Vector Coded Caching (VCC)

• Vector Coded Caching (VCC) is a physical-layer technique that employs receiver caches to enable multi-rank, interference-aware transmissions while mitigating subpacketization challenges.
• It integrates spatial multiplexing, linear precoding, and cache-aided interference cancellation to significantly enhance spectral efficiency in both terrestrial and SATCOM environments.
• By using vector-clique constructions and adaptive precoding methods, VCC delivers scalable, high-throughput performance under realistic SNRs and antenna configurations.

Vector Coded Caching (VCC) is a physical-layer technique that leverages receiver-side cached content to enable multi-rank, interference-aware transmissions in downlink multi-antenna systems. VCC fundamentally transforms the interplay between spatial multiplexing, linear precoding, and coded caching, overcoming the longstanding subpacketization bottleneck of classical coded caching and enabling a multiplicative boost in throughput or spectral efficiency under realistic deployment assumptions (Zhao et al., 2022, &&&1&&&).

1. System Model and Formal Definitions

VCC is defined for a multi-user downlink where a transmitter equipped with $M$ (wireless) or $L$ (satellite) antennas serves $K$ single-antenna receivers, each equipped with a cache capable of storing a fraction $\gamma = C/F \in [0,1)$ ($C$: cache size, $F$: file size). The server has access to a library $\mathcal{F} = \{W_1,\ldots,W_N\}$ of $N$ files. The channel is block-fading, characterized by coherence bandwidth $W_c$ and coherence time $T_c$, and either symmetric Rayleigh (terrestrial) or Rician-shadowed (SATCOM) fading.

The VCC procedure consists of two phases:

• Placement: Each file $W_n$ is split into $\binom{\Lambda}{\Lambda\gamma}$ subfiles, indexed by all subsets $\mathcal{T}\subseteq[\Lambda]$ of size $|\mathcal{T}| = \Lambda\gamma$ (for some design parameter $\Lambda$), and users are assigned to $\Lambda$ cache-states. Each user in group $g$ caches all $W_n^{\mathcal{T}}$ with $g\in\mathcal{T}$. Thus, each user stores a total of $\gamma N$ file-equivalents.
• Delivery: Upon demands, transmissions serve $G = \Lambda\gamma + 1$ groups, each containing $Q$ users (i.e., a $(G,Q)$-VCC scheme). Each group corresponds to a cache-state; in each transmission $GQ$ distinct streams are sent, combining linear precoding to address intra-group interference with cache-aided subtraction to null inter-group interference (Zhao et al., 2022, Zhao et al., 11 Jan 2026).

In the multi-beam SATCOM context, all steps are analogously realized with adjustments for the Rician-shadowed channel, FDD training, and payload constraints (Zhao et al., 11 Jan 2026).

2. VCC Transmission and Interference Management

The VCC-enabled transmitter sends

$$\mathbf{x} = \frac{1}{\sqrt{G}}\sum_{\psi\in\Psi} \rho_\psi\,\mathbf{V}_\psi\,\mathbf{s}_\psi,$$

where $|\Psi|=G$ (the active cache-states), $\mathbf{s}_\psi\in\mathbb{C}^{Q}$ is the Q-dimensional vector of coded symbols for group $\psi$, and $\mathbf{V}_\psi\in\mathbb{C}^{M \times Q}$ (terrestrial) or $\mathbb{C}^{L \times Q}$ (SATCOM) is the group’s precoding matrix. The choice of precoding scheme (ZF, RZF, MF) determines the form of $\mathbf{V}_\psi$.

Each receiver uses cached content to cancel inter-group interference, while intra-group interference is addressed by linear precoding. In the SATCOM variant with MF precoding, the received signal for user $\mathrm{U}_{\psi,b}$ is

$$y_{\psi,b} = \mathbf{h}_{\psi,b}^T \mathbf{x} + z_{\psi,b}$$

and after self-cancellation of cached signals,

$$y_{\psi,b}' = \alpha\,\mathbf{h}_{\psi,b}^T \hat{\mathbf{h}}_{\psi,b}^*\, s_{\psi,b} + \alpha \sum_{b' \neq b} \mathbf{h}_{\psi,b}^T \hat{\mathbf{h}}_{\psi,b'}^* s_{\psi,b'} + z_{\psi,b}$$

yielding the instantaneous SINR given by

$$\mathrm{SINR}_{\psi,b} = \frac{\alpha^2 \left|\mathbf{h}_{\psi,b}^T \hat{\mathbf{h}}_{\psi,b}^*\right|^2} {1 + \alpha^2 \sum_{b'\neq b} \left|\mathbf{h}_{\psi,b}^T \hat{\mathbf{h}}_{\psi,b'}^*\right|^2}$$

(Zhao et al., 11 Jan 2026).

3. Throughput and Spectral Efficiency: Closed-Form Characterization

Throughput is quantified as the sum of the achievable rates of all served users per channel coherence block:

• Raw Throughput:

\begin{align*} T_\text{no cache} &= W_c T_c\, \bar R(1, Q'), \ T_\text{VCC} &= W_c T_c\, \bar R(G, Q) \end{align*} where $\bar R(G,Q)$ is the ergodic sum-rate averaged over fading (Zhao et al., 2022).

• Effective Throughput (with CSI overhead):

\begin{align*} \mathcal{R}\text{no_cache} &= \left(1 - \frac{\beta\text{tot} Q'}{W_c T_c}\right) \bar R(1, Q'), \ \mathcal{R}\text{VCC} &= \left(1 - \frac{\beta\text{tot} GQ}{W_c T_c}\right) \bar R(G, Q) \end{align*}

• Multiplicative Gain:

$$G_\text{eff} = \frac{\mathcal{R}_\text{VCC}}{\mathcal{R}_\text{no\_cache}}$$

(Zhao et al., 2022).

Closed-form asymptotic (large-$M$) expressions are provided for $\bar R(G,Q)$ for MF, ZF, and RZF precoding:

• MF: $$\,\bar R^{\text{MF}}(G,Q) \approx GcM\,\ln\left(1 + \frac{1}{c}\frac{\rho}{\rho+G}\right)$$
• ZF: $$\,\bar R^{\text{ZF}}(G,Q) = GQ\,\ln\left(1 + \frac{\rho}{G}\left(\frac{1}{c} - 1\right)\right)$$
• RZF: See Theorem III.3 (Zhao et al., 2022)

In SATCOM, the average sum-rate with MF precoding and imperfect CSIT is (tight approximation—Theorem 1 (Zhao et al., 11 Jan 2026)): $$\bar{R}_{\rm sum} \approx \xi_{G,Q}\, GQ\, \log_2\left(1 + \frac{\alpha^2\left(\Xi_1 + \sigma_e^2 L (2\beta + \Omega)\right)} {1 + \alpha^2 (Q-1) \Xi_2}\right)$$ where $\xi_{G,Q} = 1 - {GQ\Theta}/{T}$ and $\Xi_1$, $\Xi_2$ are explicit moments of the Rician-shadowed channel.

Notably, effective spectral efficiency gains

$$\mathcal{G}_{\text{VCC}} = \frac{\displaystyle\max_{Q}\bar{R}_{\rm sum}(G,Q)}{\displaystyle\max_{Q'}\bar{R}_{\rm sum}(1,Q')}$$

are observed to reach $3\times$–$5\times$ ($300\%$–$550\%$), sustained under typical link budgets and practical SNRs (Zhao et al., 11 Jan 2026).

4. Subpacketization Bottleneck and "Vector-Clique" Construction

VCC addresses the exponential file-size (subpacketization) bottleneck of classical clique-based coded caching. Scalar clique schemes require subpacketization $\binom{\Lambda}{\Lambda\gamma}$, which becomes prohibitive for large $\Lambda$. VCC uses vector-cliques: each coded transmission involves $G = \Lambda\gamma+1$ groups, each sending $Q$-dimensional data, effectively reducing the exponent in subpacketization from $\Lambda\gamma$ to $(\Lambda\gamma)/Q$. The scheme enables confining the number of required subfiles to practical values under finite cache and file sizes (e.g., $\sim6\times10^5$ for typical parameters with $G\approx7$) (Zhao et al., 2022).

5. Numerical Results and Performance Regimes

Key findings are:

Scenario	M/L (antennas)	SNR (dB)	G	Caching gain (×)	Reference
Terrestrial, ZF/RZF	32	20	6	3.1 ($310\%$)	(Zhao et al., 2022)
Terrestrial, MF	32	20	6	4.3 ($430\%$)	(Zhao et al., 2022)
SATCOM, MF	45	18.5	6	4–5 ($300$–$400\%$)	(Zhao et al., 11 Jan 2026)
Channel hardening	64–128	15	6	$>5$ ($540\%$)	(Zhao et al., 2022)

As the cache fraction $\gamma$ increases, $G$ increases roughly linearly, which permits a larger number of simultaneously served users. Gains rise sharply at moderate–high SNR (10–20 dB). The effect is robust to channel estimation errors and limited pilot overhead, especially under MF precoding (Zhao et al., 2022, Zhao et al., 11 Jan 2026). Notably, VCC yields multiplicative—not sublinear—improvements over baseline, even in already highly optimized multiuser downlinks.

6. Channel Hardening and Feedback Overhead

In the large-antenna regime ($M \to \infty$ with $Q/M$ fixed), VCC enhances channel hardening: as $Q$ remains small relative to $M$, the effective channel for each stream tends toward determinism, reducing the required CSI feedback per stream. Caching expands the space of simultaneously served users without increasing $Q/M$. Under practical SNR and antenna dimensions, VCC offers $>540\%$ throughput improvement over traditional hardening-constrained systems (Zhao et al., 2022).

Effective feedback overhead per bit becomes negligible as $G$ increases, since the pilot and feedback cost grows linearly with the number of served streams, while aggregate throughput grows roughly proportionally with $G$.

7. Practical Implementation Aspects

• Power allocation: In the large-$M$ (or $L$) limit, group-specific normalization ensures total transmit power is equally distributed.
• Cache size selection: Subpacketization is constrained so that $$\binom{\Lambda}{\Lambda\gamma} \leq F/\text{(packet size)}$$.
• Hardware compatibility: No changes to RF frontend are needed in SATCOM; implementation reduces to updates in baseband processing and marginally at the receiver (Zhao et al., 11 Jan 2026).
• Receiver complexity: The primary additional operation is cached-aided subtraction of inter-group interference, requiring $O(GQ\cdot L)$ scalar operations per symbol (Zhao et al., 11 Jan 2026).
• Operational regime: At low SNR (<0 dB), gains are modest (1.5–2×), but at moderate/high SNR they reach $3\times$–$5\times$. Optimum multiplexing $Q^*$ balances between beamforming and spatial reuse.
• Assumptions: Symmetric Rayleigh (terrestrial) or Rician-shadowed (SATCOM) fading; perfect TDD reciprocity (terrestrial) or explicit FDD feedback (SATCOM); random-matrix approximations are validated via simulation for realistic $M/L$.

VCC achieves large gains independently of multicasting, prefetching, or file popularity; its advantage is rooted in physical-layer resource reuse and cache-enabled interference cancellation (Zhao et al., 2022, Zhao et al., 11 Jan 2026).

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References:

• (Zhao et al., 2022) "Vector Coded Caching Multiplicatively Boosts the Throughput of Realistic Downlink Systems"
• (Zhao et al., 11 Jan 2026) "Caching Yields up to 5x Spectral Efficiency in Multi-Beam Satellite Communications"