Abstract
In this chapter, we introduce another equivalent description of linear network error correction (LNEC) model so as to facilitate important and interesting problems in linear network error correction coding such as encoding, decoding, analysis and constructions of LNEC codes, etc. Actually, this description is a local approach to represent linear network error correction coding process, which can be used to restate LNEC codes. Like linear network codes, we also introduce local encoding kernels and extended global encoding kernels for LNEC codes, which respectively correspond to a so-called local description and a so-called global description of LNEC codes. And thus, we can redefine the distance and the weight for a LNEC code, which simplify their construction and decoding.
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Notes
- 1.
In order to facilitate our discussion, we assume that all imaginary message channels and imaginary error channels have no tail nodes. Actually, we can take for granted that there is an auxiliary node s′ as the tail node for all imaginary message channels, i.e., s′ generates all source messages, and similarly, there is another auxiliary node s ∗ as the tail node for all imaginary error channels, i.e., s ∗ generates all error messages. Particularly, s′ and s ∗ are allowed to be the same one.
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Guang, X., Zhang, Z. (2014). Another Description of Linear Network Error Correction Model. In: Linear Network Error Correction Coding. SpringerBriefs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0588-1_3
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DOI: https://doi.org/10.1007/978-1-4939-0588-1_3
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