Asymptotic analysis for multi-user channels

Huang, Yen-Wei

Permalink

https://hdl.handle.net/2142/46663 Copy

Description

Title

Asymptotic analysis for multi-user channels

Author(s)

Huang, Yen-Wei

Issue Date

2014-01-16T17:58:05Z

Director of Research (if dissertation) or Advisor (if thesis)

Moulin, Pierre

Doctoral Committee Chair(s)

Moulin, Pierre

Committee Member(s)

• Basar, Tamer
• Hajek, Bruce
• Veeravalli, Venugopal V.
• Milenkovic, Olgica

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Multi-User Channel
• Fingerprinting
• Traitor Tracing
• Game Theory
• Minimax Analysis
• Asymptotic Analysis
• Multiple Access Channel
• Finite Blocklength Coding

Abstract

This dissertation studies the asymptotics of two multi-user channel problems. The fingerprinting channel is associated with digital fingerprinting, which is an emerging technology to protect multimedia from unauthorized redistribution. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. The multiple access channel (MAC) is a classical problem in the field of network information theory. Multiple senders cooperate with one another to maximize their rates of communication to a single receiver. We address the problem of asymptotic analysis when the size of the problem goes to infinity. The fundamental metric of measuring the detection capability of a fingerprinting system is capacity. It has recently been derived as the limit value of a sequence of maximin games with mutual information as their payoff functions. However, these games generally do not admit saddle-point solutions and are very hard to solve. Here under a modified version of the combined digit model proposed by Skoric et al., we reformulate the capacity as the value of a single two-person zero-sum game, and show that it is achieved by a saddle-point solution. For fingerprinting capacity games with k pirates, we provide capacities along with optimal strategies for both players of the game when k is small. For large k, we show that capacity is asymptotic to A/k^2 where the constant A is specified as the maximin value of a continuous functional game. Saddle-point solutions to the game are obtained using methods of variational calculus. For multiple access channels we study the maximum achievable rate region for a given blocklength n and a desired error probability epsilon. The inner region for the discrete memoryless MAC is approximated by a single-lettered expression I-(1/sqrt(n))*Q_inv(V,epsilon) where I is associated with the capacity pentagon bounds by Ahlswede and Liao, V is the MAC dispersion matrix, and Q_inv is the inverse complementary multivariate Gaussian cumulative distribution region. For outer regions, we provide general converse bounds for both average error probability and maximal error probability criteria.

Graduation Semester

2013-12

Permalink

http://hdl.handle.net/2142/46663

Copyright and License Information

Copyright 2013 Yen-Wei Huang

Owning Collections