References & Further Reading

References

1. K. Shanmugam, M. Ji, A. M. Tulino, J. Llorca, and A. G. Dimakis, Finite Length Analysis of Caching-Aided Coded Multicasting, 2016

   Foundational CommIT paper on finite-length coded caching. Introduces graph-coloring perspective; establishes polynomial-$F$ constructions.

2. Q. Yan, M. Cheng, X. Tang, and Q. Chen, On the Placement Delivery Array Design for Centralized Coded Caching Scheme, 2017

   PDA framework introduction. Construction 1 gives polynomial- $F$ PDAs that match MAN rate. Key reference for §14.2.

3. M. A. Maddah-Ali and U. Niesen, Fundamental Limits of Caching, 2014

   Original MAN scheme. Subpacketization $\binom{K}{t}$ exponential — the bottleneck addressed by Chapter 14.

4. M. A. Maddah-Ali and U. Niesen, Decentralized Coded Caching Attains Order-Optimal Memory-Rate Tradeoff, 2015

   Decentralized alternative — independent random placement. Avoids coordination overhead; asymptotically matches MAN.

5. S. Kaji and G. Caire, Polynomial-Subpacketization Coded Caching Bounds, 2020

   Caire-group lower bounds on polynomial-subpacketization rate. Shows that polynomial $F$ implies rate $\geq $ MAN rate.

6. Q. Yu, M. A. Maddah-Ali, and A. S. Avestimehr, The Exact Rate-Memory Tradeoff for Caching with Uncoded Prefetching, 2018

   Yu-Maddah-Ali-Avestimehr uncoded-placement converse. Relevant for subpacketization lower bounds.

7. M. Salehi, A. Tölli, S. P. Shariatpanahi, and E. Peiker, Low-Complexity Linear Coded Caching for Multi-Antenna BC, 2022

   Practical polynomial-$F$ schemes implemented in prototypes. Relevant for §14.4 deployment discussion.

8. M. Ji, A. M. Tulino, J. Llorca, and G. Caire, Order-Optimal Rate of Caching and Coded Multicasting with Random Demands, 2017

   Finite-length extensions of coded caching under Zipf demand. Connects with Chapter 13's non-uniform analysis.

9. X. Tang and A. Ramamoorthy, Coded Caching Schemes with Reduced Subpacketization from Linear Block Codes, 2018

   Another polynomial-$F$ construction based on block codes. Complements graph-coloring approach.

10. P. Krishnan and A. Ramamoorthy, Resolvable Coded Caching: Reduced Subpacketization Coded Caching, 2019

    Resolvable-design based polynomial-subpacketization coded caching. Alternative construction.

11. A. El Gamal and Y.-H. Kim, Network Information Theory, Cambridge University Press, 2011

    Broad background on network information theory. Index coding (Ch 9) gives the theoretical foundation for graph- coloring.

12. Z. Bar-Yossef, Y. Birk, T. S. Jayram, and T. Kol, Index Coding With Side Information, 2011

    Index coding theoretical foundation; Chapter 4 of this book; relevant for graph-coloring perspective here.

13. G. Caire, M. Salman, and A. Zaidi, Practical 6G Coded Caching, 2023

    CommIT-adjacent 6G deployment work. Shows practical polynomial-$F$ schemes at $K \geq 100$ in prototype.

Further Reading

• Shanmugam et al. graph-coloring paper

  K. Shanmugam, M. Ji, A. M. Tulino, J. Llorca, A. G. Dimakis, 'Finite Length Analysis of Caching-Aided Coded Multicasting,' IEEE TIT 2016

  Foundational CommIT paper; the graph-coloring approach originates here.

• PDA Framework

  Q. Yan, M. Cheng, X. Tang, Q. Chen, 'On the Placement Delivery Array Design,' IEEE TIT 2017

  PDA is the right abstraction level for engineering. Construction 1 gives first polynomial-subpacketization scheme.

• Resolvable-design constructions

  P. Krishnan, A. Ramamoorthy, 'Resolvable Coded Caching,' IEEE TIT 2019

  Alternative polynomial-$F$ construction via combinatorial designs. Complementary to graph-coloring.

• Practical implementations

  M. Salehi et al., 'Low-Complexity Linear Coded Caching,' IEEE TWC 2022

  Bridges theory and practice. Real-world polynomial-$F$ implementations in prototypes.