The CEO Problem With Inter-Block Memory
The CEO Problem With Inter-Block Memory
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DOI：
10.1109/tit.2021.3111658
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发表时间：
2019-10
影响因子：
2.5
通讯作者：
V. Kostina;B. Hassibi
中科院分区：
文献类型：
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作者：
V. Kostina;B. Hassibi
一个$n$维的源与记忆观察$K$隔离编码器通过并行通道，压缩他们的意见，通过无噪声的速率约束的链接，同时利用他们的记忆过去发送到解码器。在每个时刻，解码器从观察者接收$K$新码字，将它们与过去接收的码字组合，并产生$n$源符号的最新块的最小失真估计。这种情况下扩展了经典的一次性CEO的问题，以保持过去的记忆与沟通者的多轮沟通。我们扩展的Berger-Tung的内部和外部边界的情况下，与块间记忆，显示最小的渐近（$n \to \infty $）实现目标失真所需的总和率是有界的最小有向互信息问题。对于高斯-马尔可夫源通过$K$并行AWGN信道观察，我们证明了内界是紧的，并解决了相应的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，我们明确地绑定率损失，由于缺乏观察员之间的通信，该绑定是达到平等的情况下，相同的观察渠道。一般的编码定理证明通过一个新的非渐近界，使用随机似然编码器和渐近分析产生的扩展的Berger-Tung内界的因果设置。高斯情况下的分析是通过颠倒观察者的通道来促进的。
An $n$ -dimensional source with memory is observed by $K$ isolated encoders via parallel channels, who compress their observations to transmit to the decoder via noiseless rate-constrained links while leveraging their memory of the past. 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 the memory of the past. We extend the Berger-Tung inner and outer bounds to the scenario with inter-block memory, showing that the minimum asymptotically (as $n \to \infty $ ) achievable sum rate required to achieve a target distortion is bounded by minimal directed mutual information problems. For the Gauss-Markov source observed via $K$ parallel AWGN channels, we show that the inner bound is tight and solve the corresponding 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.