The Nonlinear Network Coding and Its Application in Error-Correcting Codes

摘要

Nonlinear network coding is researched here. For determined network, Jaggi–Sanders algorithm is generalized to its nonlinear form for the the multicast network. Precise details of the algorithm implementation and the proof on the algorithm existence are given. The error-correcting codes for determined network coding is also proposed based on the traditional error-correcting codes for network coding. For random network, the nonlinear network coding scheme is proposed. It shows the nonlinear network coding has advantages in solving the so-called “all-or-nothing” problem caused by errors. Some interesting mathematical concepts such as shared agreements, composite functions and n -dimensional maximal independent set based on combinatorics are proposed. These new concepts may offer beneficial lessons for further research on nonlinear network coding.