Decoding Network Codes by Message Passing

TL;DR

This paper introduces a message passing decoding framework for network codes using factor graphs, enabling efficient decoding by leveraging network topology and support messages, with potential for complexity reduction.

Contribution

It presents a systematic factor graph-based decoding method for network codes, utilizing support messages to simplify the decoding process and improve efficiency.

Findings

Support message passing reduces decoding complexity

Framework applies to linear network codes with error-free links

Provides a basis for network code design and topology control

Abstract

In this paper, we show how to construct a factor graph from a network code. This provides a systematic framework for decoding using message passing algorithms. The proposed message passing decoder exploits knowledge of the underlying communications network topology to simplify decoding. For uniquely decodeable linear network codes on networks with error-free links, only the message supports (rather than the message values themselves) are required to be passed. This proposed simplified support message algorithm is an instance of the sum-product algorithm. Our message-passing framework provides a basis for the design of network codes and control of network topology with a view toward quantifiable complexity reduction in the sink terminals.