Tightened Upper Bounds on the ML Decoding Error Probability of Binary Linear Block Codes

The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid for any memoryless, binary-input and output-symmetric communication channel. The effectiveness of these bounds is exemplified for ensembles of turbo-like codes

[1]  Neil J. A. Sloane,et al.  Techniques of Bounding the Probability of Decoding Error for Block Coded Modulation Structures , 1994 .

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

[3]  Igal Sason,et al.  Bornes de la probabilité d’erreur pour des codes en blocs et des turbo codes en blocs avec décodage à maximum de vraisemblance , 1999 .

[4]  Radford M. Neal,et al.  Near Shannon limit performance of low density parity check codes , 1996 .

[5]  David Burshtein,et al.  On the application of LDPC codes to arbitrary discrete-memoryless channels , 2003, IEEE Transactions on Information Theory.

[6]  Frank Kienle,et al.  A synthesizable IP core for DVB-S2 LDPC code decoding , 2005, Design, Automation and Test in Europe.

[7]  Marc P. C. Fossorier.  Critical point for maximum likelihood decoding of linear block codes , 2005, IEEE Communications Letters.

[8]  Robert G. Gallager,et al.  A simple derivation of the coding theorem and some applications , 1965, IEEE Trans. Inf. Theory.

[9]  Johannes Zangl,et al.  Improved tangential sphere bound on the bit-error probability of concatenated codes , 2001, IEEE J. Sel. Areas Commun..

[10]  David J. Hunter.  An upper bound for the probability of a union , 1976, Journal of Applied Probability.

[11]  Lorenzo Piazzo,et al.  Analysis of phase noise effects in OFDM modems , 2002, IEEE Trans. Commun..

[12]  Alexander Barg,et al.  Minimal Vectors in Linear Codes , 1998, IEEE Trans. Inf. Theory.

[13]  Erik Agrell,et al.  Voronoi regions for binary linear block codes , 1996, IEEE Trans. Inf. Theory.

[14]  Shlomo Shamai,et al.  Bounds on the error probability ofml decoding for block and turbo-block codes , 1999, Ann. des Télécommunications.

[15]  Emina Soljanin,et al.  On the performance of recursive decoding schemes , 1997, Proceedings of IEEE International Symposium on Information Theory.

[16]  Gregory Poltyrev,et al.  The error probability of M-ary PSK block coded modulation schemes , 1996, IEEE Trans. Commun..

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

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

[19]  Toru Fujiwara,et al.  Determination of the Local Weight Distribution of Binary Linear Block Codes , 2006, IEEE Transactions on Information Theory.

[20]  Silvano Pupolin,et al.  Phase noise effects in QAM systems , 1997, Proceedings of 8th International Symposium on Personal, Indoor and Mobile Radio Communications - PIMRC '97.

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

[22]  Shlomo Shamai,et al.  Tightened Upper Bounds on the ML Decoding Error Probability of Binary Linear Block Codes , 2006, ISIT.

[23]  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.

[24]  Joseph Jean Boutros,et al.  Serial concatenation of interleaved convolutional codes and M -ary continuous phase modulations - Concaténation série de codes convolutifs et de modulations à phase continue m -aires séparés par un entrelaceur , 1999, Ann. des Télécommunications.

[25]  S. Yousefi,et al.  Gallager first bounding technique for the performance evaluation of maximum-likelihood decoded linear binary block codes , 2006 .

[26]  Alexander Barg,et al.  Random codes: Minimum distances and error exponents , 2002, IEEE Trans. Inf. Theory.

[27]  李幼升,et al.  Ph , 1989 .

[28]  Axthonv G. Oettinger,et al.  IEEE Transactions on Information Theory , 1998 .

[29]  David Burshtein,et al.  Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes , 2000, IEEE Trans. Inf. Theory.

[30]  A. Demir,et al.  Phase noise in oscillators: a unifying theory and numerical methods for characterization , 2000 .

[31]  Rüdiger L. Urbanke,et al.  Parity-check density versus performance of binary linear block codes over memoryless symmetric channels , 2003, IEEE Transactions on Information Theory.

[32]  Dariush Divsalar,et al.  Coding theorems for 'turbo-like' codes , 1998 .

[33]  H. Herzberg,et al.  Techniques of bounding the probability of decoding error for block coded modulation structures , 1994, IEEE Trans. Inf. Theory.

[34]  Amir K. Khandani,et al.  A new upper bound on the ML decoding error probability of linear binary block codes in AWGN interference , 2004, IEEE Transactions on Information Theory.

[35]  Janos Galambos,et al.  An extension of the method of polynomials and a new reduction formula for Bonferroni-type inequalities , 1996 .

[36]  E.R. Berlekamp,et al.  The technology of error-correcting codes , 1980, Proceedings of the IEEE.

[37]  Achilleas Anastasopoulos,et al.  Capacity-Achieving Codes with Bounded Graphical Complexity on Noisy Channels , 2005, ArXiv.

[38]  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.

[39]  Daniel A. Spielman,et al.  Expander codes , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[40]  Shlomo Shamai,et al.  Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial , 2006, Found. Trends Commun. Inf. Theory.

[41]  Masoud Salehi,et al.  Turbo codes and turbo coded modulation systems: analysis and performance bounds , 1998 .

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

[43]  Amir K. Khandani,et al.  Generalized tangential sphere bound on the ML decoding error probability of linear binary block codes in AWGN interference , 2004, IEEE Transactions on Information Theory.

[44]  C.-E. Sundberg,et al.  Continuous phase modulation , 1986, IEEE Communications Magazine.

[45]  J. Galambos,et al.  Bonferroni-type inequalities with applications , 1996 .

[46]  Igal Sason,et al.  Accumulate–Repeat–Accumulate Codes: Capacity-Achieving Ensembles of Systematic Codes for the Erasure Channel With Bounded Complexity , 2007, IEEE Transactions on Information Theory.

[47]  Igal Sason,et al.  On the Error Exponents of Some Improved Tangential-Sphere Bounds , 2006, ArXiv.

[48]  Meir Feder,et al.  Random coding techniques for nonrandom codes , 1999, IEEE Trans. Inf. Theory.

[49]  Igal Sason,et al.  On the Error Exponents of Improved Tangential Sphere Bounds , 2007, IEEE Transactions on Information Theory.

[50]  Shlomo Shamai,et al.  On improved bounds on the decoding error probability of block codes over interleaved fading channels, with applications to turbo-like codes , 2001, IEEE Trans. Inf. Theory.

[51]  Erik Agrell,et al.  On the Voronoi Neighbor Ratio for Binary Linear Block Codes , 1998, IEEE Trans. Inf. Theory.

[52]  Dariush Divsalar,et al.  Upper bounds to error probabilities of coded systems beyond the cutoff rate , 2003, IEEE Trans. Commun..

[53]  Gregory Poltyrev,et al.  Bounds on the decoding error probability of binary linear codes via their spectra , 1994, IEEE Trans. Inf. Theory.