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The Real-World Traffic Model

So far we have assumed all content is cacheable — a library known in advance, served in the delivery phase. Real networks carry a mix:

Cacheable content: movies, software updates, pre-recorded videos. Library known before peak hours; MAN applicable.
Uncacheable content: live video, video calls, interactive apps, chat messages, ads personalized at delivery time. Cannot be pre-placed in caches.

In 5G/6G deployments, both types coexist on the same channel. The question is: what is the fundamental tradeoff between cacheable rate $R_c$ and uncacheable rate $R_u$ ? The CommIT answer — Joudeh, Lampiris, Elia, Caire 2019 — is that the GDoF region has a clean separation-scheme optimum. We present it now.

Definition:
Mixed-Traffic Cache-Aided BC

The mixed cacheable/uncacheable BC has the following modifications to the cache-aided BC model:

Each user $k$ demands a cacheable file $W_{d_k^c}$ (from library $\mathcal{W}$ ) and an uncacheable message $U_k$ (revealed at delivery time, not in library).
Achievable rates $(R_c, R_u)$ : cacheable per-user rate and uncacheable per-user rate.

The capacity region is $\mathcal{C}_{\text{mixed}}(M, L) = \{(R_c, R_u) : \text{achievable by a joint scheme}\}.$ JLEC 2019 characterize this in the GDoF regime (Ch 6.4).

Theorem: JLEC 2019 GDoF-Optimal Separation

For the cache-aided $L$ -antenna Gaussian BC with $K$ users, memory ratio $\mu$ , and mixed cacheable/uncacheable traffic, the GDoF region is $\{(\mathrm{GDoF}_c, \mathrm{GDoF}_u) : \mathrm{GDoF}_c + \gamma \mathrm{GDoF}_u \leq t + L, \mathrm{GDoF}_u \leq L\},$ where $\gamma = (t+L)/L$ is a "conversion factor" capturing how much cacheable capacity is "as expensive" as uncacheable.

The optimal scheme is a SEPARATION: (i) treat cacheable traffic with Lampiris-Caire (Chapter 5), achieving DoF $_c = t + L$ ; (ii) treat uncacheable traffic with pure MU-MIMO beamforming, achieving DoF $_u = L$ . Time-share between the two phases.

Cacheable traffic benefits from both the spatial gain ( $L$ ) and the caching gain ( $t$ ). Uncacheable traffic only benefits from spatial multiplexing ( $L$ ). Hence the tradeoff "ratio" of cacheable to uncacheable GDoF is $(t+L)/L = 1 + t/L$ . Time-sharing between pure cacheable-mode and pure uncacheable-mode achieves the optimal boundary of the tradeoff pentagon.

Proof

Achievability

Construct two modes: Mode 1 (fraction $\theta$ of channel uses): Lampiris-Caire scheme for cacheable content. GDoF per-user in this mode: $(t+L)/K$ . Mode 2 (fraction $1-\theta$ ): pure MU-MIMO for uncacheable content. GDoF per-user in this mode: $L/K$ (if $L \leq K$ ).

Per-user GDoF

Cacheable GDoF $_c = \theta (t+L)/K$ . Uncacheable GDoF $_u = (1 - \theta) L/K$ . Eliminating $\theta$ : $K \mathrm{GDoF}_c/(t+L) + K \mathrm{GDoF}_u/L = 1,$ rearranging to the stated form.

Converse

A refined cut-set argument (JLEC 2019 §V) shows no scheme can exceed this region. The converse uses the fact that caching cannot help uncacheable content (it's unknown at placement time).

GDoF optimality

The separation scheme achieves the corner points and the entire boundary by convex combination. No joint coding scheme strictly improves the GDoF region. $\blacksquare$

🎓CommIT Contribution(2019)

Mixed Cacheable/Uncacheable Traffic Tradeoff

H. Joudeh, E. Lampiris, P. Elia, G. Caire — IEEE International Symposium on Information Theory

Joudeh, Lampiris, Elia, and Caire characterized the fundamental tradeoff between cacheable and uncacheable traffic rates on the cache-aided broadcast channel. The key contribution is:

GDoF region characterization: the achievable $(R_c, R_u)$ pairs form a pentagon-like region in GDoF coordinates, with corner points determined by pure-cacheable ( $t + L$ ) and pure-uncacheable ( $L$ ) operation.
Optimality of separation: time-sharing between pure-mode schemes is GDoF-optimal. No joint coding (e.g., combining cache contents with uncacheable messages via complex coding) helps.
Practical implication: system designers can simply time-share between Chapter 5's Lampiris-Caire scheme for cacheable content and pure MU-MIMO for uncacheable content, with split determined by traffic demand.

The CommIT research program has followed up with extensions to heterogeneous cache sizes (Wan-Caire 2020) and privacy constraints (Wan-Caire 2021). The separation result is one of the cleanest characterizations in the coded-caching literature.

coded-cachingmixed-trafficcommitgdofView Paper →

GDoF Region: Cacheable vs Uncacheable

The JLEC achievable GDoF region in the $(R_c, R_u)$ plane. Blue solid line: the JLEC separation boundary. Red dashed: time-sharing baseline (no caching). The blue region is strictly larger than the red due to the caching gain $t$ . Varying the memory ratio changes the position of the cacheable-corner — at $\mu = 0$ , both schemes coincide (no cache); at $\mu \geq 1$ , cacheable operation saturates.

Parameters

Number of users K6

Antennas L2

Memory ratio M/N0.3

JLEC GDoF Pentagon: Cacheable vs Uncacheable

The JLEC GDoF region in the

(R_c, R_u)

plane. Two corner points:

(t+L, 0)

for pure cacheable operation (Lampiris-Caire scheme) and

(0, L)

for pure uncacheable operation (MU-MIMO). The boundary is traced by time-sharing between the two modes; no joint coding scheme exceeds it in the GDoF regime.

Example: Dimensioning a CDN for Mixed Traffic

A CDN serves $K = 100$ users with $L = 4$ antennas, cache ratio $\mu = 0.3$ . Traffic demand: 70% cacheable (video), 30% uncacheable (live calls). Find the time-sharing parameter $\theta$ that meets demand, and the achievable per-user rate.

Solution

DoF computation

$t = 100 \cdot 0.3 = 30$ . $\mathrm{DoF}_c = t + L = 34$ ; $\mathrm{DoF}_u = L = 4$ .

Traffic demand

Demand ratio: $R_c/R_u = 0.7/0.3 = 7/3$ .

Time-share

Let $\theta$ fraction of time is cacheable mode. Per-user rate: $R_c(\theta) = \theta \cdot 34/K \cdot \log \rho$ ; $R_u(\theta) = (1-\theta) \cdot 4/K \cdot \log \rho$ . Match ratio: $\theta \cdot 34/((1-\theta) \cdot 4) = 7/3$ . $\Rightarrow \theta \approx 0.22$ .

Per-user rate

Total per-user rate = $R_c + R_u = (0.22 \cdot 34 + 0.78 \cdot 4)/100 \cdot \log \rho = (7.48 + 3.12)/100 \log \rho = 0.106 \log \rho$ per user. At 10 dB SNR: $R \approx 0.35$ bits per channel use per user.

Compare: no caching

Without caching, pure MU-MIMO yields $\mathrm{DoF}/K = 4/100 = 0.04 \log \rho$ per user. Caching triples the per-user rate. Even with only 22% of time spent on cacheable content, the caching gain dominates.

Key Takeaway

Separation is GDoF-optimal. For mixed cacheable/uncacheable traffic, time-share between (i) pure cacheable Lampiris-Caire mode (DoF = $t+L$ ) and (ii) pure MU-MIMO uncacheable mode (DoF = $L$ ). No joint coding helps in the GDoF regime. This is the JLEC 2019 separation theorem.

Finite-SNR: Joint Coding May Help

The separation theorem is a GDoF result — it holds in the high-SNR limit. At finite SNR, joint coding schemes (where cacheable and uncacheable content share transmissions) can strictly outperform pure separation. Finite-SNR tradeoffs are an active research area; the JLEC GDoF result is a useful upper bound but not always the achievable point in practice.

The CommIT group has published follow-up work on finite-SNR joint-coding schemes (e.g., Joudeh-Caire 2021 on per-file superposition), but a tight characterization in the non-asymptotic regime remains open.

Mixed Cacheable and Uncacheable Traffic (JLEC 2019)