Completion Time in Two-User Channels

An Information-Theoretic Perspective

Yuanpeng Liu, Elza Erkip

Research output: Contribution to journalArticle

Abstract

Consider a multi-user channel, where each user has a large but non-replenishable bit pool to transmit. Completion time refers to the number of channel uses spent by each user to complete its transmission. In this paper, an information-theoretic formulation of completion time is based on the concept of constrained rates, which are defined over possibly different number of channel uses. Analogous to the capacity region, the completion time region characterizes all possible trade-offs among users' completion times. For a two-user multi-access channel, it is shown that the completion time region is achieved by operating the channel in two independent phases: a multi-access phase when both users are transmitting, and a point-to-point phase when one user has finished and the other is still transmitting. Using a similar two-phase approach, the completion time regions (or inner and outer bounds) are established for a two-user Gaussian broadcast channel and a two-user Gaussian interference channel. It is observed that although consisting of two convex subregions, the completion time region may not be convex in general. Finally, optimization problems of minimizing the weighted sum completion time for a Gaussian multi-access channel and a Gaussian broadcast channel are solved, demonstrating the utility of the completion time approach.

Original languageEnglish (US)
Article number7857054
Pages (from-to)3209-3223
Number of pages15
JournalIEEE Transactions on Information Theory
Volume63
Issue number5
DOIs
StatePublished - May 1 2017

Fingerprint

broadcast
time
interference

Keywords

  • capacity region
  • Delay minimization
  • multi-access channel
  • network information theory
  • utility optimization

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Cite this

Completion Time in Two-User Channels : An Information-Theoretic Perspective. / Liu, Yuanpeng; Erkip, Elza.

In: IEEE Transactions on Information Theory, Vol. 63, No. 5, 7857054, 01.05.2017, p. 3209-3223.

Research output: Contribution to journalArticle

@article{3b56520fdaf6447985989d24a5f901c9,
title = "Completion Time in Two-User Channels: An Information-Theoretic Perspective",
abstract = "Consider a multi-user channel, where each user has a large but non-replenishable bit pool to transmit. Completion time refers to the number of channel uses spent by each user to complete its transmission. In this paper, an information-theoretic formulation of completion time is based on the concept of constrained rates, which are defined over possibly different number of channel uses. Analogous to the capacity region, the completion time region characterizes all possible trade-offs among users' completion times. For a two-user multi-access channel, it is shown that the completion time region is achieved by operating the channel in two independent phases: a multi-access phase when both users are transmitting, and a point-to-point phase when one user has finished and the other is still transmitting. Using a similar two-phase approach, the completion time regions (or inner and outer bounds) are established for a two-user Gaussian broadcast channel and a two-user Gaussian interference channel. It is observed that although consisting of two convex subregions, the completion time region may not be convex in general. Finally, optimization problems of minimizing the weighted sum completion time for a Gaussian multi-access channel and a Gaussian broadcast channel are solved, demonstrating the utility of the completion time approach.",
keywords = "capacity region, Delay minimization, multi-access channel, network information theory, utility optimization",
author = "Yuanpeng Liu and Elza Erkip",
year = "2017",
month = "5",
day = "1",
doi = "10.1109/TIT.2017.2669329",
language = "English (US)",
volume = "63",
pages = "3209--3223",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "5",

}

TY - JOUR

T1 - Completion Time in Two-User Channels

T2 - An Information-Theoretic Perspective

AU - Liu, Yuanpeng

AU - Erkip, Elza

PY - 2017/5/1

Y1 - 2017/5/1

N2 - Consider a multi-user channel, where each user has a large but non-replenishable bit pool to transmit. Completion time refers to the number of channel uses spent by each user to complete its transmission. In this paper, an information-theoretic formulation of completion time is based on the concept of constrained rates, which are defined over possibly different number of channel uses. Analogous to the capacity region, the completion time region characterizes all possible trade-offs among users' completion times. For a two-user multi-access channel, it is shown that the completion time region is achieved by operating the channel in two independent phases: a multi-access phase when both users are transmitting, and a point-to-point phase when one user has finished and the other is still transmitting. Using a similar two-phase approach, the completion time regions (or inner and outer bounds) are established for a two-user Gaussian broadcast channel and a two-user Gaussian interference channel. It is observed that although consisting of two convex subregions, the completion time region may not be convex in general. Finally, optimization problems of minimizing the weighted sum completion time for a Gaussian multi-access channel and a Gaussian broadcast channel are solved, demonstrating the utility of the completion time approach.

AB - Consider a multi-user channel, where each user has a large but non-replenishable bit pool to transmit. Completion time refers to the number of channel uses spent by each user to complete its transmission. In this paper, an information-theoretic formulation of completion time is based on the concept of constrained rates, which are defined over possibly different number of channel uses. Analogous to the capacity region, the completion time region characterizes all possible trade-offs among users' completion times. For a two-user multi-access channel, it is shown that the completion time region is achieved by operating the channel in two independent phases: a multi-access phase when both users are transmitting, and a point-to-point phase when one user has finished and the other is still transmitting. Using a similar two-phase approach, the completion time regions (or inner and outer bounds) are established for a two-user Gaussian broadcast channel and a two-user Gaussian interference channel. It is observed that although consisting of two convex subregions, the completion time region may not be convex in general. Finally, optimization problems of minimizing the weighted sum completion time for a Gaussian multi-access channel and a Gaussian broadcast channel are solved, demonstrating the utility of the completion time approach.

KW - capacity region

KW - Delay minimization

KW - multi-access channel

KW - network information theory

KW - utility optimization

UR - http://www.scopus.com/inward/record.url?scp=85018729866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018729866&partnerID=8YFLogxK

U2 - 10.1109/TIT.2017.2669329

DO - 10.1109/TIT.2017.2669329

M3 - Article

VL - 63

SP - 3209

EP - 3223

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 5

M1 - 7857054

ER -