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 is required to write $n$ incoming packets and read $k$ outgoing packets while using $m$ memory banks, each able to write and read one packet per time unit. Each set of $n$ packets written to the switch simultaneously is called a generation. The objective is to store the packets in the banks such that every request of $k$ packets, which can belong to 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 packet request 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. For binary codes, we also study an intermediate model in which a coded packet is formed by the XOR operations of at most two input packets. We present several code constructions and prove the optimality of one family of these codes by providing the corresponding lower bound. Finally, we introduce a construction of conventional switch codes, which improves upon the best known results for the case $n=k$ . [ABSTRACT FROM AUTHOR]