An Error-correcting Code in Delay Linear Network Coding

Delay linear network coding (DLNC) is the problem of network coding, in which coding operation takes time. A coherent DLNC network, where coding operation at each node takes 1 unit time, can be modeled as a linear time invariant (LTI) system. Based on the Gauss Jordan elimination, we develop an algorithm to reconstruct source processes and introduce new concepts, which are decoding delay and transmission rate. The network error control problem in such networks can be done by extending the classical network error-correcting code (NEC). We construct a DLNC based linear operation channel (LOC) and apply the distance measure proposed in the previous works to our LOC. It turns out that extension of classical NEC works well for the case of DLNC. We also develop a codebook design algorithm, which achieves maximum possible size.