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Wireless Pers Commun (2008) 46:365–370

DOI 10.1007/s11277-007-9439-0

A Low Complexity Algorithm for Generating Turbo

Code s-Random Interleavers

Kostas V. Koutsouvelis · Christos E. Dimakis

Published online: 20 December 2007

© Springer Science+Business Media, LLC. 2007

Abstract In this paper we present a low complexity algorithm based on the bubble search

sorting method that can be used to generate Turbo code interleavers that fulﬁll several crite-

ria like spreading (s-randomness), code matched criteria and even the odd–even property for

Turbo Trellis Coded Modulation. Simulation results show that for s <

√

N/2 the algorithm

is extremely efﬁcient for short to medium interleaver lengths.

Keywords Turbo codes · Turbo Trellis Coded Modulation (TTCM) · s-Random ·

Code-matched interleaver (CMI)

1 Introduction

The initial discovery of Turbo codes by Berrou et al. [1] in 1993 opened an enormous new

ﬁeld for research in communication theory. Since then, researchers worldwide have done

major efforts in order to reveal the secrets of the excellent performance of the new turbo

codecs and even to improve them. Very soon [2,3], the interleaver was identiﬁed to play a

central role on the performance of the overall turbo coding scheme, since it affects the dis-

tance spectrum of the code. Furthermore, for high SNR, it determines the error ﬂoor region

where the BER curve does not decrease as quickly as in the waterfall region. Several types of

interleavers have been constructed in order to improve the performance of the turbo coding

system. In the following we will give a brief overview of the most popular interleavers:

S. Dolinar et al. [2] veriﬁed that the performance of a turbo coding scheme could be

improved if the interleaver has the capability to eliminate input sequences that produce code-

words of low Hamming weight. They proposed a pseudorandom permutation, the s-random

interleaver (s denotes the spread factor) with the following property: if π is the interleaving

law the new selected position π(i) is accepted only if its absolute difference from the previous

s selected numbers π(j) is greater than s. This property is expressed mathematically as:

K. V. Koutsouvelis (

B

) · C. E. Dimakis

Aristotle University of Thessaloniki, Thessaloniki, Greece

e-mail: koutote@yahoo.gr

123

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2013-08-11

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