Delete-and-Conquer: Rateless coding with constrained feedback

Traditional rateless codes were designed without the use of a feedback channel, though one is available in many applications. In this work, we build upon recent interest in rateless coding with feedback to produce a novel approach, dubbed Delete-and-Conquer coding, for rateless coding with very little feedback. In our scheme, the feedback used is a measure of distance between a received word and the symbols already decoded at the receiver. This distance, in turn, permits a transmitter to deduce which symbols have been decoded and exclude them from subsequent transmissions. Our approach can be tuned to the specific transmission properties of a given feedback channel, and we empirically show that a very small amount of feedback from receiver back to the transmitter can significantly reduce coding overhead and encoding/decoding complexity. We also provide some analytically backed intuition for this improvement.