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Recent research indicates that packet transmission employing random linearnetwork coding can be regarded as transmitting subspaces over a linear operatorchannel (LOC). In this paper we propose the framework of linear operatorbroadcast channels (LOBCs) to model packet broadcasting over LOCs, and we doinitial work on the capacity region of constant-dimension multiplicativeLOBCs(CMLOBCs), a generalization of broadcast erasure channels. Two fundamentalproblems regarding CMLOBCs are addressed-finding necessary and sufficientconditions for degradation and deciding whether time sharing suffices toachieve the boundary of the capacity region in the degraded case.

Towards the Capacity Region of Multiplicative Linear Operator Broadcast Channels