A new upper bound on the minimum distance of turbo codes

In this paper, a new upper bound on the minimum distance of turbo codes is derived. The new bound is obtained by construction of an undirected graph which reflects the characteristics of the constituent codes and the interleaver. The resulting expression shows that the minimum distance of a turbo code grows approximately with the base-3 logarithm of the information word length. The new bound is easy to compute, applies to rate k/sub 0//n/sub 0/ constituent encoders, and often improves over existing results.

[1]  Sergio Benedetto,et al.  Unveiling turbo codes: some results on parallel concatenated coding schemes , 1996, IEEE Trans. Inf. Theory.

[2]  Journal of the Association for Computing Machinery , 1961, Nature.

[3]  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.

[4]  Richard D. Wesel,et al.  Turbo-encoder design for symbol-interleaved parallel concatenated trellis-coded modulation , 2001, IEEE Trans. Commun..

[5]  Roberto Garello,et al.  Computing the free distance of turbo codes and serially concatenated codes with interleavers: algorithms and applications , 2001, IEEE J. Sel. Areas Commun..

[6]  Pascal O. Vontobel,et al.  On the construction of turbo code interleavers based on graphs with large girth , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[7]  S. Dolinar,et al.  Weight distributions for turbo codes using random and nonrandom permutations , 1995 .

[8]  Marco Breiling,et al.  A logarithmic upper bound on the minimum distance of turbo codes , 2004, IEEE Transactions on Information Theory.

[9]  Johannes B. Huber,et al.  Combinatorial analysis of the minimum distance of turbo codes , 2001, IEEE Trans. Inf. Theory.

[10]  G. Solomon,et al.  A Connection Between Block and Convolutional Codes , 1979 .

[11]  Norman Biggs,et al.  Constructions for Cubic Graphs with Large Girth , 1998, Electron. J. Comb..

[12]  R. Urbanke,et al.  On the minimum distance of parallel and serially concatenated codes , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[13]  Johannes B. Huber,et al.  Upper bound on the minimum distance of turbo codes , 2001, IEEE Trans. Commun..

[14]  R. Möhring.  Algorithmic graph theory and perfect graphs , 1986 .

[15]  Amir Pnueli,et al.  Permutation Graphs and Transitive Graphs , 1972, JACM.

[16]  Dariush Divsalar,et al.  Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding , 1997, IEEE Trans. Inf. Theory.

[17]  Claude Berrou,et al.  The advantages of non-binary turbo codes , 2001, Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494).

[18]  Michael Lentmaier,et al.  Some Results Concerning the Design and Decoding of Turbo-Codes , 2001, Probl. Inf. Transm..