On Minimum Distances for Error Correction and Detection of Generalized Network Code
This work addresses error control in network coding, which is incremental as it builds on prior nonlinear network code research.
The paper tackles the problem of error correction and detection in generalized network codes, establishing a framework to define and characterize distances for these purposes and proving bounds on these distances.
It is well known that the minimum distance for linear network codes plays the same role as the minimum distance for classical error control codes. However, Yang and Yeung (2008) discovered that for nonlinear network codes, the minimum distance for error correction is not always the same as the minimum distance for error detection. Inspired by the idea that the channel will affect the distances between the codewords, we establish the scheme of a generalized network channel and a generalized network code. Then, we systematically define the distances for error correction and error detection under the scheme of the generalized network code. We consider the joint error correction and detection in the generalized network code and obtain a complete characterization by introducing a distance and its refined version for this purpose. We enhance our understanding of the relation between various distances for error correction and detection in generalized network codes by proving some bounds on these distances.