Batched network codes (BNCs) are a low-complexity solution for communication through networks with packet loss. Although their belief propagation (BP) performance is proved to approach capacity in the asymptotic regime, there is no evidence indicating that their BP performance is equally good in the finite-length regime. In this paper, we propose a protograph-based construction for BNCs, referred to as protograph-based BNCs (P-BNCs), which significantly differs from existing BNCs in three aspects: 1) The vast majority of existing construction methods mainly focus on the degree distribution of check nodes (CNs), whereas P-BNCs not only specify the degree distributions of CNs and variable nodes (VNs) but also partially constrain the connectivity between CNs and VNs. 2) Traditional BNCs use a fixed degree distribution to generate all batches, making their performance highly sensitive to channel conditions, but P-BNCs achieve good performance under varying channel conditions due to their rate-compatible structures. 3) The construction of PBNCs takes into account joint BP decoding with a sparse precode, whereas traditional constructions typically do not consider a precode, or assume the presence of a precode that can recover a certain fraction of erasures. Thanks to these three improvements, P-BNCs not only have higher achievable rates under varying channel conditions, but more importantly, their BP performance is significantly improved at practical lengths.

翻译：批量网络编码（BNCs）是一种用于在存在丢包的网络中进行通信的低复杂度解决方案。尽管其置信传播（BP）性能在渐近区域被证明接近容量，但尚无证据表明其BP性能在有限长度区域同样优异。本文提出了一种基于原型的BNC构造方法，称为基于原型的批量网络编码（P-BNCs），该方法在三个方面与现有BNC显著不同：1）绝大多数现有构造方法主要关注校验节点（CNs）的度分布，而P-BNCs不仅指定了CNs和变量节点（VNs）的度分布，还部分约束了CNs与VNs之间的连接关系。2）传统BNC使用固定的度分布生成所有批次，导致其性能对信道条件高度敏感，而P-BNCs凭借其速率兼容结构，能够在变化的信道条件下实现良好性能。3）P-BNCs的构造考虑了与稀疏预编码的联合BP解码，而传统构造通常不考虑预编码，或假设存在能够恢复一定比例删除的预编码。得益于这三项改进，P-BNCs不仅在变化的信道条件下具有更高的可达速率，更重要的是，其实用长度下的BP性能得到了显著提升。