Martínez-Peñas and Kschischang (IEEE Trans. Inf. Theory 65(8):4785–4803, 2019) proposed lifted linearized Reed–Solomon codes as suitable codes for error control in multishot network coding. We show how to construct and decode lifted interleaved linearized Reed–Solomon (LILRS) codes. Compared to the construction by Martínez-Peñas–Kschischang, interleaving allows to increase the decoding region significantly and decreases the overhead due to the lifting (i.e., increases the code rate), at the cost of an increased packet size. We propose two decoding schemes for LILRS that are both capable of correcting insertions and deletions beyond half the minimum distance of the code by either allowing a list or a small decoding failure probability. We propose a probabilistic unique Loidreau–Overbeck-like decoder for LILRS codes and an efficient interpolation-based decoding scheme that can be either used as a list decoder (with exponential worst-case list size) or as a probabilistic unique decoder. We derive upper bounds on the decoding failure probability of the probabilistic-unique decoders which show that the decoding failure probability is very small for most channel realizations up to the maximal decoding radius. The tightness of the bounds is verified by Monte Carlo simulations.

Martínez-Peñas 和 Kschischang（IEEE Trans. Inf. Theory 65(8):4785–4803, 2019）提出了提升线性化 Reed-Solomon 码作为多射网络编码中错误控制的合适代码。我们展示了如何构建和解码提升的交错线性化里德所罗门 (LILRS) 码。与 Martínez-Peñas-Kschischang 的构造相比，交织可以显着增加解码区域，并减少由于提升而产生的开销（即增加码率），但代价是增加数据包大小。我们提出了两种 LILRS 解码方案，它们都能够通过允许列表或较小的解码失败概率来纠正超过代码最小距离一半的插入和删除。我们提出了一种用于 LILRS 码的概率唯一的 Loidreau-Overbeck 式解码器和一种基于插值的高效解码方案，该方案可以用作列表解码器（具有指数最坏情况列表大小）或用作概率唯一解码器。我们推导了概率唯一解码器的解码失败概率的上限，这表明对于大多数信道实现，直到最大解码半径，解码失败概率非常小。边界的紧密性通过蒙特卡罗模拟得到验证。