Abstract | For the construction of low rate turbo{codes, the concept of multiple parallel concatenatedcodes, i.e. the \multiple{turbo{code" has been suc-cessfully employed e.g. in [13, 16]. Analysis of thisstructure has been done via simulations [16] or theanalysis of equivalent coding schemes [13].In this paper we extend the method of EXIT charts[5], that has been applied to multiple{turbo{codesconsisting of identical component codes via serial{to{parallel conversion [13], to the analysis of asym-metric structures which employ difierent componentcodes. With this method, convergence analysis of thewhole class of multiple{turbo{codes and their designbecomes tractable. Keywords : Turbo{Codes, Convergence Analysis.I. Introduction Recently new constructions of turbo{codes [13, 16] have beenfound that outperform the original turbo{code [3] in both, thewaterfall and error{°oor regions. Additionally, these codeshave a signiflcantly lower decoding complexity.One of the ways to flnd such improved coding schemes,is the technique of code design via EXIT charts [5], whichhas been applied very successfully for serial concatenations[6] and classical turbo{codes [7]. In [13] it has been usedto analyze symmetric multiple{turbo{codes, which consist ofidentical constituent codes. This structure has been convertedto an equivalent serial concatenation of an outer repetitioncode and an inner rate{1 scrambler, that fltted within theframework of EXIT charts.In this paper we will focus on multiple{turbo{codes, asdescribed in Section II. We extend the method of conver-gence analysis by means of EXIT charts to the general caseof asymmetric multiple{turbo{codes, where we are no longerrestricted to use identical constituent codes. The properties ofthe component codes are determined by measuring their trans-fer characteristics in Section III. In Section IV, an abstractmodel for the information processing within the iterative de-coder of a multiple{turbo{code is established. This model en-ables us to determine the convergence properties of any codingscheme without simulation of the decoding procedure or theentire digital communication scheme. An algorithm for thisconvergence analysis is given in Section V. Examples for suc-cessful code designs of asymmetric multiple{turbo{codes aregiven in Section VI. Finally, in Section VII some conclusionsare given.
[1]
Joachim Hagenauer,et al.
Iterative decoding of binary block and convolutional codes
,
1996,
IEEE Trans. Inf. Theory.
[2]
O. Y. Takeshita,et al.
On the decoding structure for multiple turbo codes
,
2001,
Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).
[3]
Daniel J. Costello,et al.
New low-complexity turbo-like codes
,
2001,
Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494).
[4]
S. ten Brink,et al.
Code doping for triggering iterative decoding convergence
,
2001
.
[5]
S. Brink.
Convergence of iterative decoding
,
1999
.
[6]
Daniel J. Costello,et al.
Some Reflections on the Design of Bandwidth Efficient Turbo Codes
,
.
[7]
D. G. Brennan,et al.
Linear diversity combining techniques
,
2003
.
[8]
Lajos Hanzo,et al.
The super-trellis structure of turbo codes
,
2000,
IEEE Trans. Inf. Theory.
[9]
D. Divsalar,et al.
Multiple turbo codes for deep-space communications
,
1995
.
[10]
Rolf Johannesson,et al.
Soft-output-decoding: Some aspects from information theory
,
2002
.
[11]
Johannes B. Huber,et al.
Extrinsic and intrinsic information in systematic coding
,
2002,
Proceedings IEEE International Symposium on Information Theory,.
[12]
A. Glavieux,et al.
Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1
,
1993,
Proceedings of ICC '93 - IEEE International Conference on Communications.
[13]
Stephan ten Brink,et al.
Design of Serially Concatenated Codes based on Iterative Decoding Convergence
,
2000
.
[14]
Stephan ten Brink,et al.
Convergence behavior of iteratively decoded parallel concatenated codes
,
2001,
IEEE Trans. Commun..
[15]
John Cocke,et al.
Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)
,
1974,
IEEE Trans. Inf. Theory.