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We examine the problem of minimizing feedback in reliable wireless broadcasting by pairing rateless coding with extreme value theory. Our key observation is that, in a broadcast environment, this problem resolves into estimating the maximum number of packets dropped among many receivers rather than for each individual receiver. With rateless codes, this estimation relates to the number of redundant transmissions needed at the source in order for all receivers to correctly decode a message with high probability. We develop and analyze two new data dissemination protocols, called Random Sampling (RS) and Full Sampling with Limited Feedback (FSLF), based on the moment and maximum likelihood estimators in extreme value theory. Both protocols rely on a single-round learning phase, requiring the transmission of a few feedback packets from a small subset of receivers. With fixed overhead, we show that FSLF has the desirable property of becoming more accurate as the receivers' population gets larger. Our protocols are channel-agnostic, in that they do not require a priori knowledge of (i.i.d.) packet loss probabilities, which may vary among receivers. We provide simulations and an improved full-scale implementation of the Rateless Deluge over-the-air programming protocol on sensor motes as a demonstration of the practical benefits of our protocols, which translate into about 30% latency and energy consumption savings. Furthermore, we apply our protocols to real-time (RT) oblivious rateless codes in broadcast settings. Through simulations, we demonstrate a 100-fold reduction in the amount of feedback packets while incurring an increase of only 10%–20% in the number of encoded packets transmissions.