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

翻译：LT（Luby变换）码是一类著名的无速率纠删码（RECs）。现有LT码多数针对集中式编码器场景设计，即编码器拥有所有消息块并独立完成编码。尽管分布式应用日益重要，但针对消息块物理分散于多个不同位置（编码器）需协同编码的分布式LT码，此前尚未得到系统性研究。本文首次系统研究了分布式场景下的LT码，并提出以下三项主要贡献：第一，证明仅部分LT码适用于分布式场景，并给出其可行性充要条件；第二，提出一种分布式编码协议，可高效实现任意可行码。该协议由仅数KB大小的所谓动作概率阵列（APA）参数化，任意可行码对应有效的APA设定，反之亦然；第三，提出两种启发式搜索算法，由此发现比现有技术效率显著更高的可行码。