A Binary Coding Approach for Combination Networks and General Erasure Networks
Paper in proceeding, 2007
We investigate a deterministic binary coding approach for
combination networks. In the literature, network coding schemes
with large alphabet sizes achieve the min-cut capacity. Here, we
propose an approach using binary (GF($2$)) sequences instead of
going to a large alphabet size. In the encoding process, only
cyclic-shifting and XOR operations are used. The encoding
complexity is linear with the length of information bits. The
transfer matrix is sparse, and the decoder can perfectly decode
source information by a sparse-matrix processing approach. Our
approach does not use any redundant bits, and achieves the min-cut
capacity. Further, the code blocks can be produced in a rateless
way. The sink can decode source information from any subset of
code blocks, if the number of received distinct blocks is the same
as that of the information blocks. Thus, we use the code for
general networks with erasure channels. The proposed binary
rateless codes have quite small overheads and can work with a
small number of blocks. With high probability, the codes behave as
maximum distance separable (MDS) codes.