Performance of Parallel Concatenated Coding Schemes

In this paper, ensembles of parallel concatenated codes are studied and rigorous results on their asymptotic performance, under the assumption of maximum-likelihood (ML) decoding, are presented. In particular, it is proven that in any parallel concatenation scheme with k branches where all k encoders are recursive and the Bhattacharyya parameter of the channel is sufficiently small, the bit-error rate (BER) and the word-error rate go to 0 exactly like N 1- k and N 2- k, respectively. Different types of ensembles by changing the subgroup of permutations used to interconnect the various encoders, are considered.

[1]  D. Divsalar A Simple Tight Bound on Error Probability of Block Codes with Application to Turbo Codes , 1999 .

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

[3]  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).

[4]  Robert J. McEliece,et al.  Coding theorems for turbo code ensembles , 2002, IEEE Trans. Inf. Theory.

[5]  Desmond P. Taylor,et al.  Near Optimum Error Correcting Coding and Decoding: TurboCodes , 2007 .

[6]  R. Urbanke,et al.  On the ensemble performance of turbo codes , 1997, Proceedings of IEEE International Symposium on Information Theory.

[7]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[8]  Roberto Garello,et al.  Some results on combined parallel concatenated schemes with trellis-coded modulation , 2002, Proceedings IEEE International Symposium on Information Theory,.

[9]  Hesham El Gamal,et al.  Analyzing the turbo decoder using the Gaussian approximation , 2001, IEEE Trans. Inf. Theory.

[10]  Claude Berrou,et al.  Turbo codes with rate-m/(m+1) constituent convolutional codes , 2005, IEEE Transactions on Communications.

[11]  Shlomo Shamai,et al.  Improved upper bounds on the ML decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum , 2000, IEEE Trans. Inf. Theory.

[12]  Shlomo Shamai,et al.  Variations on the Gallager bounds, connections, and applications , 2002, IEEE Trans. Inf. Theory.

[13]  Thomas J. Richardson,et al.  The geometry of turbo-decoding dynamics , 2000, IEEE Trans. Inf. Theory.

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

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

[16]  Dariush Divsalar,et al.  Iterative turbo decoder analysis based on density evolution , 2001, IEEE J. Sel. Areas Commun..

[17]  Emre Telatar,et al.  On the Asymptotic Input-Output Weight Distributions and Thresholds of Convolutional and Turbo-Like Codes , 2006 .

[18]  Masoud Salehi,et al.  New performance bounds for turbo codes , 1998, IEEE Trans. Commun..

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

[20]  Alain Glavieux,et al.  Reflections on the Prize Paper : "Near optimum error-correcting coding and decoding: turbo codes" , 1998 .

[21]  Sergio Benedetto,et al.  Design of parallel concatenated convolutional codes , 1996, IEEE Trans. Commun..

[22]  Mohammad Mahdian,et al.  The Minimum Distance of Turbo-Like Codes , 2009, IEEE Transactions on Information Theory.