Recently, Martinez-Penas and Kschischang (IEEE Trans. Inf. Theory, 2019) showed that lifted linearized Reed-Solomon codes are suitable codes for error control in multishot network coding. We show how to construct and decode lifted interleaved linearized Reed-Solomon codes. Compared to the construction by Martinez-Penas-Kschischang, interleaving allows to increase the decoding region significantly (especially w.r.t. the number of insertions) and decreases the overhead due to the lifting (i.e., increases the code rate), at the cost of an increased packet size. The proposed decoder is a list decoder that can also be interpreted as a probabilistic unique decoder. Although our best upper bound on the list size is exponential, we present a heuristic argument and simulation results that indicate that the list size is in fact one for most channel realizations up to the maximal decoding radius.
翻译:最近,Martinez-Penas和Kschischang (IEEE Trans. Inf. Theory, 2019) 显示, 解除线性Reed- Solomon 代码是适合多发网络编码中错误控制的代码。 我们展示了如何构建和解码被解除的线性Reed- Solomon 代码。 与 Martinez- Penas- Kschisschang 的构造相比, 互连使得解码区域( 特别是插入数量) 大幅扩大, 并且由于升码( 即增加代码率), 成本会增加包的大小, 降低管理管理 。 提议的解码器是一个列表解码器, 也可以被解释为一种概率性独有的解码器。 尽管我们在列表大小上的最佳上限是指数性, 我们提出了一个超理论和模拟结果, 表明大多数频道实现最大解码半径时, 列表的大小实际上是一个。