---
title: Vector Coded Caching (VCC)
url: https://www.emergentmind.com/topics/vector-coded-caching-vcc
type: topic
---

# Vector Coded Caching (VCC)

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 [2202.07047][2601.06925].

## 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 [2202.07047][2601.06925].

In the multi-beam SATCOM context, all steps are analogously realized with adjustments for the Rician-shadowed channel, FDD training, and payload constraints [2601.06925].

## 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
\[
\mathrm{SINR}_{\psi,b} = \frac{\alpha^2 \left|\mathbf{h}_{\psi,b}^T \hat{\mathbf{h}}_{\psi,b}^*\right|^2}
  {1 + \alpha^2 \sum_{b'\neq b} \left|\mathbf{h}_{\psi,b}^T \hat{\mathbf{h}}_{\psi,b'}^*\right|^2}
\]
[2601.06925].

## 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 [2202.07047].

- **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:**
  \[
  G_\text{eff} = \frac{\mathcal{R}_\text{VCC}}{\mathcal{R}_\text{no\_cache}}
  \]
  [2202.07047].

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 [2202.07047]

In SATCOM, the average sum-rate with MF precoding and imperfect CSIT is (tight approximation—Theorem 1 [2601.06925]):
\[
\bar{R}_{\rm sum} \approx \xi_{G,Q}\, GQ\, \log_2\left(1 + \frac{\alpha^2\left(\Xi_1 + \sigma_e^2 L (2\beta + \Omega)\right)}
    {1 + \alpha^2 (Q-1) \Xi_2}\right)
\]
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 [2601.06925].

## 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 $G\approx7$) [2202.07047].

## 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 ($310\%$)     | [2202.07047]        |
| Terrestrial, MF     | 32             | 20       | 6 | 4.3 ($430\%$)     | [2202.07047]        |
| SATCOM, MF          | 45             | 18.5     | 6 | 4–5 ($300$–$400\%$) | [2601.06925]      |
| Channel hardening   | 64–128         | 15       | 6 | $>5$ ($540\%$)    | [2202.07047]        |

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 [2202.07047][2601.06925]. 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 [2202.07047].

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 [2601.06925].
- **Receiver complexity:** The primary additional operation is cached-aided subtraction of inter-group interference, requiring $O(GQ\cdot L)$ scalar operations per symbol [2601.06925].
- **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 [2202.07047][2601.06925].

---
**References:**
- [2202.07047] "Vector Coded Caching Multiplicatively Boosts the Throughput of Realistic Downlink Systems"
- [2601.06925] "Caching Yields up to 5x Spectral Efficiency in Multi-Beam Satellite Communications"

Source: https://www.emergentmind.com/topics/vector-coded-caching-vcc