Decoding Network Codes using the Sum-Product Algorithm

TL;DR

This paper introduces a decoding method for network codes using the sum-product algorithm over Boolean semiring, aiming to reduce computational complexity and enable fast decoding at sink nodes.

Contribution

It proposes a novel decoding approach employing the sum-product algorithm and traceback, along with conditions for fast decodability in network coding.

Findings

Sum-product algorithm effectively decodes network codes with reduced complexity.

Traceback technique further lowers decoding computational costs.

Identifies sufficient conditions for fast decodability of network codes.

Abstract

While feasibility and obtaining a solution of a given network coding problem are well studied, the decoding procedure and complexity have not garnered much attention. We consider the decoding problem in a network wherein the sources generate multiple messages and the sink nodes demand some or all of the source messages. We consider both linear and non-linear network codes over a finite field and propose to use the sum-product (SP) algorithm over Boolean semiring for decoding at the sink nodes in order to reduce the computational complexity. We use traceback to further lower the computational complexity incurred by SP decoding. We also define and identify a sufficient condition for fast decodability of a network code at a sink that demands all the source messages.