Identification over Compound Multiple-Input Multiple-Output Broadcast Channels

Abstract

The identification (ID) capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter ID capacity formulas for discrete channels and MIMO Gaussian channels, under an average input constraint. The capacity theorems apply to general broadcast channels. This is in contrast to the transmission setting, where the capacity is only known for special cases, notably the degraded broadcast channel and the MIMO broadcast channel with private messages. Furthermore, the ID capacity region of the compound MIMO broadcast channel is in general larger than the transmission capacity region. This is a departure from the single-user behavior of ID, since the ID capacity of a single-user channel equals the transmission capacity.

Identification Over Quantum Broadcast Channels

“…Related settings were also considered in [26][27][28]. The authors of the present paper have recently considered ID over the classical compound multiple-input multiple-output (MIMO) broadcast channel [29,30].…”

“…While the properties above are analogous to the classical setting [29], the analysis is more involved. To prove the direct part, we extend the pool-selection method due to Bracher and Lapidoth [24,25] to the quantum setting.…”