Exercises

Coded placement: caches store functions (e.g., linear combinations) of file bits.

Coded delivery: server broadcasts XOR combinations of file subfiles (MAN style).

Uncoded placement + coded delivery. Open question: can coded placement help?

Under uncoded placement ($\mathcal{Z}_k \subseteq \mathcal{W}$ raw bits), the MAN rate $R^* = K(1-\mu)/(1+K\mu)$ is optimal.

Uncoded placement → delivery is an index-coding problem. Tight via local-chromatic-number analysis.

Coded storage across nodes; repair bandwidth reduced via coding. Coded placement strictly beats uncoded.

Coded placement at user caches; delivery rate reduced via coding. Coded placement optimality unknown.

Regenerating: repair is local (one node failing). Coded caching: delivery is global (all users). Different constraints; different optimal structures.

$\bar M = 2$. $\bar \mu = 0.2$. $K \bar \mu = 0.6$.

$R \leq 3 \cdot 0.8 / 1.6 = 1.5$.

$R \geq 1 - M_3/N = 0.7$.

$[0.7, 1.5]$ unresolved. Memory-sharing scheme achieves something like the mean. Tight rate unknown.

$\binom{20}{5} = 15504$.

$\sqrt{\binom{K}{t}/F} = \sqrt{15504/10^5} \approx 0.39$.

FB penalty $\sim 40\%$ — very substantial. Would need $F \gg \binom{K}{t}$ for negligible penalty.

PDA with $K^2$ subpacketization: $400/10^5 = 0.004$. Far better.

Construct a specific instance where coded placement achieves rate $< R_\text{MAN}$. If found, MAN suboptimal.

Novel converse: show that any coded-placement scheme's rate is at least MAN's. Requires new Fano-style arguments with coded caches.

Neither has been done. Partial: Gohari et al. show factor-2 gap; Wang-Liu-Ji show equality for $K \leq 3$. No general result.

Uniform demand: popularity-aware placement irrelevant (all files equally likely). MAN optimal.

Some files more popular. Worst-case rate unchanged from MAN. Expected rate: popularity-aware placement strictly better.

Expected metric: popularity helps. Worst-case: MAN cannot be beaten (adversary picks unpopular files).

Real operators care about expected; Zipf-aware placement useful.

Joint optimization: waveform $x(t)$ serves data (coded MAN XORs) + sensing probe (chirp / frequency hop).

Data: must satisfy MAN XOR structure per user. Sensing: Fisher info bound per target.

Alternating optimization: fix waveform shape, optimize sensing parameters. Fix sensing parameters, optimize XOR combinations. Converge.

Better joint tradeoff than orthogonal split. Rate and CRB both improved. Open research direction.

Disaggregated RAN: separate radio unit (RU), distributed unit (DU), centralized unit (CU). Open interfaces.

Cache at CU (serves many DUs); coded delivery via CU to DUs. Aligned with MAN's broadcast model.

O-RAN Alliance working on xApp/rApp APIs. Caching APIs (admission, eviction, coded placement) could be standardized.

O-RAN commercialization: 2024-2026. Coded caching integration: 2025-2028 target.

Wan-Caire privacy extends to heterogeneous: each user has permutation $\pi_k$. Per-user masking unchanged.

STC requires $M \geq 1$ per user. Large-cache users exceed this; small-cache users may not. Secrecy feasibility requires all users above threshold.

Optimal rate in heterogeneous + STC + privacy setting is open. Composite open problem.

LEO footprint covers many terrestrial terminals simultaneously. Single broadcast reaches many users — MAN- style delivery natural.

Gateway link to terrestrial backbone is limited. Caching at satellites reduces gateway pressure.

Satellites move; cache content must travel with them or be pre-positioned. Multi-access coded caching (Ch 18) handles dynamic associations.

$1 + K\mu$ gain directly applicable. At LEO scale ($K = 10^4$ users per footprint), massive savings.

MAN rate, achievable schemes, converses — well understood.

(i) Cross-layer coordination between L3 (caching) and L1 (delivery); (ii) subpacketization for large $K$; (iii) standards APIs; (iv) operator ROI.

Integration with existing CDN / streaming stacks. LRU-based CDNs work well enough commercially; switching is risky without standardized coded-caching primitives.

5G MBMS + 6G coded primitives. Standards enable deployment.

Federated learning with coded data shuffling (Ch 15). Reduce cross-client gradient upload bandwidth.

Cache ML model parameters at edge; coded updates serve multiple users. Model serving with coded delivery.

Cache inference outputs; coded multicast of common results. Reduces inference server load for popular queries.

Online RL for adaptive coded caching; formalize as stochastic online learning (Ch 20).

Founding contribution. Established the field. Everything else follows.

Unified caching gain + spatial multiplexing gain. Extended coded caching to wireless fundamentally.

Foundational D2D caching result; established the $\Theta(M/N)$ scaling. Shaped D2D research for a decade.

Argue via impact, novelty, subsequent citations, or practical influence. Each of the above is a defensible answer.

Resolution of coded-placement optimality. Either MAN is truly optimal (closure) or a strictly better scheme (revolution).

First commercial deployment at scale. 5G MBMS + coded caching in a major operator.

ISAC + coded caching in standardized 6G framework. Bridges theory to practice for the next generation.

Defend a choice. Arguments for (1): intellectual centrality. For (2): practical impact. For (3): trend alignment with 6G standards.