Equivalent Conditions to Determine the GEKs by the LEKs in a Convolutional Network Code over a Cyclic Network

Xubo ZHAO  Wangmei GUO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.9   pp.1570-1576
Publication Date: 2012/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.1570
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
convolutional network code,  cyclic network,  weighted line graph,  Mason signal flow graph,  Mason theorem,  

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In this paper, the correspondence between the weighted line graph and the Mason signal flow graph (MSFG) has been established, which gives an interpretation of a convolutional network code (CNC) over a cyclic network from a different perspective. Furthermore, by virtue of Mason theorem, we present two new equivalent conditions to evaluate whether the global encoding kernels (GEKs) can be uniquely determined by the given complete set of local encoding kernels (LEKs) in a CNC over a cyclic network. These two new equivalent conditions turn out to be more intuitive. Moreover, we give an alternative simple proof of an existing result.