Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Coding Theorems for "Turbo-Like" Codes Dariush Divsalar, Hui Jin, and Robert J. McEliece

Summary: Coding Theorems for "Turbo-Like" Codes
Dariush Divsalar, Hui Jin, and Robert J. McEliece
Jet Propulsion Laboratory and California Institute of Technology
Pasadena, California USA
E-mail: dariush@shannon.jpl.nasa.gov, (hui, rjm)@systems.caltech.edu
In this paper we discuss AWGN coding theorems for ensembles of coding systems which
are built from fixed convolutional codes interconnected with random interleavers. We
call these systems "turbo-like" codes and they include as special cases both the classical
turbo codes [1,2,3] and the serial concatentation of interleaved convolutional codes [4].
We offer a general conjecture about the behavior of the ensemble (maximum-likelihood
decoder) word error probability as the word length approches infinity. We prove this
conjecture for a simple class of rate 1/q serially concatenated codes where the outer
code is a q-fold repetition code and the inner code is a rate 1 convolutional code with
transfer function 1/(1 + D). We believe this represents the first rigorous proof of a
coding theorem for turbo-like codes.
1. Introduction.
The 1993 discovery of turbo codes by Berrou, Glavieux, and Thitimajshima [1] has
revolutionized the field of error-correcting codes. In brief, turbo codes have enough
randomness to achieve reliable communication at data rates near capacity, yet enough


Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology


Collections: Computer Technologies and Information Sciences