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Minquan Cheng chengqinshi @ hotmail

On the Placement Delivery Array Design for Coded Caching Scheme. Minquan Cheng chengqinshi @ hotmail.com. Joint work with: Q . Yan, X. Tang , and Q . Chen. Outline. Introduction Cache systems Placement delivery array. 1. Wireless traffic.

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Minquan Cheng chengqinshi @ hotmail

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  1. On the Placement Delivery Array Design for Coded Caching Scheme Minquan Cheng chengqinshi@hotmail.com Joint work with: Q. Yan, X. Tang,and Q. Chen

  2. Outline • Introduction • Cache systems • Placement delivery array 1

  3. Wireless traffic • Video-on-demand drives wireless traffic growth • The Available bandwidth is finite [1] Cisco Visual Networking Index, Global Mobile Data Traffic Forecast Update, 2014-2019, White Paper, 2015.

  4. Temporal High temporal variability

  5. System setting N Files K Size M • A server stores N files, each of size F packets (N = 3) • K users, each access a cache of size MF packets (K = 3)

  6. Caching System • Placement Phase • parts of each file is partially cached at each user • without the knowledge of user's demands • Delivery Phase • each user proposes a demand, the requested files are • d = (d1, d2, … , dK) • the server sends a signal Xd to users • each user decodes its requested file according to Xd and its cached contents • Xd has the size of RF packets.

  7. System setting In 2014, Ali and Niesen proposed that coded caching scheme can be used to further reduce the congestion in the wireless network. • Best paper award of IEEE IT • Cited by 408 times [4] M. A. Maddah-Ali and U. Niesen, IEEE Trans. Inf. Theory, 60(5): 2856–2867(2014).

  8. A-N scheme (N, K, M, F, t=KM/N) Placement Phase • N files W1, W2, ...,WN • Each file is split into F= packets, i.e., • User k caches:

  9. A-N scheme (N, K, M, F, t=KM/N) Delivery Phase Assume k requests Wdk • Sever sends for all such that

  10. A-N scheme (N, K, M, F, t=KM/N) • It is widely used in heterogeneous wireless network , such as D2D, hierarchical network and so on. • Disadvantage: Each file has to be split into F packets, which usually increases exponentially with the number of users K. • Difficult: They can not consider placement phase and delivery phase together. [5] M. Ji, G. Caire, A. Molisch, IEEE Trans. Inform. Theory, 62(2): 849-869 (2016) [6] N. Karamchandani, U. Niesen, M. A. Maddah-Ali, S. N. Diggavi, IEEE Trans. Inform. Theory , 62(6): 3212-3229 (2016) [7] M. A. Maddah-Ali and U. Niesen, IEEE/ACM Trans. Netw. 23(4): 1029-1040 (2015)

  11. Placement Delivery Array Definition: An array on is called PDA if satisfies the following conditions: ̶ Each integer occurs at most once in each row and each column ̶ For any subarray , if (resp. ), then it must be of the form (resp. )

  12. Definitions of PDA • For an PDA P, • ̶ P is said to be a (K,F,Z,S) PDA if each column of P has • non-integer cells • ̶ P is a g-regular PDA (g-PDA) if the occurrence of each integer in P is exactly g times

  13. Examples K=F=3

  14. PDA for caching system • PDA can depict both placement phase and delivery phase together • The problem of finding a proper coded caching scheme can be translated into designing a proper PDA • The rate of the system for any request is S/F

  15. PDA: Ali-Niesen • A-N scheme corresponds to a regular PDA • Smaller F Smaller g  Larger R

  16. New PDA Theorem For any integers q≥2 and m≥1, a g- (K,F,Z,S) PDA is constructed with K=q(m+1) F=qm Z=qm-1 S=qm+1 ‒ qm g= m+1 such that M/N=1/q and R=q-1

  17. Comparison：Ali-Niesen VS New

  18. Comparison：Example K=N=6, M=3 RA-N=3/4 VS RN=1 FA-N=20 VS FN=4

  19. Papers [1] Q. Yan,M. Cheng, X. Tang and Q. Chen, On the placement delivery array design in centralized coded caching scheme,已投IEEE Trans. Inf. Theory, Oct. 2015. arXiv: 1510.05064v1. [cs.IT] [2] M. Cheng, J. Jiang, Q. Yan, X. Tang, H. Cao, Optimal placement delivery arrays, submitted to IEEE Trans. Inf. Theory, Nov. 2016. arXiv:1611.04213 [cs.IT] [3] M. Cheng, Q. Yan, X. Tang and J. Jiang, Optimal placement delivery arrays with minimum number of rows, submitted to IEEE Trans. Commun., Mar. 2017. arXiv: 1703. 01548. [cs.IT] [4] Q. Yan, X. Tang, Q. Chen, M. Cheng, Placement delivery array design through strong edge coloring of bipartite graphs, CSCIT, 2017. Hong Kong.

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