Motivated by control with communication constraints, in this work we develop a time-invariant data compression architecture for linear-quadratic-Gaussian (LQG) control with minimum bitrate prefix-free feedback. For any fixed control performance, the approach we propose nearly achieves known directed information (DI) lower bounds on the time-average expected codeword length. We refine the analysis of a classical achievability approach, which required quantized plant measurements to be encoded via a time-varying lossless source code. We prove that the sequence of random variables describing the quantizations has a limiting distribution and that the quantizations may be encoded with a fixed source code optimized for this distribution without added time-asymptotic redundancy. Our result follows from analyzing the long-term stochastic behavior of the system, and permits us to additionally guarantee that the time-average codeword length (as opposed to expected length) is almost surely within a few bits of the minimum DI. To our knowledge, this time-invariant achievability result is the first in the literature. The originally published version of the supplementary material included a proof that contained an error that turned out to be inconsequential. This updated preprint corrects this error, which originally appeared under Lemma A.7.

翻译：受通信约束控制的启发，本文针对线性二次高斯（LQG）控制问题，提出了一种具有最小比特率无前缀反馈的时间不变数据压缩架构。对于任意固定的控制性能，所提方法几乎达到了时间平均期望码字长度的已知有向信息（DI）下界。我们改进了经典可实现性方法的分析——该方法需要用时变无损信源编码对量化后的系统状态测量值进行编码。我们证明了描述量化过程的随机变量序列具有极限分布，并且可以通过针对该分布优化的固定信源编码进行无时间渐近冗余的编码。该结论源于对系统长期随机行为的分析，并进一步保证时间平均码字长度（而非期望长度）几乎必然与最小DI相差几个比特以内。据我们所知，这一时间不变可实现性结果是文献中的首个成果。原版发表的补充材料中包含一个被证明无实质性影响的证明错误，本更新预印本已修正该错误（原见于引理A.7）。