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We consider the following packet coding scheme: The coding node has a fixed, finite memory in which it stores packets formed from an incoming packet stream, and it sends packets formed from random linear combinations of its memory contents. We analyze the scheme in two settings: as a self-contained component in a network providing reliability on a single link, and as a component employed at intermediate nodes in a block-coded end-to-end connection. We believe that the scheme is a good alternative to automatic repeat request when feedback is too slow, too unreliable, or too difficult to implement.