Chapter Summary

Chapter Summary

Key Points

• 1.

  The shared-link coded caching network is defined by four parameters: $K$ users, $N$ files, per-user cache $M$, delivery rate $R$. A placement phase (off-peak) fills the caches without knowing future demands; a delivery phase (peak) sends a single coded message from which each user recovers its requested file using the message and its cache.

• 2.

  Popularity (uncoded) caching places the $\lfloor M \rfloor$ most popular files in every cache, achieving cache-hit ratio $h = \sum_{n=1}^{M} P_n$ and expected delivery rate $K(1 - h)$. This is provably optimal within the uncoded regime — no whole-file placement + unicast delivery scheme does better.

• 3.

  The worst-case rate under uncoded caching is $K(1 - M/N)$. Caching saves each user's own miss rate by a factor $1 - M/N$ (the local caching gain), but uncoded delivery cannot multicast usefully when users want different files.

• 4.

  The figure of merit is the memory ratio $M/N$, not absolute $M$. With fixed $M$ and growing $N$, the popularity- caching hit ratio collapses — caches cannot keep up with libraries. The right x-axis is the fractional cache size $M/N$, which is bounded in $[0, 1]$ regardless of how large the library gets.

• 5.

  Coded caching preview. The Maddah-Ali–Niesen scheme achieves $R_{\text{MAN}} = K(1-M/N)/(1+t)$ where $t = K M/N$ is the coded caching gain parameter. Each coded multicast message simultaneously serves $t + 1$ users. For large networks this gain is unbounded.

• 6.

  Two gains, not one. Caching provides a local gain $(1 - M/N)$ — the miss-rate reduction captured by any caching strategy — and a coded multicasting gain $(1 + t)^{-1}$ — the combinatorial savings from sharing coded messages across users. Popularity caching captures only the first. The two gains multiply, so coded caching dominates whenever $t$ is non-negligible.

• 7.

  Practical caveats. The MAN scheme requires $\binom{K}{t}$ subfiles per file (exponential in $K$), assumes uniform demand, and uses an error-free shared link. Each caveat defines a theme of a later chapter: subpacketization (Ch 14), non-uniform demand (Ch 13), and wireless channels (Chs 5–9).