Selection of Parity Check Equations For the Iterative Message-Passing Detection of M-Sequences

We consider the joint detection and decoding of m-sequences. The receiver has to decide whether an m-sequence is received and possibly to decode its initial state. To do so, it implements an iterative message-passing decoding algorithm that operates on a parity check matrix, built upon a number of reference parity-check equations satisfied by the m-sequence. This matrix concatenates several elementary parity check matrices which are derived from reference equations. Unlike the conventional decoding case, the detection problem imposes to consider false alarms that may occur when the decoder is only fed with noise. While absorbing sets are known to be responsible for the error floor phenomenon of iterative message-passing decoders, we show that they may have a beneficial effect on the detection performance, in that they may prevent the decoder to produce false alarms. We further compute the number of hybrid cycles of length six and eight in the Tanner graph of the decoder and use the minimization of this number as criterion to derive an algorithm for selecting the reference parity check equations. This algorithm was found to be efficient for minimizing the probability of false alarm and decreases also the probability of wrong detection in the very small SNR region. This has been achieved at the cost of a reduction of the probability of correct detection.

[1]  Ayineedi Venkateswarlu,et al.  Results on multiples of primitive polynomials and their products over GF(2) , 2005, Theor. Comput. Sci..

[2]  Andreas Polydoros,et al.  A Unified Approach to Serial Search Spread-Spectrum Code Acquisition - Part I: General Theory , 1984, IEEE Transactions on Communications.

[3]  Mark A. Richards,et al.  Fundamentals of Radar Signal Processing , 2005 .

[4]  Keith M. Chugg,et al.  An Iterative Algorithm and Low Complexity Hardware Architecture for Fast Acquisition of Long PN Codes in UWB Systems , 2006, J. VLSI Signal Process..

[5]  Keith M. Chugg,et al.  An algorithm for counting short cycles in bipartite graphs , 2006, IEEE Transactions on Information Theory.

[6]  Neri Merhav,et al.  Codeword or Noise? Exact Random Coding Exponents for Joint Detection and Decoding , 2014, IEEE Transactions on Information Theory.

[7]  Antoine Joux,et al.  Fast Correlation Attacks: An Algorithmic Point of View , 2002, EUROCRYPT.

[8]  Qiuju Diao,et al.  Trapping sets of structured LDPC codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[9]  Solomon W. Golomb,et al.  Shift Register Sequences , 1981 .

[10]  Emina Soljanin,et al.  Asymptotic Spectra of Trapping Sets in Regular and Irregular LDPC Code Ensembles , 2007, IEEE Transactions on Information Theory.

[11]  David A. Wagner,et al.  A Generalized Birthday Problem , 2002, CRYPTO.

[12]  Lara Dolecek,et al.  Analysis of Absorbing Sets and Fully Absorbing Sets of Array-Based LDPC Codes , 2009, IEEE Transactions on Information Theory.

[13]  Valentin Savin,et al.  Improving the decoding of m-sequences by exploiting their decimation property , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[14]  Roger L. Peterson,et al.  Introduction to Spread Spectrum Communications , 1995 .

[15]  Niclas Wiberg,et al.  Codes and Decoding on General Graphs , 1996 .

[16]  Valentin Savin,et al.  Blind identification of the uplink scrambling code index of a WCDMA transmission and application to femtocell networks , 2013, 2013 IEEE International Conference on Communications (ICC).

[17]  Elliott D. Kaplan.  Understanding GPS : principles and applications , 1996 .

[18]  C. Cook,et al.  An introduction to spread spectrum , 1983, IEEE Communications Magazine.

[19]  Lara Dolecek,et al.  GEN03-6: Investigation of Error Floors of Structured Low-Density Parity-Check Codes by Hardware Emulation , 2006, IEEE Globecom 2006.

[20]  Thomas J. Richardson,et al.  Error Floors of LDPC Codes , 2003 .

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

[22]  Lara Dolecek,et al.  Predicting error floors of structured LDPC codes: deterministic bounds and estimates , 2009, IEEE Journal on Selected Areas in Communications.

[23]  Willi Meier,et al.  Fast correlation attacks on certain stream ciphers , 1989, Journal of Cryptology.

[24]  Thomas Johansson,et al.  Improved Fast Correlation Attacks on Stream Ciphers via Convolutional Codes , 1999, EUROCRYPT.

[25]  Valentin Savin,et al.  Iterative decoding of Gold sequences , 2015, 2015 IEEE International Conference on Communications (ICC).

[26]  Keith M. Chugg,et al.  A new approach to rapid PN code acquisition using iterative message passing techniques , 2005, IEEE Journal on Selected Areas in Communications.

[27]  William E. Ryan,et al.  Low-floor decoders for LDPC codes , 2009, IEEE Transactions on Communications.

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

[29]  Valentin Savin,et al.  Blind identification of the scrambling code of a reverse link CDMA2000 transmission , 2013, 2013 IEEE International Conference on Communications (ICC).

[30]  Marco Luise,et al.  Rapid Acquisition of Gold Codes and Related Sequences Using Iterative Message Passing on Redundant Graphical Models , 2006, MILCOM 2006 - 2006 IEEE Military Communications conference.

[31]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[32]  Anne Canteaut,et al.  Improved Fast Correlation Attacks Using Parity-Check Equations of Weight 4 and 5 , 2000, EUROCRYPT.

[33]  Ron Kerr,et al.  Iterative Signal Processing for Blind Code Phase Acquisition of CDMA 1x Signals for Radio Spectrum Monitoring , 2010, J. Electr. Comput. Eng..

[34]  Marco Luise,et al.  Performance Evaluation of Message-Passing-Based Algorithms for Fast Acquisition of Spreading Codes with Application to Satellite Positioning , 2006 .