Multiset Codes for Permutation Channels

This paper introduces the notion of multiset codes as relevant to the problem of reliable information transmission over permutation channels. The motivation for studying permutation channels comes from the effect of out of order delivery of packets in some types of packet networks. The proposed codes are a generalization of the so-called subset codes, recently proposed by the authors. Some of the basic properties of multiset codes are established, among which their equivalence to integer codes under the Manhattan metric. The presented coding-theoretic framework follows closely the one proposed by Koetter and Kschischang for the operator channels. The two mathematical models are similar in many respects, and the basic idea is presented in a way which admits a unified view on coding for these types of channels.