Chapter Summary

Chapter Summary

Key Points

• 1.

  Coded caching converts memory into bandwidth. The MAN scheme achieves delivery load $R = K(1-M/N)/(1+KM/N)$, where the coded multicasting gain $1+KM/N$ grows linearly with the number of users. Each coded multicast message (an XOR of sub-files) simultaneously satisfies the demands of $t+1$ users, each using its cached side information to cancel unwanted terms.

• 2.

  The MAN scheme is optimal under uncoded placement. For $N \ge K$, no scheme with uncoded cache placement can achieve a lower worst-case delivery load. Even with arbitrarily complex coded placement, the load cannot be reduced by more than a factor of 2. The optimality proof uses an induction argument combined with index coding converses.

• 3.

  Multi-antenna coded caching achieves additive DoF $L + t$. With $L$ transmit antennas and coded caching parameter $t = KM/N$, the spatial multiplexing gain and coded multicasting gain are complementary. The server can serve $\min(L+t, K)$ user-demands per time slot by combining zero-forcing beamforming with coded multicast messages.

• 4.

  D2D coded caching achieves $\Theta(M/N)$ per-user throughput independent of $K$. In serverless D2D networks, coded caching combined with spatial reuse provides perfect throughput scaling: adding users does not reduce per-user throughput because each new user contributes both demand and cached content.

• 5.

  Extensions preserve the core gain. Correlated files reduce the effective library size (Wan/Tuninetti/Ji/Caire). Demand privacy can be achieved with negligible overhead (Wan/Caire). The Fog-RAN extension combines edge caching with user caching for two-layer gains.

• 6.

  Subpacketization is the main practical barrier. The MAN scheme requires splitting each file into $\binom{K}{t}$ sub-files, which grows exponentially in $K$. Practical deployments use user clustering, combinatorial designs, or placement delivery arrays to control subpacketization at the cost of reduced multicasting gain.