Asymptotic Behavior of Error Probability in Continuous-Time Gaussian Channels with Feedback

Shunsuke IHARA

doi:10.1587/transfun.E99.A.2107

IEICE TRANSACTIONS on Fundamentals

Asymptotic Behavior of Error Probability in Continuous-Time Gaussian Channels with Feedback

Shunsuke IHARA

Full Text Views

0

Cite this

Summary :

We investigate the coding scheme and error probability in information transmission over continuous-time additive Gaussian noise channels with feedback. As is known, the error probability can be substantially reduced by using feedback, namely, under the average power constraint, the error probability may decrease more rapidly than the exponential of any order. Recently Gallager and Nakibolu proposed, for discrete-time additive white Gaussian noise channels, a feedback coding scheme such that the resulting error probability P_e(N) at time N decreases with an exponential order αN which is linearly increasing with N. The multiple-exponential decay of the error probability has been studied mostly for white Gaussian channels, so far. In this paper, we treat continuous-time Gaussian channels, where the Gaussian noise processes are not necessarily white nor stationary. The aim is to prove a stronger result on the multiple-exponential decay of the error probability. More precisely, for any positive constant α, there exists a feedback coding scheme such that the resulting error probability P_e(T) at time T decreases more rapidly than the exponential of order αT as T→∞.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.12 pp.2107-2115

Publication Date: 2016/12/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E99.A.2107

Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Shannon Theory

Authors

Shunsuke IHARA
Nagoya University

Keyword

additive Gaussian noise channel, feedback, multiple-exponential decrease of error probability

Cite this

Copy

Shunsuke IHARA, "Asymptotic Behavior of Error Probability in Continuous-Time Gaussian Channels with Feedback" in IEICE TRANSACTIONS on Fundamentals, vol. E99-A, no. 12, pp. 2107-2115, December 2016, doi: 10.1587/transfun.E99.A.2107.
Abstract: We investigate the coding scheme and error probability in information transmission over continuous-time additive Gaussian noise channels with feedback. As is known, the error probability can be substantially reduced by using feedback, namely, under the average power constraint, the error probability may decrease more rapidly than the exponential of any order. Recently Gallager and Nakibolu proposed, for discrete-time additive white Gaussian noise channels, a feedback coding scheme such that the resulting error probability P_e(N) at time N decreases with an exponential order αN which is linearly increasing with N. The multiple-exponential decay of the error probability has been studied mostly for white Gaussian channels, so far. In this paper, we treat continuous-time Gaussian channels, where the Gaussian noise processes are not necessarily white nor stationary. The aim is to prove a stronger result on the multiple-exponential decay of the error probability. More precisely, for any positive constant α, there exists a feedback coding scheme such that the resulting error probability P_e(T) at time T decreases more rapidly than the exponential of order αT as T→∞.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.2107/_p

Copy

@ARTICLE{e99-a_12_2107,
author={Shunsuke IHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Asymptotic Behavior of Error Probability in Continuous-Time Gaussian Channels with Feedback},
year={2016},
volume={E99-A},
number={12},
pages={2107-2115},
abstract={We investigate the coding scheme and error probability in information transmission over continuous-time additive Gaussian noise channels with feedback. As is known, the error probability can be substantially reduced by using feedback, namely, under the average power constraint, the error probability may decrease more rapidly than the exponential of any order. Recently Gallager and Nakibolu proposed, for discrete-time additive white Gaussian noise channels, a feedback coding scheme such that the resulting error probability P_e(N) at time N decreases with an exponential order αN which is linearly increasing with N. The multiple-exponential decay of the error probability has been studied mostly for white Gaussian channels, so far. In this paper, we treat continuous-time Gaussian channels, where the Gaussian noise processes are not necessarily white nor stationary. The aim is to prove a stronger result on the multiple-exponential decay of the error probability. More precisely, for any positive constant α, there exists a feedback coding scheme such that the resulting error probability P_e(T) at time T decreases more rapidly than the exponential of order αT as T→∞.},
keywords={},
doi={10.1587/transfun.E99.A.2107},
ISSN={1745-1337},
month={December},}

Copy

TY - JOUR
TI - Asymptotic Behavior of Error Probability in Continuous-Time Gaussian Channels with Feedback
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2107
EP - 2115
AU - Shunsuke IHARA
PY - 2016
DO - 10.1587/transfun.E99.A.2107
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2016
AB - We investigate the coding scheme and error probability in information transmission over continuous-time additive Gaussian noise channels with feedback. As is known, the error probability can be substantially reduced by using feedback, namely, under the average power constraint, the error probability may decrease more rapidly than the exponential of any order. Recently Gallager and Nakibolu proposed, for discrete-time additive white Gaussian noise channels, a feedback coding scheme such that the resulting error probability P_e(N) at time N decreases with an exponential order αN which is linearly increasing with N. The multiple-exponential decay of the error probability has been studied mostly for white Gaussian channels, so far. In this paper, we treat continuous-time Gaussian channels, where the Gaussian noise processes are not necessarily white nor stationary. The aim is to prove a stronger result on the multiple-exponential decay of the error probability. More precisely, for any positive constant α, there exists a feedback coding scheme such that the resulting error probability P_e(T) at time T decreases more rapidly than the exponential of order αT as T→∞.
ER -

IEICE TRANSACTIONS on Fundamentals