On Capacity of Network Error Correction Coding With Random Errors

In this letter, we consider the capacity results of network error correction coding over a general multicast network, where a malicious error occurs on each edge with a fixed probability <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> at each transmission. A pair of upper and lower bounds on the capacity are given, which are proved to coincide for a unicast network with <inline-formula> <tex-math notation="LaTeX">$|\mathcal {E}|$ </tex-math></inline-formula> parallel channels connected directly from source to sink node, where <inline-formula> <tex-math notation="LaTeX">$\mathcal {E}$ </tex-math></inline-formula> is the edge set of the network. A scheme with non-linear coding at the source and linear coding at the intermediate nodes is proposed, which achieves a strictly higher transmission rate than linear network coding.