喂养或不喂养
To Feed or Not to Feed Back
摘要：
我们研究了有限状态信道（FSC）上的通信，其中编码器和解码器可以控制无噪声反馈的可用性或质量。具体地，瞬时反馈是编码器采取的动作、解码器采取的动作和通道输出的函数。编码器和解码器动作采用有限字母表中的值，并且可能受到平均成本约束。我们证明容量的结果，这样的设置，通过构建一个序列的可实现的速率，使用一个简单的计划的基础上“代码树”的生成，生成信道输入符号以及编码器和解码器的动作。我们证明了这个序列的极限存在。对于给定的块长度和错误概率，我们给出了一个上限的最大可达速率。我们的上限和下限相吻合，从而产生的情况下，初始状态的概率是积极的所有状态的容量。此外，对于静止的不可分解的信道，没有符号间干扰（ISI），容量被给定为输入和输出序列之间的归一化有向信息的限制，最大化超过一个适当的因果关系的条件分布。作为一个重要的特殊情况下，我们考虑的框架“反馈或不反馈”的编码器或解码器采取二进制动作，这决定了当前的通道输出是否将被反馈到编码器，与反馈的通道输出的分数的约束。作为我们的框架的另一个特殊情况下，我们的特点的能力“编码的反向链路”在FSC，即当解码器发送有限速率的瞬时编码的无噪声反馈的反向链路。最后，我们提出了一个扩展的Blahut-Arimoto算法评估的能力时，行动可以成本约束，并证明其应用程序的几个例子。
英文摘要：
We study the communication over Finite State Channels (FSCs), where the encoder and the decoder can control the availability or the quality of the noise-free feedback. Specifically, the instantaneous feedback is a function of an action taken by the encoder, an action taken by the decoder, and the channel output. Encoder and decoder actions take values in finite alphabets, and may be subject to average cost constraints. We prove capacity results for such a setting by constructing a sequence of achievable rates, using a simple scheme based on 'code tree' generation, that generates channel input symbols along with encoder and decoder actions. We prove that the limit of this sequence exists. For a given block length and probability of error, we give an upper bound on the maximum achievable rate. Our upper and lower bounds coincide and hence yield the capacity for the case where the probability of initial state is positive for all states. Further, for stationary indecomposable channels without intersymbol interference (ISI), the capacity is given as the limit of normalized directed information between the input and output sequence, maximized over an appropriate set of causally conditioned distributions. As an important special case, we consider the framework of 'to feed or not to feed back' where either the encoder or the decoder takes binary actions, which determine whether current channel output will be fed back to the encoder, with a constraint on the fraction of channel outputs that are fed back. As another special case of our framework, we characterize the capacity of 'coding on the backward link' in FSCs, i.e. when the decoder sends limited-rate instantaneous coded noise-free feedback on the backward link. Finally, we propose an extension of the Blahut-Arimoto algorithm for evaluating the capacity when actions can be cost constrained, and demonstrate its application on a few examples.
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