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We study fixed data rate communication schemes for wireless relay-interference networks with any number of transmitters, relays, and receivers. The transmitters and the relays have individual short-term power constraints. We analyze both amplify- and-forward (AF) and decode-and-forward (DF) relaying strategies with a two channel use quantized network beamforming protocol. We design the quantizer of the channel state information to minimize the probability that at least one receiver incorrectly decodes its desired symbol(s). Correspondingly, we introduce a generalized diversity measure that encapsulates the conventional one as the first-order diversity. Additionally, it incorporates the second-order diversity, which is concerned with the transmitter power dependent logarithmic terms that appear in the error rate expression. We first show that for AF relays, the maximal achievable diversity in the presence of interference is strictly less than the transmit diversity bound in terms of the second-order diversity. We then prove that it is possible to achieve the transmit diversity bound using DF relays as if there is no interference and as if coding over an arbitrary number of channel uses is allowed. Relay selection provides the best possible diversity gain for both relaying strategies. Finally, we show that all the aforementioned diversity gains can be achieved using distributed decision making with asymptotically zero feedback rate per receiver. Such a performance is made possible by a special distributed quantizer design method we have called localization.