[Paper Review] Communication for Omniscience.

Ni Ding, Chung Chan+3 more|arXiv (Cornell University)|Nov 25, 2016

Cooperative Communication and Network Coding61 references3 citations

TL;DR

This paper proposes efficient algorithms for achieving omniscience in a network of users observing a discrete memoryless multiple source, minimizing total communication rate (sum-rate). By leveraging submodularity and Dilworth truncation, it formulates a maximization problem whose solution yields the minimum sum-rate, with a modified decomposition algorithm (MDA) and sum-rate increment algorithm (SIA) enabling polynomial-time computation for asymptotic and non-asymptotic models, respectively.

ABSTRACT

This paper considers the communication for omniscience (CO) problem: A set of users observe a discrete memoryless multiple source and want to recover the entire multiple source via noise-free broadcast communications. We study the problem of how to attain omniscience with the minimum sum-rate, the total number of communications, and determine a corresponding optimal rate vector. The results cover both asymptotic and non-asymptotic models where the transmission rates are real and integral, respectively. Based on the concepts of submodularity and Dilworth truncation, we formulate a maximization problem. The maximum is the highest Slepian-Wolf constraint over all multi-way cuts of the user set, which determines the minimum sum-rate. For solving this maximization problem and searching for an optimal rate vector, we propose a modified decomposition algorithm (MDA) and a sum-rate increment algorithm (SIA) for asymptotic and non-asymptotic models, respectively, both of which complete in polynomial time. For solving the Dilworth truncation problem as the subroutine in both algorithms, we propose a fusion method to implement the existing coordinate saturation capacity (CoordSatCap) algorithm, where the submodular function minimization (SFM) is done over a merged user set. We show by experimental results that this fusion method contributes to a reduction in computation complexity as compared to the original CoordSatCap algorithm.

Motivation & Objective

• To determine the minimum sum-rate required for all users to recover the entire multiple source via noise-free broadcast communication.
• To design polynomial-time algorithms for computing an optimal rate vector under both asymptotic (real rates) and non-asymptotic (integral rates) models.
• To address the computational challenge of solving the Dilworth truncation problem efficiently within the optimization framework.
• To reduce the complexity of existing submodular function minimization algorithms through a fusion method for user set merging.
• To establish theoretical bounds on achievable rates using Slepian-Wolf constraints over multi-way cuts of the user set.

Proposed method

• Formulates the CO problem as a maximization of the Slepian-Wolf constraint over all multi-way cuts, which determines the minimum sum-rate.
• Applies submodularity and Dilworth truncation to model the rate allocation problem as a structured optimization task.
• Proposes a modified decomposition algorithm (MDA) for the asymptotic model, operating in polynomial time.
• Introduces a sum-rate increment algorithm (SIA) for the non-asymptotic model, also running in polynomial time.
• Develops a fusion method to accelerate the coordinate saturation capacity (CoordSatCap) algorithm by merging user sets before submodular function minimization.
• Uses the fused CoordSatCap algorithm as a subroutine in both MDA and SIA, improving computational efficiency over the original implementation.

Experimental results

Research questions

• RQ1 What is the minimum sum-rate required for all users to achieve omniscience in a distributed source network with noise-free broadcast?
• RQ2 How can an optimal rate vector be computed efficiently under both real and integral rate constraints?
• RQ3 Can the computational complexity of solving the Dilworth truncation problem be reduced through user set fusion?
• RQ4 What is the role of Slepian-Wolf constraints over multi-way cuts in determining the minimum sum-rate?
• RQ5 How do the proposed MDA and SIA algorithms compare in performance and complexity to existing approaches?

Key findings

• The minimum sum-rate is determined by the maximum Slepian-Wolf constraint over all multi-way cuts of the user set.
• The modified decomposition algorithm (MDA) computes the optimal rate vector in polynomial time for the asymptotic model.
• The sum-rate increment algorithm (SIA) achieves the same goal in polynomial time for the non-asymptotic model with integral rates.
• The fusion method for the CoordSatCap algorithm reduces computation complexity compared to the original version by minimizing submodular functions over merged user sets.
• Both MDA and SIA are proven to complete in polynomial time, ensuring scalability for large user sets.
• Experimental results confirm that the fusion method significantly improves efficiency in solving the Dilworth truncation problem.