Randomized Polynomial Time Protocol for Combinatorial Slepian-Wolf Problem

We consider the following combinatorial version of the Slepian–Wolf coding scheme. Two isolated Senders are given binary strings X and Y respectively; the length of each string is equal to n, and the Hamming distance between the strings is at most \(\alpha n\). The Senders compress their strings and communicate the results to the Receiver. Then the Receiver must reconstruct both strings X and Y. The aim is to minimise the lengths of the transmitted messages.

[1]  Aleksandr Chuklin.  Effective protocols for low-distance file synchronization , 2011, ArXiv.

[2]  Pier Luigi Dragotti,et al.  Symmetric and asymmetric Slepian-Wolf codes with systematic and nonsystematic linear codes , 2005, IEEE Communications Letters.

[3]  Nikolai K. Vereshchagin,et al.  Inequalities for Shannon Entropy and Kolmogorov Complexity , 1997, J. Comput. Syst. Sci..

[4]  Aaron D. Wyner,et al.  Recent results in the Shannon theory , 1974, IEEE Trans. Inf. Theory.

[5]  Larry Carter,et al.  Universal Classes of Hash Functions , 1979, J. Comput. Syst. Sci..

[6]  Moni Naor,et al.  Derandomized Constructions of k-Wise (Almost) Independent Permutations , 2005, APPROX-RANDOM.

[7]  Nikolai K. Vereshchagin,et al.  Combinatorial interpretation of Kolmogorov complexity , 2002 .

[8]  Ho-Leung Chan,et al.  A combinatorial approach to information inequalities , 1999, 1999 Information Theory and Networking Workshop (Cat. No.99EX371).

[9]  Alon Orlitsky.  Interactive Communication of Balanced Distributions and of Correlated Files , 1993, SIAM J. Discret. Math..

[10]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[11]  Ronen Shaltiel,et al.  Constant-Round Oblivious Transfer in the Bounded Storage Model , 2004, Journal of Cryptology.

[12]  Venkatesan Guruswami,et al.  Codes for Computationally Simple Channels: Explicit Constructions with Optimal Rate , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[13]  Kannan Ramchandran,et al.  Distributed source coding using syndromes (DISCUS): design and construction , 2003, IEEE Trans. Inf. Theory.

[14]  A. Kolmogorov.  Three approaches to the quantitative definition of information , 1968 .

[15]  Jack K. Wolf,et al.  Noiseless coding of correlated information sources , 1973, IEEE Trans. Inf. Theory.

[16]  Andrej Muchnik,et al.  Conditional complexity and codes , 2002, Theor. Comput. Sci..

[17]  Aravind Srinivasan,et al.  Chernoff-Hoeffding bounds for applications with limited independence , 1995, SODA '93.

[18]  R. Urbanke,et al.  Polar codes for Slepian-Wolf, Wyner-Ziv, and Gelfand-Pinsker , 2010, 2010 IEEE Information Theory Workshop on Information Theory (ITW 2010, Cairo).

[19]  R. Hartley.  Transmission of information , 1928 .

[20]  Saygun Onay.  Polar Codes for Nonasymmetric Slepian-Wolf Coding , 2012, ArXiv.

[21]  Ying Zhao,et al.  Compression of correlated binary sources using turbo codes , 2001, IEEE Communications Letters.

[22]  Zixiang Xiong,et al.  Compression of binary sources with side information at the decoder using LDPC codes , 2002, IEEE Communications Letters.

[23]  Adam D. Smith.  Scrambling adversarial errors using few random bits, optimal information reconciliation, and better private codes , 2007, SODA '07.

[24]  Bernd Girod,et al.  Compression with side information using turbo codes , 2002, Proceedings DCC 2002. Data Compression Conference.

[25]  Zixiang Xiong,et al.  On code design for the Slepian-Wolf problem and lossless multiterminal networks , 2006, IEEE Transactions on Information Theory.

[26]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[27]  Klaus Jansen,et al.  Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques , 2006, Lecture Notes in Computer Science.

[28]  Terence Chan.  A combinatorial approach to information inequalities , 2001, Commun. Inf. Syst..