# Cache-Aided Interference Management with Subexponential Subpacketization

## TL;DR

This paper introduces a new cache-aided interference management scheme that reduces subpacketization complexity and employs projective geometries to achieve near-logarithmic degrees of freedom with subexponential subpacketization.

## Contribution

It presents a scheme matching the optimal DoF with reduced subpacketization and a novel approach using projective geometries for subexponential subpacketization in interference channels.

## Key findings

- Achieves the same DoF with smaller subpacketization than previous schemes.
- Introduces a projective geometry-based caching scheme with subexponential subpacketization.
- Attains a one-shot DoF of Θ(log_q K_R + K_T) for small cache fractions.

## Abstract

Consider an interference channel consisting of $K_T$ transmitters and $K_R$ receivers with AWGN noise and complex channel gains, and with $N$ files in the system. The one-shot $\mathsf{DoF}$ for this channel is the maximum number of receivers which can be served simultaneously with vanishing probability of error as the $\mathsf{SNR}$ grows large, under a class of schemes known as \textit{one-shot} schemes. Consider that there exists transmitter and receiver side caches which can store fractions $\frac{M_T}{N}$ and $\frac{M_R}{N}$ of the library respectively. Recent work for this cache-aided interference channel setup shows that, using a carefully designed prefetching(caching) phase, and a one-shot coded delivery scheme combined with a proper choice of beamforming coefficients at the transmitters, we can achieve a $\mathsf{DoF}$ of $t_T+t_R$, where $t_T=\frac{M_T K_T}{N}$ and $t_R=\frac{M_R K_R}{N},$ which was shown to be almost optimal. The existing scheme involves splitting the file into $F$ subfiles (the parameter $F$ is called the \textit{subpacketization}), where $F$ can be extremely large (in fact, with constant cache fractions, it becomes exponential in $K_R$, for large $K_R$). In this work, our first contribution is a scheme which achieves the same $\mathsf{DoF}$ of $t_T+t_R$ with a smaller subpacketization than prior schemes. Our second contribution is a new coded caching scheme for the interference channel based on projective geometries over finite fields which achieves a one-shot $\mathsf{DoF}$ of $\Theta(log_qK_R+K_T)$, with a subpacketization $F=q^{O(K_T+(log_qK_R)^2)}$ (for some prime power $q$) that is \textit{subexponential} in $K_R$, for small constant cache fraction at the receivers. To the best of our knowledge, this is the first coded caching scheme with subpacketization subexponential in the number of receivers for this setting.