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Efficient Coding for Interactive Communicalion

机译:交互式交流的高效编码

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摘要

We revisit the problem of reliable interactive communication over a noisy channel and obtain the first fully (randomized) efficient constant-rate emulation procedure for reliable interactive communication. Our protocol works for any discrete memoryless noisy channel with constant capacity and fails with exponentially small probability in the total length of the protocol. Following a work by Schulman (1993), our simulation uses a tree-code, yet as opposed to the nonefficient construction of absolute tree-code used by Schulman, we introduce a relaxation in the notion of goodness for a tree code and define a potent tree code. This relaxation allows us to construct an efficient emulation procedure for any two-party protocol. Our results also extend to the case of interactive multiparty communication. We show that a randomly generated tree code (with suitable constant alphabet size) is an efficiently decodable potent tree code with overwhelming probability. Furthermore, we are able to partially derandomize this result by means of epsilon-biased distributions using only $O(N)$ random bits, where $N$ is the depth of the tree.
机译:我们重新审视了在嘈杂的信道上进行可靠的交互式通信的问题,并获得了第一个用于可靠的交互式通信的完全(随机)有效的恒定速率仿真过程。我们的协议适用于任何具有恒定容量的离散无记忆噪声通道,并且在协议总长度中以极小的概率失败。在Schulman(1993)的工作之后,我们的模拟使用树代码,但是与Schulman使用的绝对树代码的效率低下相反,我们引入了树代码善意的概念,并定义了有效的树代码。这种放松使我们能够为任何两方协议构建有效的仿真过程。我们的结果还扩展到交互式多方通信的情况。我们表明,随机生成的树代码(具有适当的恒定字母大小)是具有压倒性概率的可有效解码的有效树代码。此外,我们可以通过仅使用$ O(N)$个随机位的ε偏分布对部分结果进行随机化处理,其中$ N $是树的深度。

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