Protocol coding with reordering of user resources: Capacity results for the Z-channel

We consider protocol coding that gives a rise to secondary communication channels, defined by combinatorial ordering of the user resources (packets, channels) in a primary (legacy) communication system. In general, the capacity analysis of the secondary communication channel depends on the way the errors are introduced in the communication. Here we extend the previous results for the capacity of secondary communication channels obtained for the binary erasure channel model, to the case of the Z-channel model. This error model is of practical relevance in secondary communication channels because they are often asymmetric, i.e the probability that a packet will not be detected is much higher than the probability that noise can produce detection of a valid packet, since packet existence is detected through very robust preamble/synchronization sequences. The capacity results are obtained by modelling the secondary channel by a cascade of channels, which proves to be an effective framework for capacity analysis.