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In this paper, we discuss the joint precoding with finite rate feedback in the so-called network multiple-input multiple-output (MIMO) where the TXs share the knowledge of the data symbols to be transmitted. We introduce a distributed channel state information (DCSI) model where each TX has its own local estimate of the overall multiuser MIMO channel and must make a precoding decision solely based on the available local CSI. We refer to this channel as the DCSI-MIMO channel and the precoding problem as distributed precoding. We extend to the DCSI setting the work from Jindal in 2006 for the conventional MIMO broadcast channel (BC) in which the number of degrees of freedom (DoFs) achieved by zero forcing (ZF) was derived as a function of the scaling in the logarithm of the signal-to-noise ratio of the number of quantizing bits. Particularly, we show the seemingly pessimistic result that the number of DoFs at each user is limited by the worst CSI across all users and across all TXs. This is in contrast to the conventional MIMO BC where the number of DoFs at one user is solely dependent on the quality of the estimation of his own feedback. Consequently, we provide precoding schemes improving on the achieved number of DoFs. For the two-user case, the derived novel precoder achieves a number of DoFs limited by the best CSI accuracy across the TXs instead of the worst with conventional ZF. We also advocate the use of hierarchical quantization of the CSI, for which we show that considerable gains are possible. Finally, we use the previous analysis to derive the DoFs optimal allocation of the feedback bits to the various TXs under a constraint on the size of the aggregate feedback in the network, in the case where conventional ZF is used.