Network Coding Based on Byte-wise Circular Shift and Integer Addition

TL;DR

This paper introduces a new network coding method utilizing byte-wise circular shifts and integer addition, leveraging a special Galois ring structure for efficient implementation in microprocessors.

Contribution

It presents a novel approach to network coding based on Galois rings with primitive operations suitable for microprocessor efficiency.

Findings

Efficient implementation of network codes using byte-wise shifts and integer addition.

Application of the method to array codes.

Potential for high-speed network coding in practical systems.

Abstract

A novel implementation of a special class of Galois ring, in which the multiplication can be realized by a cyclic convolution, is applied to the construction of network codes. The primitive operations involved are byte-wise shifts and integer additions modulo a power of 2. Both of them can be executed efficiently in microprocessors. An illustration of how to apply this idea to array code is given at the end of the paper.