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LT (Luby transform) codes are a celebrated family of rateless erasure codes(RECs). Most of existing LT codes were designed for applications in which acentralized encoder possesses all message blocks and is solely responsible forencoding them into codewords. Distributed LT codes, in which message blocks arephysically scattered across multiple different locations (encoders) that needto collaboratively perform the encoding, has never been systemically studiedbefore despite its growing importance in applications. In this work, we presentthe first systemic study of LT codes in the distributed setting, and make thefollowing three major contributions. First, we show that only a proper subsetof LT codes are feasible in the distributed setting, and give the sufficientand necessary condition for such feasibility. Second, we propose a distributedencoding protocol that can efficiently implement any feasible code. Theprotocol is parameterized by a so-called action probability array (APA) that isonly a few KBs in size, and any feasible code corresponds to a valid APAsetting and vice versa. Third, we propose two heuristic search algorithms thathave led to the discovery of feasible codes that are much more efficient thanthe state of the art.

RECIPE: Rateless Erasure Codes Induced by Protocol-Based Encoding