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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
Abstract.
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
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