Consecutive switch codes

Switch codes, first proposed by Wang et al., are codes that are designed to increase the parallelism of data writing and reading processes in network switches. A network switch consists of n input ports, k output ports, and m banks which store new arriving packets from the input ports in each time slot, called a generation. The objective is to store the packets in the banks such that every request of k packets by the output ports, which can be from previous generations, can be handled by reading at most one packet from every bank. In this paper we study a new type of switch codes that can simultaneously deliver large symbol requests and good coding rate. These attractive features are achieved by relaxing the request model to a natural sub-class we call consecutive requests. For this new request model we define a new type of codes called consecutive switch codes. These codes are studied in both the computational and combinatorial models, corresponding to whether the data can be encoded or not. We present several code constructions and prove the optimality of one family of these codes by providing the corresponding lower bound. Lastly, we introduce a construction of switch codes for the case n = k, which improves upon the best known results for this case.