Average Throughput with Linear Network Coding over the Binary Field

We introduce the concept of average linear coding throughput when the alphabet is restricted to the binary field. We further investigate the maximum achievable coding throughput compared to integer routing throughput, average integer routing throughput and average linear coding throughput over GF(2) for some networks. We also show that there exist a multicast network solvable over the binary field whose linear coding throughput is a factor Theta (radic|V|) greater than its integer routing throughput, where |V| is the number of nodes in the network