A Binary Coding Approach for Combination Networks and General Erasure Networks

Abstract

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.