Code-Aided Turbo Synchronization

The introduction of turbo and low-density parity-check (LDPC) codes with iterative decoding that almost attain Shannon capacity challenges the synchronization subsystems of a data modem. Fast and accurate signal synchronization has to be performed at a much lower value of signal-to-noise ratio (SNR) than in previous less efficiently coded systems. The solution to this issue is developing specific synchronization techniques that take advantage of the presence of the channel code and of the iterative nature of decoding: the so-called turbo-synchronization algorithms. The aim of this paper within this special issue devoted to the turbo principle is twofold: on the one hand, it shows how the many turbo-synchronization algorithms that have already appeared in the literature can be cast into a simple and rigorous theoretical framework. On the other hand, it shows the application of such techniques in a few simple cases, and evaluates improvement that can be obtained from them, especially in the low-SNR regime.

[1]  L. Vandendorpe,et al.  Turbo synchronization: a combined sum-product and expectation-maximization algorithm approach , 2005, IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, 2005..

[2]  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.

[3]  Luc Vandendorpe,et al.  EM algorithm-based timing synchronization in turbo receivers , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[4]  X. Jin Factor graphs and the Sum-Product Algorithm , 2002 .

[5]  Umberto Mengali,et al.  The modified Cramer-Rao bound and its application to synchronization problems , 1994, IEEE Trans. Commun..

[6]  Umberto Mengali,et al.  Synchronization Techniques for Digital Receivers , 1997, Applications of Communications Theory.

[7]  Haige Xiang,et al.  Iterative carrier phase recovery methods in turbo receivers , 2005, IEEE Commun. Lett..

[8]  Achilleas Anastasopoulos,et al.  Polynomial-complexity noncoherent symbol-by-symbol detection with application to adaptive iterative decoding of turbo-like codes , 2003, IEEE Trans. Commun..

[9]  David J. C. MacKay,et al.  Good Error-Correcting Codes Based on Very Sparse Matrices , 1997, IEEE Trans. Inf. Theory.

[10]  S. Kay Fundamentals of statistical signal processing: estimation theory , 1993 .

[11]  Robert J. McEliece,et al.  The generalized distributive law , 2000, IEEE Trans. Inf. Theory.

[12]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[13]  Xiaofu Wu,et al.  Iterative carrier phase recovery methods in turbo receivers , 2005, IEEE Communications Letters.

[14]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[15]  Alex J. Grant,et al.  Differential space-time turbo codes , 2003, IEEE Trans. Inf. Theory.

[16]  H. Vincent Poor,et al.  Iterative (turbo) soft interference cancellation and decoding for coded CDMA , 1999, IEEE Trans. Commun..

[17]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[18]  Costas N. Georghiades,et al.  Frame synchronization for coded systems over AWGN channels , 2004, IEEE Transactions on Communications.

[19]  Henk Wymeersch,et al.  Iterative Code-Aided ML Phase Estimation and Phase Ambiguity Resolution , 2005, EURASIP J. Adv. Signal Process..

[20]  Heinrich Meyr,et al.  Digital communication receivers - synchronization, channel estimation, and signal processing , 1997, Wiley series in telecommunications and signal processing.

[21]  Luc Vandendorpe,et al.  A Theoretical Framework for Soft-Information-Based Synchronization in Iterative (Turbo) Receivers , 2005, EURASIP J. Wirel. Commun. Netw..

[22]  Giulio Colavolpe,et al.  Noncoherent iterative (turbo) decoding , 2000, IEEE Trans. Commun..

[23]  Marc Moeneclaey,et al.  On the true and the modified Cramer-Rao bounds for the estimation of a scalar parameter in the presence of nuisance parameters , 1998, IEEE Trans. Commun..

[24]  Luc Vandendorpe,et al.  Frame-Error-Rate-wise Optimal Code-Aided Hypothesis Testing , 2006, 2006 IEEE International Conference on Communications.

[25]  Heinrich Meyr,et al.  Digital communication receivers , 1997 .

[26]  Heidi Steendam,et al.  The true Cramer-Rao bound for carrier frequency estimation from a PSK signal , 2004, IEEE Transactions on Communications.

[27]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[28]  Giuseppe Caire,et al.  Algorithms for iterative decoding in the presence of strong phase noise , 2005, IEEE Journal on Selected Areas in Communications.

[29]  Achilleas Anastasopoulos,et al.  Adaptive iterative detection for phase tracking in turbo-coded systems , 2001, IEEE Trans. Commun..

[30]  Cédric Herzet Code-aided synchronization for digital burst communications , 2006 .

[31]  Heinrich Meyr,et al.  Digital filter and square timing recovery , 1988, IEEE Trans. Commun..

[32]  Michael Tüchler,et al.  Performance of soft iterative channel estimation in turbo equalization , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[33]  Marco Luise,et al.  Embedding carrier phase recovery into iterative decoding of turbo-coded linear modulations , 2004, IEEE Transactions on Communications.

[34]  Andrew J. Viterbi,et al.  Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission , 1983, IEEE Trans. Inf. Theory.

[35]  Luc Vandendorpe,et al.  EM algorithm-based multiuser synchronization in turbo receivers , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[36]  S. ten Brink,et al.  Iterative demapping and decoding for multilevel modulation , 1998, IEEE GLOBECOM 1998 (Cat. NO. 98CH36250).

[37]  Tom Heskes,et al.  Approximate Expectation Maximization , 2003, NIPS.

[38]  Umberto Mengali,et al.  The modified Cramer-Rao bound in vector parameter estimation , 1998, IEEE Trans. Commun..

[39]  J. Mendel Lessons in Estimation Theory for Signal Processing, Communications, and Control , 1995 .

[40]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[41]  Bartosz Mielczarek,et al.  Phase offset estimation using enhanced turbo decoders , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[42]  John Cocke,et al.  Optimal decoding of linear codes for minimizing symbol error rate (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[43]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[44]  Wayne E. Stark,et al.  Unified design of iterative receivers using factor graphs , 2001, IEEE Trans. Inf. Theory.

[45]  Heidi Steendam,et al.  The Cramer-Rao bound for phase estimation from coded linearly modulated signals , 2003, IEEE Communications Letters.

[46]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[47]  Luc Vandendorpe,et al.  Turbo synchronization: an EM algorithm interpretation , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[48]  Christian Schlegel,et al.  Differential turbo-coded modulation with APP channel estimation , 2006, IEEE Transactions on Communications.

[49]  Heidi Steendam,et al.  Carrier and Clock Recovery in (Turbo-) Coded Systems: Cramér-Rao Bound and Synchronizer Performance , 2005, EURASIP J. Adv. Signal Process..

[50]  Brendan J. Frey,et al.  Factor graphs and the sum-product algorithm , 2001, IEEE Trans. Inf. Theory.

[51]  Luc Vandendorpe,et al.  A Theoretical Framework for Iterative Synchronization Based on the Sum–Product and the Expectation-Maximization Algorithms , 2007, IEEE Transactions on Signal Processing.

[52]  Marie-Laure Boucheret,et al.  A carrier phase estimator for multimedia satellite payloads suited to RSC coding schemes , 2000, 2000 IEEE International Conference on Communications. ICC 2000. Global Convergence Through Communications. Conference Record.

[53]  Justin Dauwels,et al.  Phase estimation by message passing , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[54]  Maryline Helard,et al.  Synchronization in the carrier recovery of a Satellite link using Turbo-Code with the help of Tentative Decisions , 1999 .

[55]  Henk Wymeersch,et al.  True Cramer-Rao bound for timing recovery from a bandlimited linearly Modulated waveform with unknown carrier phase and frequency , 2004, IEEE Transactions on Communications.