Skip-Sliding Window Codes

Constrained coding is used widely in digital communication and storage systems. In this paper, we study a generalized sliding window constraint called the skip-sliding window constraint. A skip-sliding window (SSW) code is defined in terms of the length <tex>$L$</tex> of a sliding window, skip length <tex>$J$</tex>, and cost constraint <tex>$E$</tex> in each sliding window. Each valid codeword of length <tex>$L+kJ$</tex> is determined by <tex>$k+1$</tex> windows of length <tex>$L$</tex> where window <tex>$i$</tex> starts at <tex>$(iJ+1)$</tex>th symbol for all non-negative integers <tex>$i$</tex> such that <tex>$i\leq k$</tex>; and the cost constraint <tex>$E$</tex> in each window must be satisfied. In this work, two methods are given to enumerate the size of SSW codes. Using the proposed enumeration methods, the noiseless capacity of binary SSW codes is determined and observations such as greater capacity than other classes of codes are made. Moreover, some noisy capacity bounds are given. SSW coding constraints arise in various applications including simultaneous energy and information transfer.

[1]  Schouhamer Immink,et al.  Codes for mass data storage systems , 2004 .

[2]  Mehul Motani,et al.  Binary subblock energy-constrained codes: Bounds on code size and asymptotic rate , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[3]  Kaibin Huang,et al.  Energy Harvesting Wireless Communications: A Review of Recent Advances , 2015, IEEE Journal on Selected Areas in Communications.

[4]  Krzysztof R. Apt,et al.  Principles of constraint programming , 2003 .

[5]  Aaron D. Wyner,et al.  A theorem on the entropy of certain binary sequences and applications-II , 1973, IEEE Trans. Inf. Theory.

[6]  Richard E. Blahut,et al.  Computation of channel capacity and rate-distortion functions , 1972, IEEE Trans. Inf. Theory.

[7]  Michel Rigo,et al.  Formal Languages, Automata and Numeration Systems 2: Applications to Recognizability and Decidability , 2014 .

[8]  Mehul Motani,et al.  Subblock-Constrained Codes for Real-Time Simultaneous Energy and Information Transfer , 2015, IEEE Transactions on Information Theory.

[9]  Pavel A Pevzner,et al.  How to apply de Bruijn graphs to genome assembly. , 2011, Nature biotechnology.

[10]  Gilles Pesant,et al.  Revisiting the Sequence Constraint , 2006, CP.

[11]  P. V. Salimov On Rauzy graph sequences of infinite words , 2010 .

[12]  V. Kozyakin On accuracy of approximation of the spectral radius by the Gelfand formula , 2008, 0810.2856.

[13]  de Ng Dick Bruijn A combinatorial problem , 1946 .

[14]  Lav R. Varshney,et al.  Transporting information and energy simultaneously , 2008, 2008 IEEE International Symposium on Information Theory.

[15]  Shlomo Shamai,et al.  Extension of an entropy property for binary input memoryless symmetric channels , 1989, IEEE Trans. Inf. Theory.

[16]  Jack K. Wolf,et al.  On runlength codes , 1988, IEEE Trans. Inf. Theory.

[17]  Aaron D. Wyner,et al.  A theorem on the entropy of certain binary sequences and applications-I , 1973, IEEE Trans. Inf. Theory.

[18]  Richard P. Stanley,et al.  Algebraic Combinatorics: Walks, Trees, Tableaux, and More , 2013 .

[19]  I. Goulden,et al.  AN INVERSION THEOREM FOR CLUSTER DECOMPOSITIONS OF SEQUENCES WITH DISTINGUISHED SUBSEQUENCES , 1979 .

[20]  Angela I. Barbero,et al.  Coding for Inductively Coupled Channels , 2012, IEEE Transactions on Information Theory.

[21]  Mehul Motani,et al.  On code design for simultaneous energy and information transfer , 2014, 2014 Information Theory and Applications Workshop (ITA).

[22]  Elza Erkip,et al.  Constrained Codes for Joint Energy and Information Transfer , 2014, IEEE Transactions on Communications.

[23]  Gérard D. Cohen,et al.  On Bounded Weight Codes , 2010, IEEE Transactions on Information Theory.

[24]  Kees A. Schouhamer Immink,et al.  Runlength-limited sequences , 1990, Proc. IEEE.

[25]  Gérard D. Cohen,et al.  Heavy weight codes , 2010, 2010 IEEE International Symposium on Information Theory.

[26]  Suguru Arimoto,et al.  An algorithm for computing the capacity of arbitrary discrete memoryless channels , 1972, IEEE Trans. Inf. Theory.