  One key requirement for fountain (rateless) coding schemes is to achieve a
high intermediate symbol recovery rate. Recent coding schemes have incorporated
the use of a feedback channel to improve intermediate performance of
traditional rateless codes; however, these codes with feedback are designed
based on uniformly at random selection of input symbols. In this paper, on the
other hand, we develop feedback-based fountain codes with dynamically-adjusted
nonuniform symbol selection distributions, and show that this characteristic
can enhance the intermediate decoding rate. We provide an analysis of our
codes, including bounds on computational complexity and failure probability for
a maximum likelihood decoder; the latter are tighter than bounds known for
classical rateless codes. Through numerical simulations, we also show that
feedback information paired with a nonuniform selection distribution can highly
improve the symbol recovery rate, and that the amount of feedback sent can be
tuned to the specific transmission properties of a given feedback channel.
