[Paper Review] Network Throughput Optimization via Error Correcting Codes

Ratko V. Tomic|arXiv (Cornell University)|Jan 17, 2013

Interconnection Networks and Systems9 references4 citations

TL;DR

This paper introduces Long Hop networks—scalable, high-throughput, low-latency networks—by leveraging an exact equivalence between maximizing bisection bandwidth in Cayley graphs and optimizing codeword distance in linear error-correcting codes. By translating existing optimal error-correcting codes into network topologies, the method reduces switch count by 1.5–5×, internal cables by 2–6×, and average hops by 1.2–2× compared to state-of-the-art networks for the same port count and throughput.

ABSTRACT

A new network construction method is presented for building of scalable, high throughput, low latency networks. The method is based on the exact equivalence discovered between the problem of maximizing network throughput (measured as bisection bandwidth) for a large class of practically interesting Cayley graphs and the problem of maximizing codeword distance for linear error correcting codes. Since the latter problem belongs to a more mature research field with large collections of optimal solutions available, a simple translation recipe is provided for converting the existent optimal error correcting codes into optimal throughput networks. The resulting networks, called here Long Hop networks, require 1.5-5 times fewer switches, 2-6 times fewer internal cables and 1.2-2 times fewer `average hops' than the best presently known networks for the same number of ports provided and the same total throughput. These advantage ratios increase with the network size and switch radix. Independently interesting byproduct of the discovered equivalence is an efficient O(n*log(n)) algorithm based on Walsh-Hadamard transform for computing exact bisections of this class of Cayley graphs (this is NP complete problem for general graphs).

Motivation & Objective

• To address the challenge of designing scalable, high-throughput, low-latency networks with minimal hardware cost.
• To identify a fundamental equivalence between maximizing bisection bandwidth in a class of Cayley graphs and maximizing minimum codeword distance in linear error-correcting codes.
• To enable direct reuse of well-established, optimal error-correcting codes for constructing optimal network topologies.
• To provide an efficient algorithm for computing exact bisections in this class of Cayley graphs, solving an NP-complete problem for general graphs.
• To demonstrate significant improvements in network efficiency, including reduced switch count, cabling, and average hop count.

Proposed method

• Established an exact mathematical equivalence between the problem of maximizing bisection bandwidth in a class of Cayley graphs and maximizing the minimum distance of linear error-correcting codes.
• Used a translation recipe to convert known optimal error-correcting codes into corresponding network topologies, forming Long Hop networks.
• Leveraged the structure of Cayley graphs based on abelian groups and symmetric generating sets to model network interconnects.
• Applied the Walsh-Hadamard transform to design an O(n log n) algorithm for computing exact bisections in these Cayley graphs, bypassing the NP-completeness of the general problem.
• Validated network performance through comparative analysis against known topologies, measuring switch count, internal cabling, and average hop count.
• Utilized existing databases of optimal error-correcting codes (e.g., from coding theory) as a source of high-performance network designs.

Experimental results

Research questions

• RQ1 Can the problem of maximizing bisection bandwidth in a class of Cayley graph networks be formally mapped to the problem of maximizing minimum codeword distance in linear error-correcting codes?
• RQ2 To what extent can existing optimal error-correcting codes be directly translated into high-throughput, low-latency network topologies?
• RQ3 What performance gains in terms of hardware reduction (switches, cables, hops) can be achieved by using code-based network designs compared to state-of-the-art alternatives?
• RQ4 Is there an efficient algorithm to compute exact bisections in this class of Cayley graphs, given that the problem is NP-complete for general graphs?
• RQ5 How do the performance advantages of the proposed Long Hop networks scale with increasing network size and switch radix?

Key findings

• The proposed Long Hop networks achieve 1.5–5 times fewer switches than the best-known networks for the same number of ports and total throughput.
• The method reduces internal cabling by 2–6 times, significantly lowering hardware and deployment costs.
• Average hop count is reduced by 1.2–2 times, improving network latency and performance.
• The performance gains increase with network size and switch radix, indicating stronger scalability benefits for large systems.
• An O(n log n) algorithm based on the Walsh-Hadamard transform enables exact bisection computation for this class of Cayley graphs, solving an NP-complete problem efficiently.
• The discovered equivalence allows direct reuse of decades of research and optimal solutions from coding theory to design high-performance network topologies.