New Results on the Computation-Communication Tradeoff for Heterogeneous Coded Distributed Computing

Xu, Fan; Shao, Shuo; Tao, Meixia

doi:10.1109/tcomm.2021.3049821

Cited by 19 publications

(4 citation statements)

References 25 publications

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“…Several works proposed to reduce this delivery time through smart coding. More specifically, in wired networks, delivery time is decreased by sending appropriate linear combinations of the IVAs [15]- [17], over wireless cellular networks [18], [19] a similar effect is achieved through simple interference cancellation at the receiving nodes, and over wireless interference networks a gain was achieved by zero-forcing [20]. In this paper, we show further improvement in wireless interference networks using a novel IA scheme.…”

Section: Introductionmentioning

confidence: 72%

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DoF of a Cooperative X-Channel with an Application to Distributed Computing

Bi,

Wigger,

Ciblat

et al. 2022

Preprint

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We consider a cooperative X-channel with K transmitters (TXs) and K receivers (Rxs) where Txs and Rxs are gathered into groups of size r respectively. Txs belonging to the same group cooperate to jointly transmit a message to each of the K − r Rxs in all other groups, and each Rx individually decodes all its intended messages. By introducing a new interference alignment (IA) scheme, we prove that when K/r is an integer the sum Degrees of Freedom (SDoF) of this channel is lower bounded by 2r if K/r ∈ {2, 3} and byWe also prove that the SDoF is upper bounded by K(K−r) 2K−3r . The proposed IA scheme finds application in a wireless distributed MapReduce framework, where it improves the normalized data delivery time (NDT) compared to the state of the art.

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Section: Introductionmentioning

confidence: 72%

“…We focus on the fundamental NDT-computation tradeoff ∆ * (r), which is defined as the infimum over all values of ∆ satisfying (17) for some choice of file assignments {M p }, transmission time T, function assignment {Q p }, and encoding and decoding functions {f…”

Section: Application To Wireless Distributed Computing a The Mapreduc...mentioning

confidence: 99%

DoF of a Cooperative X-Channel with an Application to Distributed Computing

Bi,

Wigger,

Ciblat

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…From (7), it is shown that each leaf WD simply multiplies the (effective) inverse channel coefficient from itself to the destination WD (i.e.,…”

Section: ) Leaf Wd Transmissionmentioning

confidence: 99%

Multi-Level Over-the-Air Aggregation of Mobile Edge Computing over D2D Wireless Networks

Wang¹,

Lau²

2021

Preprint

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In this paper, we consider a wireless multihop device-to-device (D2D) based mobile edge computing (MEC) system, where the destination wireless device (WD) is scheduled to compute nomographic functions. Under the MapReduce framework and motivated by reducing communication resource overhead, we propose a new multi-level over-the-air (OTA) aggregation scheme for the destination WD to collect the individual partially aggregated intermediate values (IVAs) for reduction from multiple source WDs in the data shuffling phase. For OTA aggregation per level, the source WDs employ a channelinverse structure multiplied by their individual transmit coefficients in transmission over the same timefrequency resource blocks, and the destination WD finally uses a receive filtering factor to construct the aggregated IVA. Under this setup, we develop a unified transceiver design framework that minimizes the mean squared error (MSE) of the aggregated IVA at the destination WD subject to the source WDs' individual power constraints, by jointly optimizing the source WDs' individual transmit coefficients and the destination WD's receive filtering factor. The formulated power-constrained MSE minimization problem is non-convex. First, based on the primal decomposition method, we derive the closed-form solution under the special case of a common transmit coefficient. It shows that all the source WDs' common transmit is determined by the minimal transmit power budget among the source WDs. Next, for the general case, we transform the original problem into a quadratic fractional programming problem, and then develop a low-complexity algorithm to obtain the (near-) optimal solution by leveraging Dinkelbach's algorithm along with the Gaussian randomization method. Numerical results are provided to demonstrate the significant performance gains achieved by the proposed multi-level OTA aggregation scheme over various existing schemes.

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“…For example, the works [9]- [11] focused on coded distributed computing (CDC) schemes to reduce the communication load (i.e., the number of information bits) of the Shuffle phase via coding, at the expense of increasing the computational load of the Map phase. The work [12] proposed a joint mapping and data shuffling scheme for a general heterogeneous CDC systems, with the aim of achieving a upper bound of the optimal communication load. Based on a low-rank optimization model for wireless MapReduce systems, the work [13] aimed to maximize the achieved degree-of-freedom via building the interference alignment condition for data shuffling, where a difference-of-convex-function algorithm was developed.…”

Section: Introductionmentioning

confidence: 99%

Dynamic RAT Selection and Transceiver Optimization for Mobile Edge Computing Over Multi-RAT Heterogeneous Networks

Wang¹,

Lau²

2021

Preprint

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Mobile edge computing (MEC) integrated with multiple radio access technologies (RATs) is a promising technique for satisfying the growing low-latency computation demand of emerging intelligent internet of things (IoT) applications. Under the distributed MapReduce framework, this paper investigates the joint RAT selection and transceiver design for over-theair (OTA) aggregation of intermediate values (IVAs) in wireless multiuser MEC systems, while taking into account the energy budget constraint for the local computing and IVA transmission per wireless device (WD). We aim to minimize the weighted sum of the computation mean squared error (MSE) of the aggregated IVA at the RAT receivers, the WDs' IVA transmission cost, and the associated transmission time delay, which is a mixedinteger and nonconvex problem. Based on the Lagrange duality method and primal decomposition, we develop a low-complexity algorithm by solving the WDs' RAT selection problem, the WDs' transmit coefficients optimization problem, and the aggregation beamforming problem. Extensive numerical results are provided to demonstrate the effectiveness and merit of our proposed algorithm as compared with other existing schemes.

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New Results on the Computation-Communication Tradeoff for Heterogeneous Coded Distributed Computing

Cited by 19 publications

References 25 publications

DoF of a Cooperative X-Channel with an Application to Distributed Computing

DoF of a Cooperative X-Channel with an Application to Distributed Computing

Multi-Level Over-the-Air Aggregation of Mobile Edge Computing over D2D Wireless Networks

Dynamic RAT Selection and Transceiver Optimization for Mobile Edge Computing Over Multi-RAT Heterogeneous Networks

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