Batched sparse (BATS) code is a class of batched network code that can achieve a close-to-optimal rate when an optimal degree distribution is provided. We observed that most probability masses in this optimal distribution are very small, i.e., the distribution "looks" sparse. In this paper, we investigate the sparsity optimization of degree distribution for BATS codes that produces sparse degree distributions. There are many advantages to use a sparse degree distribution, say, it is robust to precision errors when sampling the degree distribution during encoding and decoding in practice. We discuss a few heuristics and also a way to obtain an exact sparsity solution. These approaches give a trade-off between computational time and achievable rate, thus give us the flexibility to adopt BATS codes in various scenarios, e.g., device with limited computational power, stable channel condition, etc.

翻译：批处理稀疏（BATS）码是一类批处理网络编码，当提供最优度分布时能够实现接近最优的传输速率。我们观察到该最优分布中的大部分概率质量非常小，即该分布“呈现”稀疏特性。本文研究BATS码度分布的稀疏优化，以生成稀疏度分布。采用稀疏度分布具有诸多优势，例如在实际编码和解码过程中对度分布进行采样时，其对精度误差具有鲁棒性。我们探讨了几种启发式方法以及获得精确稀疏解的途径。这些方法在计算时间与可达速率之间提供了权衡，从而使我们能够灵活地在不同场景中应用BATS码，例如计算能力受限的设备、信道条件稳定的环境等。