We propose $(k,k')$ stabilizing codes, which is a type of delayless error correction codes that are useful for control over networks with erasures. For each input symbol, $k$ output symbols are generated by the stabilizing code. Receiving at least $k'$ of these outputs guarantees stability. Thus, both the system to be stabilized and the channel is taken into account in the design of the erasure codes. Receiving more than $k'$ outputs further improves the performance of the system. In the case of i.i.d. erasures, we further demonstrate that the erasure code can be constructed such that stability is achieved if on average at least $k'$ output symbols are received. Our focus is on LTI systems, and we construct codes based on independent encodings and multiple descriptions. Stability is assessed via Markov jump linear system theory. The theoretical efficiency and performance of the codes are assessed, and their practical performances are demonstrated in a simulation study. There is a significant gain over other delayless codes such as repetition codes.
翻译:我们建议使用$(k,k')$稳定代码, 这是一种无拖延的错误校正代码, 可用于控制带有删除的网络。 对于每个输入符号, 由稳定代码生成 $k$ 输出符号。 接收这些输出的至少 $k$ 就能保证稳定性。 因此, 在删除代码的设计中, 需要稳定的系统和频道都会得到考虑。 接收超过 $k' 的输出会进一步提高系统的性能。 在 i. d. 删除 的情况下, 我们进一步证明, 取消代码可以构建为稳定, 如果平均接收至少 $k' 输出符号。 我们的焦点是 LTI 系统, 我们根据独立的编码和多个描述构建代码。 稳定是通过Markov 跳跃线性系统理论进行评估的。 代码的理论效率和性能会得到评估, 并在模拟研究中展示其实际性能。 在重复代码等其他不延迟的代码上, 有显著的收益。