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We propose $(k,k')$ stabilizing codes, which is a type of delayless errorcorrection codes that are useful for control over networks with erasures. Foreach input symbol, $k$ output symbols are generated by the stabilizing code.Receiving at least $k'$ of these outputs guarantees stability. Thus, both thesystem to be stabilized and the channel is taken into account in the design ofthe erasure codes. Receiving more than $k'$ outputs further improves theperformance of the system. In the case of i.i.d. erasures, we furtherdemonstrate that the erasure code can be constructed such that stability isachieved if on average at least $k'$ output symbols are received. Our focus ison LTI systems, and we construct codes based on independent encodings andmultiple descriptions. Stability is assessed via Markov jump linear systemtheory. The theoretical efficiency and performance of the codes are assessed,and their practical performances are demonstrated in a simulation study. Thereis a significant gain over other delayless codes such as repetition codes.

Stabilizing Error Correction Codes for Control over Erasure Channels