[Paper Review] On Achievability for Downlink Cloud Radio Access Networks with Base Station Cooperation

Chien-Yi Wang, Michèle Wigger+1 more|arXiv (Cornell University)|Oct 28, 2016

Cooperative Communication and Network Coding16 references3 citations

TL;DR

This paper proposes two novel coding schemes—Generalized Data-Sharing (G-DS) and Generalized Compression (G-Compression)—for downlink cloud radio access networks (C-RANs) with base station (BS) cooperation via rate-limited conferencing links. It corrects a flawed application of the multivariate covering lemma in prior work, extends the Liu–Kang scheme to include common codewords for BS cooperation, and shows that the G-Compression scheme generalizes the original compression scheme to discrete memoryless channels. The key contribution is a new inner bound that achieves within a constant gap of the cut-set outer bound in the Gaussian case, specifically within $\min\{\frac{L+N}{2}, \frac{L+L\log N}{2}\}$ bits per dimension.

ABSTRACT

This work investigates the downlink of a cloud radio access network (C-RAN) in which a central processor communicates with two mobile users through two base stations (BSs). The BSs act as relay nodes and cooperate with each other through error-free rate-limited links. We develop and analyze two coding schemes for this scenario. The first coding scheme is based on Liu-Kang scheme for C-RANs without BS cooperation; and extends it to scenarios allowing conferencing between the BSs. Among few other features, our new coding scheme enables arbitrary correlation among the auxiliary codewords that are recovered by the BSs. It also introduces common codewords to be described to both BSs. For the analysis of this coding scheme, we extend the multivariate covering lemma to non-Cartesian product sets, thereby correcting an erroneous application of this lemma in Liu-Kang's related work. We highlight key aspects of this scheme by studying three important instances of it. The second coding scheme extends the so-called compression scheme that was originally developed for memoryless Gaussian C-RANs without BS cooperation to general discrete memoryless C-RANs with BS cooperation. We show that this scheme subsumes the original compression scheme when applied to memoryless Gaussian C-RAN models. In the analysis of this scheme, we also highlight important connections with the so-called distributed decode--forward scheme, and refine the approximate capacity of a general $N$-BS $L$-user C-RAN model in the memoryless Gaussian case.

Motivation & Objective

• To address the flawed achievability proof in Liu–Kang’s data-sharing scheme for C-RANs without BS cooperation, particularly the erroneous use of the multivariate covering lemma.
• To extend the Liu–Kang scheme to incorporate base station cooperation via conferencing links, introducing common codewords recoverable at both BSs.
• To generalize the compression scheme—originally designed for memoryless Gaussian C-RANs without cooperation—to general discrete memoryless channels with BS cooperation.
• To establish a new inner bound for the $N$-BS $L$-user C-RAN model with BS cooperation and refine its approximate capacity in the Gaussian case.
• To demonstrate that the distributed decode–forward (DDF) scheme subsumes the proposed G-Compression scheme and achieves a constant-gap approximation to the cut-set outer bound.

Proposed method

• Proposes the Generalized Data-Sharing (G-DS) scheme, which extends Liu–Kang’s scheme by introducing common codewords $U_0^n, V_0^n$ intended for both base stations, enabling arbitrary correlation among auxiliary codewords.
• Introduces a corrected achievability proof by extending the multivariate covering lemma to non-Cartesian product sets, resolving a flaw in Liu–Kang’s original analysis.
• Develops the Generalized Compression (G-Compression) scheme, which generalizes Park et al.’s compression scheme to discrete memoryless channels with BS cooperation, allowing joint compression and conferencing.
• Analyzes the G-Compression scheme by linking it to the distributed decode–forward (DDF) scheme, showing that DDF subsumes G-Compression in the Gaussian case.
• Derives an inner bound for the $N$-BS $L$-user C-RAN with BS cooperation and compares it to the cut-set outer bound using matrix determinant inequalities and eigenvalue bounds.
• Uses Sylvester’s determinant identity and Hadamard’s inequality to relax the cut-set bound and compare it with the inner bound, establishing a constant-gap approximation.

Experimental results

Research questions

• RQ1 How can the Liu–Kang data-sharing scheme be corrected and extended to incorporate base station cooperation through conferencing links?
• RQ2 Can the compression scheme for Gaussian C-RANs be generalized to discrete memoryless channels while accounting for BS cooperation?
• RQ3 What is the relationship between the proposed G-Compression scheme and the distributed decode–forward (DDF) scheme in the context of C-RANs with BS cooperation?
• RQ4 To what extent does the proposed inner bound approximate the cut-set outer bound in the Gaussian C-RAN model with BS cooperation?
• RQ5 What is the gap between the achievable rate region and the capacity region in terms of number of users and base stations?

Key findings

• The G-DS scheme corrects a flawed application of the multivariate covering lemma in Liu–Kang’s original work by extending the lemma to non-Cartesian product sets, ensuring a valid achievability proof.
• The G-DS scheme introduces common codewords $U_0^n, V_0^n$ recoverable at both base stations, enabling arbitrary correlation among auxiliary codewords and improving cooperation gains.
• The G-Compression scheme generalizes the original compression scheme to discrete memoryless channels and subsumes it when applied to memoryless Gaussian C-RANs.
• The distributed decode–forward (DDF) scheme is shown to subsume the G-Compression scheme in the Gaussian case, establishing a strong connection between the two approaches.
• The proposed inner bound achieves within $\min\left\{\frac{L+N}{2}, \frac{L+L\log N}{2}\right\}$ bits per dimension of the cut-set outer bound in the Gaussian $N$-BS $L$-user C-RAN model with BS cooperation.
• The gap is shown to be constant and independent of channel gains, power, or signal-to-noise ratio, establishing a constant-gap approximation to capacity.