User Manual CAI version-1.0: An Open-Source Toolbox for Computer-Aided Investigation on the Fundamental Limits of Information Systems.

We provide an open source toolbox on https://github.com/ct2641/CAI/releases/tag/1.0 to conduct computer-aided investigation on the fundamental limits of information systems. The toolbox relies on either Gurobi or Cplex as the linear program solving engine. The program can read a problem description file, and then fulfill the following tasks: 1) compute a bound for a given linear combination of information measures and provide the value of information measures at the optimal solution; 2) efficiently compute a polytope tradeoff outer bound between two information quantities; 3) produce a proof (as a weighted sum of known information inequalities; and 4) provide the range for information quantities between which the optimal value does not change (sensitivity analysis). This technical report provides an overview of this toolbox, a detailed description of the syntax of the problem description file, and a few example use cases.

[1]  Yunnan Wu,et al.  Network coding for distributed storage systems , 2010, IEEE Trans. Inf. Theory.

[2]  Zhen Zhang,et al.  A non-Shannon-type conditional inequality of information quantities , 1997, IEEE Trans. Inf. Theory.

[3]  Chao Tian,et al.  On the Storage Cost of Private Information Retrieval , 2019, IEEE Transactions on Information Theory.

[4]  Randall Dougherty,et al.  Six New Non-Shannon Information Inequalities , 2006, 2006 IEEE International Symposium on Information Theory.

[5]  Satyajit Thakor,et al.  Minimal Characterization of Shannon-Type Inequalities Under Functional Dependence and Full Conditional Independence Structures , 2019, IEEE Transactions on Information Theory.

[6]  Kai Zhang,et al.  On the Symmetry Reduction of Information Inequalities , 2018, IEEE Transactions on Communications.

[7]  Raymond W. Yeung,et al.  A First Course in Information Theory , 2002 .

[8]  Raymond W. Yeung,et al.  A framework for linear information inequalities , 1997, IEEE Trans. Inf. Theory.

[9]  Jayant Apte,et al.  Algorithms for computing network coding rate regions via single element extensions of matroids , 2014, 2014 IEEE International Symposium on Information Theory.

[10]  Yunnan Wu,et al.  A Survey on Network Codes for Distributed Storage , 2010, Proceedings of the IEEE.

[11]  John MacLaren Walsh,et al.  Multilevel Diversity Coding Systems: Rate Regions, Codes, Computation, & Forbidden Minors , 2014, IEEE Transactions on Information Theory.

[12]  Andrei E. Romashchenko,et al.  How to Use Undiscovered Information Inequalities: Direct Applications of the Copy Lemma , 2019, 2019 IEEE International Symposium on Information Theory (ISIT).

[13]  Urs Niesen,et al.  Fundamental Limits of Caching , 2014, IEEE Trans. Inf. Theory.

[14]  Chao Tian,et al.  Multilevel Diversity Coding With Regeneration , 2016, IEEE Trans. Inf. Theory.

[15]  Raymond W. Yeung,et al.  Information Theory and Network Coding , 2008 .

[16]  Chao Tian,et al.  A Shannon-Theoretic Approach to the Storage-Retrieval Tradeoff in PIR Systems , 2018, 2018 IEEE International Symposium on Information Theory (ISIT).

[17]  Haim H. Permuter,et al.  Fourier-Motzkin Elimination Software for Information Theoretic Inequalities , 2016, ArXiv.

[18]  Steven P. Weber,et al.  A new computational approach for determining rate regions and optimal codes for coded networks , 2013, 2013 International Symposium on Network Coding (NetCod).

[19]  Raymond W. Yeung,et al.  Information-theoretic characterizations of conditional mutual independence and Markov random fields , 2002, IEEE Trans. Inf. Theory.

[20]  Chao Tian.  A computer-aided investigation on the fundamental limits of caching , 2017, ISIT.

[21]  Chee Wei Tan,et al.  Proving and disproving information inequalities , 2014, 2014 IEEE International Symposium on Information Theory.

[22]  Chao Tian.  Characterizing the Rate Region of the (4,3,3) Exact-Repair Regenerating Codes , 2014, IEEE Journal on Selected Areas in Communications.

[23]  Randall Dougherty,et al.  Insufficiency of linear coding in network information flow , 2005, IEEE Transactions on Information Theory.

[24]  Jayant Apte,et al.  Exploiting symmetry in computing polyhedral bounds on network coding rate regions , 2015, 2015 International Symposium on Network Coding (NetCod).

[25]  Frantisek Matús,et al.  Infinitely Many Information Inequalities , 2007, 2007 IEEE International Symposium on Information Theory.

[26]  Lin Ling,et al.  Proving and Disproving Information Inequalities: Theory and Scalable Algorithms , 2020, IEEE Transactions on Information Theory.