On Encoding and Decoding of Circular-Shift Linear Network Codes

Abstract

In a multicast network, a circular-shift linear code can be induced from a scalar linear code such that equipped with a nontrivially constructed source encoding matrix, and the induced code qualifies to be a circular-shift linear solution at a certain rate. However, for such an induced solution, there was no explicit characterization of the corresponding decoding matrix at every receiver. In this letter, we formulate a general rule to construct a source encoding matrix and a corresponding decoding matrix at every receiver. By application of the general rule, we further design new instances of the encoding and the decoding matrices, which can be expressed in a systematic form and involve fewer binary operations.