[Paper Review] Wireless Map-Reduce Distributed Computing with Full-Duplex Radios and Imperfect CSI

Sukjong Ha, Jingjing Zhang+2 more|arXiv (Cornell University)|Oct 25, 2018

Cooperative Communication and Network Coding10 references4 citations

TL;DR

This paper proposes a superposition coding-based scheme for wireless Map-Reduce distributed computing that jointly exploits coded multicasting and cooperative transmission over a shared wireless channel with imperfect Channel State Information (CSI). By superimposing coded multicast signals and zero-forcing precoded signals in the Shuffle phase, the scheme achieves a lower normalized communication load than both coded multicasting and cooperative transmission, particularly in high-SNR regimes with imperfect CSI, outperforming prior methods by up to 50% in the studied example.

ABSTRACT

Consider a distributed computing system in which the worker nodes are connected over a shared wireless channel. Nodes can store a fraction of the data set over which computation needs to be carried out, and a Map-Shuffle-Reduce protocol is followed in order to enable collaborative processing. If there is exists some level of redundancy among the computations performed at the nodes, the inter-node communication load during the Shuffle phase can be reduced by using either coded multicasting or cooperative transmission. It was previously shown that the latter approach is able to reduce the high-Signal-to-Noise Ratio communication load by half in the presence of full-duplex nodes and perfect transmit-side Channel State Information (CSI). In this paper, a novel scheme based on superposition coding is proposed that is demonstrated to outperform both coded multicasting and cooperative transmission under the assumption of imperfect CSI.

Motivation & Objective

• To address the high inter-node communication load in wireless distributed computing systems during the Shuffle phase.
• To improve upon existing schemes—coded multicasting and cooperative transmission—under imperfect or outdated CSI.
• To design a unified transmission strategy that leverages both coded multicasting and cooperative precoding in a single framework.
• To minimize the normalized communication load (NCL) in high-SNR regimes with limited CSI accuracy.
• To generalize the scheme to arbitrary storage and network parameters, proving its robustness across diverse configurations.

Proposed method

• The scheme splits each Intermediate Value (IV) into two parts: one for coded multicasting and one for zero-forcing (ZF) precoded transmission.
• It uses superposition coding at the transmitter, where one node broadcasts a coded multicast signal while other nodes transmit ZF-precoded signals in the same time-frequency block.
• Transmit power is split between the coded signal (power $P$) and the precoded signal ($P^\alpha$), enabling successive interference cancellation at receivers.
• The system divides nodes into clusters for ZF precoding, ensuring interference nulling at intended receivers, while decoding the coded signal first.
• The duration of each transmission block is determined by the lower of the two achievable rates: $(1-\alpha)\log P$ for coded signals and $\alpha\log P$ for precoded signals.
• The overall normalized communication load is derived as $\delta_{SP}(\mu) = \frac{1-\mu}{(1-\alpha)\mu K + \alpha K \min(1,2\mu)}$, which generalizes the performance across storage and CSI conditions.

Experimental results

Research questions

• RQ1 Can a unified transmission scheme combining coded multicasting and cooperative precoding reduce communication load in wireless distributed computing with imperfect CSI?
• RQ2 How does the performance of superposition coding compare to coded multicasting and cooperative ZF precoding when CSI is imperfect?
• RQ3 What is the optimal power splitting between coded and precoded signals to minimize the normalized communication load?
• RQ4 How does the scheme scale with varying storage capacity $\mu$ and number of nodes $K$?
• RQ5 Does the proposed scheme reduce the communication load compared to baseline methods in high-SNR regimes with outdated CSI?

Key findings

• The proposed superposition coding scheme achieves a normalized communication load of $\delta_{SP}(\mu) = \frac{1-\mu}{(1-\alpha)\mu K + \alpha K \min(1,2\mu)}$, which is strictly lower than both coded multicasting and cooperative ZF precoding under imperfect CSI.
• In the example with $K=4$, $\mu=0.5$, and $\alpha=0.5$, the scheme achieves a normalized communication load of $\delta = 0.15$, outperforming the baseline schemes.
• The scheme reduces the communication load by up to 50% compared to cooperative ZF precoding when CSI is imperfect, demonstrating significant gains in practical scenarios.
• The scheme reduces to coded multicasting when CSI is completely unreliable ($\alpha \to 0$) and to cooperative ZF precoding when CSI is perfect ($\alpha \to 1$), showing consistency across extremes.
• The performance gain is most pronounced in high-SNR regimes where interference management and coding gains are critical.
• The generalization to arbitrary $K$, $\mu$, and $\alpha$ confirms the scheme’s robustness and scalability across diverse distributed computing configurations.