Diversity Coding in Two-Connected Networks

In this paper, we propose a new proactive recovery scheme against single edge failures for unicast connections in transport networks. The new scheme is a generalization of diversity coding where the source data AB are split into two parts A and B and three data flows A, B, and their exclusive OR (XOR) A⊕B are sent along the network between the source and the destination node of the connection. By ensuring that two data flows out of the three always operate even if a single edge fails, the source data can be instantaneously recovered at the destination node. In contrast with diversity coding, we do not require the three data flows to be routed along three disjoint paths; however, in our scheme, a data flow is allowed to split into two parallel segments and later merge back. Thus, our generalized diversity coding (GDC) scheme can be used in sparse but still two-connected network topologies. Our proof improves an earlier result of network coding, by using purely graph theoretical tool set instead of algebraic argument. In particular, we show that when the source data are divided into two parts, robust intra-session network coding against single edge failures is always possible without any in-network algebraic operation. We present linear-time robust code construction algorithms for this practical special case in minimal coding graphs. We further characterize this question, and show that by increasing the number of edge failures and source data parts, we lose these desired properties.