Fairness in Multiterminal Data Compression: Decomposition of Shapley Value

TL;DR

This paper introduces a decomposition method for calculating the Shapley value to fairly allocate source coding rates in multiterminal networks, significantly reducing computational complexity for large source sets.

Contribution

It presents a novel decomposition approach for the Shapley value in source coding, enabling efficient fair rate allocation in large multiterminal networks.

Findings

Decomposition reduces computational complexity in large source networks.

The method effectively computes fair rate allocations in the Slepian-Wolf region.

Experiments show significant complexity reduction with increasing sources.

Abstract

We consider the problem of how to determine a fair source coding rate allocation method for the lossless data compression problem in multiterminal networks, e.g, the wireless sensor network where there are a large number of sources to be encoded. We model this problem by a game-theoretic approach and present a decomposition method for obtaining the Shapley value, a fair source coding rate vector in the Slepian-Wolf achievable region. We formulate a coalitional game model where the entropy function quantifies the cost incurred due to the source coding rates in each coalition. In the typical case for which the game is decomposable, we show that the Shapley value can be obtained separately for each subgame. The complexity of this decomposition method is determined by the maximum size of subgames, which is strictly smaller than the total number of sources and contributes to a considerable reduction in computational complexity. Experiments demonstrate large complexity reduction when the number of sources becomes large.