedback
is bounded from above by the sphere packing exponent. Both results are proved
by first establishing a non-asymptotic SPB. The latter result continues to hold
under a milder stationarity hypothesis.Comment: 30 pages. An error in the statement of Lemma 2 is corrected. The
change is inconsequential for the rest of the pape