  In this paper, we propose a noisy network coding integrated with partial
decode-and-forward relaying for single-source multicast discrete memoryless
networks (DMN's). Our coding scheme generalizes the
partial-decode-compress-and-forward scheme (Theorem 7) by Cover and El Gamal.
This is the first time the theorem is generalized for DMN's such that each
relay performs both partial decode-and-forward and compress-and-forward
simultaneously. Our coding scheme simultaneously generalizes both noisy network
coding by Lim, Kim, El Gamal, and Chung and distributed decode-and-forward by
Lim, Kim, and Kim. It is not trivial to combine the two schemes because of
inherent incompatibility in their encoding and decoding strategies. We solve
this problem by sending the same long message over multiple blocks at the
source and at the same time by letting the source find the auxiliary covering
indices that carry information about the message simultaneously over all
blocks.
