New binary sequences with good correlation based on high-order difference and interleaving techniques

An important and well-studied problem with many applications in communication systems is to find sequences with good correlation property that means auto- and cross-correlations of the sequences are all very small comparing with their periods. This paper focuses on sequences of period 2r - 1(r>> 1) with infinite third depth and shows that the difference operator really works with the interleaving technique on producing sequences with good correlation property and long period N = 22r-2r+1+1, which are constructed from 2-level autocorrelation sequences of period 2r - 1 except m-sequences. The method is lightweight since the computational complexity is O(p√N) and only the XOR logical operator is used.

[1]  Ram Zamir.  The modulo loss in lattice dirty-paper coding , 2014, 2014 IEEE International Symposium on Information Theory.

[2]  Fernando Pérez-Cruz,et al.  New information-estimation results for poisson, binomial and negative binomial models , 2014, 2014 IEEE International Symposium on Information Theory.

[3]  Emina Soljanin,et al.  Successive Segmentation-Based Coding for Broadcasting Over Erasure Channels , 2016, IEEE Transactions on Information Theory.

[4]  Victor K.-W. Wei,et al.  On the depth distribution of linear codes , 2000, IEEE Trans. Inf. Theory.

[5]  R. Brualdi.  Introductory Combinatorics , 1992 .

[6]  Tuvi Etzion.  The depth distribution-a new characterization for linear codes , 1997, IEEE Trans. Inf. Theory.

[7]  Wai Ho Mow,et al.  A quadratic programming relaxation approach to compute-and-forward network coding design , 2014, 2014 IEEE International Symposium on Information Theory.

[8]  Vinod M. Prabhakaran,et al.  Writing on a dirty paper in the presence of jamming , 2014, 2014 IEEE International Symposium on Information Theory.

[9]  Jean-Claude Belfiore,et al.  Shifted inverse determinant sums and new bounds for the DMT of space-time lattice codes , 2014, 2014 IEEE International Symposium on Information Theory.

[10]  Yu-Chih Huang,et al.  Multistage compute-and-forward with multilevel lattice codes based on product constructions , 2014, 2014 IEEE International Symposium on Information Theory.

[11]  Guang Gong,et al.  Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar , 2005 .

[12]  Vincent Yan Fu Tan,et al.  The third-order term in the normal approximation for the AWGN channel , 2014, 2014 IEEE International Symposium on Information Theory.

[13]  Guang Gong,et al.  Theory and applications of q-ary interleaved sequences , 1995, IEEE Trans. Inf. Theory.

[14]  Tor Helleseth,et al.  A Three-Valued Walsh Transform From Decimations of Helleseth–Gong Sequences , 2012, IEEE Transactions on Information Theory.

[15]  Ron M. Roth,et al.  When data must satisfy constraints upon writing , 2014, 2014 IEEE International Symposium on Information Theory.

[16]  Chris J. Mitchell.  On Integer-Valued Rational Polynomials and Depth Distributions of Binary Codes , 1998, IEEE Trans. Inf. Theory.

[17]  T. Helleseth,et al.  A New Family of Ternary Sequences with Ideal Two-level Autocorrelation Function , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[18]  Nicolas Macris,et al.  Analysis of coupled scalar systems by displacement convexity , 2014, 2014 IEEE International Symposium on Information Theory.

[19]  Panos M. Pardalos,et al.  On maximum clique problems in very large graphs , 1999, External Memory Algorithms.

[20]  Shlomo Shamai,et al.  On the degrees-of-freedom of the 3-user MISO broadcast channel with hybrid CSIT , 2014, 2014 IEEE International Symposium on Information Theory.

[21]  Sarit Buzaglo,et al.  Perfect Permutation Codes with the Kendall's $\tau$-Metric , 2013 .

[22]  Shlomo Shamai,et al.  The Impact of Phase Fading on the Dirty Paper Channel , 2014, ArXiv.

[23]  Jian Song,et al.  Extensions of the I-MMSE relation , 2014, 2014 IEEE International Symposium on Information Theory.

[24]  Anxiao Jiang,et al.  Error correction and partial information rewriting for flash memories , 2014, 2014 IEEE International Symposium on Information Theory.

[25]  Evyatar Hemo,et al.  Codes for high performance write and read processes in multi-level NVMs , 2014, 2014 IEEE International Symposium on Information Theory.

[26]  Michael G. Rabbat,et al.  Subspace synchronization: A network-coding approach to object reconciliation , 2014, 2014 IEEE International Symposium on Information Theory.

[27]  Chenwei Wang,et al.  Beyond one-way communication: Degrees of freedom of the 4-user relay MIMO Y channel , 2014, 2014 IEEE International Symposium on Information Theory.

[28]  Rami Cohen,et al.  LDPC codes for partial-erasure channels in multi-level memories , 2014, 2014 IEEE International Symposium on Information Theory.

[29]  Jong-Seon No,et al.  New family of p-ary sequences with optimal correlation property and large linear span , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[30]  Guang Gong,et al.  New designs for signal sets with low cross correlation, balance property, and largelinear span: GF(p) case , 2002, IEEE Trans. Inf. Theory.

[31]  Jun Chen,et al.  A Source-Channel Separation Theorem With Application to the Source Broadcast Problem , 2016, IEEE Trans. Inf. Theory.

[32]  Tor Helleseth,et al.  A New Family of Ternary Sequences with Ideal Two-level Autocorrelation Function , 2001, Des. Codes Cryptogr..

[33]  Hong-Yeop Song,et al.  New construction for families of binary sequences with optimal correlation properties , 1997, IEEE Trans. Inf. Theory.

[34]  Pablo M. Olmos,et al.  Improved performance of LDPC-coded MIMO systems with EP-based soft-decisions , 2014, 2014 IEEE International Symposium on Information Theory.

[35]  Arya Mazumdar.  On a duality between recoverable distributed storage and index coding , 2014, 2014 IEEE International Symposium on Information Theory.

[36]  Joachim M. Buhmann,et al.  How informative are Minimum Spanning Tree algorithms? , 2014, 2014 IEEE International Symposium on Information Theory.

[37]  Reuven Bar-Yehuda,et al.  Rotating-Table Games and Derivatives of Words , 1993, Theor. Comput. Sci..

[38]  Keigo Takeuchi.  A generalization of threshold saturation: application to spatially coupled BICM-ID , 2014, 2014 IEEE International Symposium on Information Theory.

[39]  Guang Gong,et al.  Rotating-table game and construction of periodic sequences with lightweight calculation , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[40]  Aaron B. Wagner,et al.  Feedback can improve the second-order coding performance in discrete memoryless channels , 2014, 2014 IEEE International Symposium on Information Theory.

[41]  Richard A. Games,et al.  Crosscorrelation of M-sequences and GMW-sequences with the same primitive polynomial , 1985, Discret. Appl. Math..

[42]  John B. Anderson,et al.  Analysis of best high rate convolutional codes for faster than Nyquist turbo equalization , 2014, 2014 IEEE International Symposium on Information Theory.

[43]  Eckehard Olbrich,et al.  Reconsidering unique information: Towards a multivariate information decomposition , 2014, 2014 IEEE International Symposium on Information Theory.

[44]  Yu-Chih Huang,et al.  Multilevel lattices based on spatially-coupled LDPC codes with applications , 2014, 2014 IEEE International Symposium on Information Theory.

[45]  Qing Li,et al.  Noise modeling and capacity analysis for NAND flash memories , 2014, 2014 IEEE International Symposium on Information Theory.

[46]  Maxim Raginsky,et al.  A new information-theoretic lower bound for distributed function computation , 2014, 2014 IEEE International Symposium on Information Theory.

[47]  Arkadii G. D'yachkov,et al.  Bounds on the rate of superimposed codes , 2014, 2014 IEEE International Symposium on Information Theory.

[48]  A. Robert Calderbank,et al.  Large families of quaternary sequences with low correlation , 1996, IEEE Trans. Inf. Theory.