[Paper Review] Degrees of Freedom of Interference Networks with Transmitter-Side Caches

Antonious M. Girgis, Özgür Erçetin+2 more|arXiv (Cornell University)|Dec 16, 2017

Cooperative Communication and Network Coding30 references3 citations

TL;DR

This paper studies interference networks with transmitter-side caching, proposing a novel delivery scheme that achieves higher sum degrees of freedom (sum-DoF) than prior work under uncoded placement. It derives an information-theoretic bound on sum-DoF, showing that reciprocal sum-DoF decreases linearly with increasing transmitter cache size, thereby enhancing network capacity at high SNR.

ABSTRACT

This paper studies cache-aided interference networks with arbitrary number of transmitters and receivers, whereby each transmitter has a cache memory of finite size. Each transmitter fills its cache memory from a content library of files in the placement phase. In the subsequent delivery phase, each receiver requests one of the library files, and the transmitters are responsible for delivering the requested files from their caches to the receivers. The objective is to design schemes for the placement and delivery phases to maximize the sum degrees of freedom (sum-DoF) which expresses the capacity of the interference network at the high signal-to-noise ratio regime. Our work mainly focuses on a commonly used uncoded placement strategy. We provide an information-theoretic bound on the sum-DoF for this placement strategy. We demonstrate by an example that the derived bound is tighter than the bounds existing in the literature for small cache sizes. We propose a novel delivery scheme with a higher achievable sum-DoF than those previously given in the literature. The results reveal that the reciprocal of sum-DoF decreases linearly as the transmitter cache size increases. Therefore, increasing cache sizes at transmitters translates to increasing the sum-DoF and, hence, the capacity of the interference networks.

Motivation & Objective

• To analyze the sum degrees of freedom (sum-DoF) in interference networks with transmitter-side caching under uncoded placement.
• To derive an information-theoretic upper bound on sum-DoF for this caching strategy, tighter than existing bounds for small cache sizes.
• To design a new delivery scheme that achieves higher achievable sum-DoF than previously reported schemes.
• To establish the relationship between transmitter cache size and sum-DoF, showing a linear decrease in the reciprocal of sum-DoF with increasing cache size.

Proposed method

• Uses an uncoded placement strategy where transmitters prefetch content from a library into their finite-sized caches during the placement phase.
• Proposes a novel linear delivery scheme based on interference alignment (IA) and monomial independence over random channel coefficients.
• Employs cofactor expansion and linear independence of minors of channel gain matrices to prove full rank of key design matrices.
• Applies Lemma 3 from [29] to establish almost-sure full rank of matrices V_j^IA and V_j1^IA based on monomial independence.
• Uses annihilating polynomial analysis to prove full rank of matrix R_k, ensuring interference alignment feasibility.
• Derives a bound on sum-DoF by analyzing linear independence of channel minor determinants across transmitter and receiver indices.

Experimental results

Research questions

• RQ1 What is the information-theoretic upper bound on sum-DoF for interference networks with transmitter-side caching under uncoded placement?
• RQ2 How does the proposed delivery scheme improve upon existing achievable sum-DoF in the literature?
• RQ3 What is the scaling behavior of sum-DoF with respect to transmitter cache size?
• RQ4 Can the linear independence of minors of channel matrices be leveraged to ensure successful interference alignment in the delivery phase?

Key findings

• The proposed scheme achieves a higher sum-DoF than previously known schemes under the same uncoded placement strategy.
• The derived information-theoretic bound on sum-DoF is tighter than existing bounds for small transmitter cache sizes.
• The reciprocal of sum-DoF decreases linearly with increasing transmitter cache size, indicating a proportional gain in network capacity.
• The linear independence of minors of channel matrices is essential for ensuring full rank of interference alignment design matrices.
• The full rank of key matrices V_j^IA, V_j1^IA, and R_k is established almost surely using monomial independence and i.i.d. channel coefficients.
• The analysis confirms that transmitter caching enables effective interference management through coordinated transmission and alignment.