Blind frame synchronization of reed-solomon codes: Non-binary VS. binary approach

We consider in this paper the problem of blind frame synchronization of systems using Reed-Solomon (RS) codes and other related families. We present first of all three techniques of blind frame synchronization based on the non-binary parity check matrix of RS codes. While the first two techniques involve the calculation of hard and soft values of the syndrome elements respectively, the third one perform an adaptation step of the parity check matrix before applying the soft criterion. Although RS codes are constructed from non-binary symbols, we show in this paper that it is also possible to synchronize them using the binary image expansion of their parity check matrix. Simulation results show that the synchronization algorithm based on the adaptation of the binary parity check matrix of RS codes has the best synchronization performance among all other techniques. Furthermore, the Frame Error Rate (FER) curves obtained after synchronization and decoding are very close to the perfect synchronization curves.

[1]  P. Robertson.  A generalized frame synchronizer , 1992, [Conference Record] GLOBECOM '92 - Communications for Global Users: IEEE.

[2]  Mostofa K. Howlader,et al.  Decoder-assisted frame synchronization for packet transmission , 2001, IEEE J. Sel. Areas Commun..

[3]  Rodrigue Imad,et al.  Blind frame synchronization for error correcting codes having a sparse parity check matrix , 2009, IEEE Transactions on Communications.

[4]  Sébastien Houcke,et al.  Blind frame synchronisation for block code , 2006, 2006 14th European Signal Processing Conference.

[5]  David Declercq,et al.  Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$ , 2007, IEEE Transactions on Communications.

[6]  J. Massey,et al.  Optimum Frame Synchronization , 1972, IEEE Trans. Commun..

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

[8]  Harry H. Tan,et al.  Frame Synchronization for Gaussian Channels , 1987, IEEE Trans. Commun..

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

[10]  M.C. Valenti,et al.  Optimum frame synchronization for preamble-less packet transmission of turbo codes , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[11]  Christophe Jégo,et al.  Turbo Decoding of Product Codes based on the Modified Adaptive Belief Propagation Algorithm , 2007, 2007 IEEE International Symposium on Information Theory.

[12]  Christophe Jégo,et al.  Blind Frame Synchronization of Product Codes Based on the Adaptation of the Parity Check Matrix , 2009, 2009 IEEE International Conference on Communications.

[13]  Krishna R. Narayanan,et al.  Iterative soft decoding of Reed-Solomon codes , 2004, IEEE Communications Letters.

[14]  Krishna R. Narayanan,et al.  Iterative Soft-Input Soft-Output Decoding of Reed–Solomon Codes by Adapting the Parity-Check Matrix , 2005, IEEE Transactions on Information Theory.