  To reduce computational complexity and delay in randomized network coded
content distribution (and for some other practical reasons), coding is not
performed simultaneously over all content blocks but over much smaller subsets
known as generations. A penalty is throughput reduction. We model coding over
generations as the coupon collector's brotherhood problem. This model enables
us to theoretically compute the expected number of coded packets needed for
successful decoding of the entire content, as well as a bound on the
probability of decoding failure, and further, to quantify the tradeoff between
computational complexity and throughput. Interestingly, with a moderate
increase in the generation size, throughput quickly approaches link capacity.
As an additional contribution, we derive new results for the generalized
collector's brotherhood problem which can also be used for further study of
many other aspects of coding over generations.
