Fundamental limits of distributed tracking
Fundamental limits of distributed tracking
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DOI：
10.1109/isit44484.2020.9174006
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
V. Kostina;Babak Hassibi
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文献类型：
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作者：
V. Kostina;Babak Hassibi
考虑以下通信场景。具有记忆的 n 维源由 K 个隔离编码器通过并行通道进行观察，编码器因果性地压缩其观察结果，以通过无噪声速率约束链路传输到解码器。在每个时刻，解码器从观察者接收K个新码字，将它们与过去接收到的码字组合，并产生n个源符号的最新块的最小失真估计。这种情况将经典的一次性 CEO 问题扩展到与保持过去记忆的通信者进行多轮通信。我们证明了一个编码定理，表明实现目标失真所需的最小渐近（n → ∞）可实现和率等于从观察者到解码器的定向互信息，该信息在失真约束和单独编码约束下最小化。对于通过 K 个并行 AWGN 通道观察到的高斯-马尔可夫源，我们解决了最小有向互信息问题，从而建立了最小渐近可实现的和率。最后，我们明确限制了由于观察者之间缺乏沟通而导致的速率损失；在相同观察通道的情况下，可以平等地获得该界限。一般编码定理通过使用随机似然编码器的新非渐近界限来证明，其渐近分析产生了 Berger-Tung 内界到因果设置的扩展。通过反转观察者的通道可以促进高斯情况的分析。
Consider the following communication scenario. An n-dlmensional source with memory is observed by K isolated encoders via parallel channels, who causally compress their observations to transmit to the decoder via noiseless rate-constrained links. At each time instant, the decoder receives K new codewords from the observers, combines them with the past received codewords, and produces a minimum- distortion estimate of the latest block of n source symbols. This scenario extends the classical one-shot CEO problem to multiple rounds of communication with communicators maintaining memory of the past.We prove a coding theorem showing that the minimum asymptotically (as n → ∞) achievable sum rate required to achieve a target distortion is equal to the directed mutual information from the observers to the decoder minimized subject to the distortion constraint and the separate encoding constraint. For the Gauss-Markov source observed via K parallel AWGN channels, we solve that minimal directed mutual information problem, thereby establishing the minimum asymptotically achievable sum rate. Finally, we explicitly bound the rate loss due to a lack of communication among the observers; that bound is attained with equality in the case of identical observation channels.The general coding theorem is proved via a new nonasymptotic bound that uses stochastic likelihood coders and whose asymptotic analysis yields an extension of the Berger-Tung inner bound to the causal setting. The analysis of the Gaussian case is facilitated by reversing the channels of the observers.