A new converse bound for coded caching

An information-theoretic lower bound is developed for the caching system studied by Maddah-Ali and Niesen. By comparing the proposed lower bound with the decentralized coded caching scheme of Maddah-Ali and Niesen, the optimal memory-rate tradeoff is characterized to within a multiplicative gap of 4.7 for the worst case, improving the previous analytical gap of 12. Furthermore, for the case when users' requests follow the uniform distribution, the multiplicative gap is tightened to 4.7, improving the previous analytical gap of 72. As an independent result of interest, for the single-user average case in which the user requests multiple files, it is proved that caching the most requested files is optimal.

[1]  Urs Niesen,et al.  Decentralized coded caching attains order-optimal memory-rate tradeoff , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[2]  P. C. Wang.  Function Computation over Networks: Efficient Information Processing for Cache and Sensor Applications , 2015 .

[3]  Xinbing Wang,et al.  Coded caching under arbitrary popularity distributions , 2015, ITA.

[4]  Jaime Llorca,et al.  Order-Optimal Rate of Caching and Coded Multicasting With Random Demands , 2015, IEEE Transactions on Information Theory.

[5]  Zhi Chen.  Fundamental Limits of Caching: Improved Bounds For Small Buffer Users , 2014, ArXiv.

[6]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[7]  Xinbing Wang,et al.  Coded caching under arbitrary popularity distributions , 2015, 2015 Information Theory and Applications Workshop (ITA).

[8]  Urs Niesen,et al.  Coded Caching With Nonuniform Demands , 2017, IEEE Transactions on Information Theory.

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

[10]  Hooshang Ghasemi,et al.  Improved lower bounds for coded caching , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).