Two Classes of Optimal Multi-Input Structures for Node Computations in Message Passing Algorithms

TL;DR

This paper introduces two classes of optimal multi-input node structures for message-passing algorithms, focusing on minimizing complexity or latency depending on the scenario, and provides their optimal configurations.

Contribution

It proposes and analyzes star-tree and directed-rooted-tree structures for node computations, optimizing for either complexity or latency in message-passing algorithms.

Findings

Star-tree structures achieve near-lowest complexity with low latency.

Directed-rooted-tree structures attain lowest latency with minimal complexity.

Optimal configurations are derived for different priority scenarios.

Abstract

In this paper, we delve into the computations performed at a node within a message-passing algorithm. We investigate low complexity/latency multi-input structures that can be adopted by the node for computing outgoing messages y = (y1, y2, . . . , yn) from incoming messages x = (x1, x2, . . . , xn), where each yj , j = 1, 2, . . . , n is computed via a multi-way tree with leaves x excluding xj . Specifically, we propose two classes of structures for different scenarios. For the scenario where complexity has a higher priority than latency, the star-tree-based structures are proposed. The complexity-optimal ones (as well as their lowest latency) of such structures are obtained, which have the near-lowest (and sometimes the lowest) complexity among all structures. For the scenario where latency has a higher priority than complexity, the isomorphic-directed-rooted-tree-based structures are proposed. The latency-optimal ones (as well as their lowest complexity) of such structures are obtained, which are proved to have the lowest latency among all structures.