Title :
A necessary condition for reliable communication with feedback based upon Lyapunov exponents of dynamical systems
Author :
Ebeid, Hani-James ; Gorantla, Siva K. ; Coleman, Todd P.
Author_Institution :
ECE Dept., Univ. of Illinois, Urbana, IL, USA
fDate :
Oct. 31 2010-Nov. 3 2010
Abstract :
In this paper we use control theoretic techniques to provide a new perspective for understanding what makes a channel coding scheme good. We show that for a broad class of causal feedback channels, including some with memory, the Lyapunov exponent of the transmission function - when it exists - is fundamentally linked to the maximum rate which the scheme can attain. More generally, we can upper-bound the set of achievable rates for a given encoding scheme by considering a generalization of the Lyapunov exponent of the transmission function. By approaching the problem from a dynamical systems perspective, we hope to provide the intuition to motivate the evaluation and design of new coding schemes.
Keywords :
Lyapunov methods; causality; channel coding; feedback; telecommunication network reliability; Lyapunov exponent; causal feedback channel; channel coding; dynamical system; encoding; reliable communication; transmission function; Decoding; Encoding; Feedback communications; Memoryless systems; Noise measurement; Random variables; Receivers;
Conference_Titel :
MILITARY COMMUNICATIONS CONFERENCE, 2010 - MILCOM 2010
Conference_Location :
San Jose, CA
Print_ISBN :
978-1-4244-8178-1
DOI :
10.1109/MILCOM.2010.5680215