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arXiv 1306.1632cs.ITmath.IT
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分布式通信中的广义信道编码理论

A Generalized Channel Coding Theory for Distributed Communication

Jie Luo

摘要:

本文给出了一个时隙分布式通信系统的广义信道编码定理,其中一个发射机-接收机对与其他发射机并行通信。假设在每个时隙中任意选择每个发射机的信道码。发射机的编码选择由码索引参数表示,该码索引参数既不为其他发射机所知,也不为接收机所知。系统的基本性能限制的特征在于使用在代码索引向量的空间中定义的可实现区域。当码字长度取为无穷大时,对于区域内的所有代码索引向量,接收器将可靠地解码消息,而对于区域外的所有代码索引向量,接收器将可靠地报告冲突。一个广义的系统错误性能指标被定义为不同类型的通信错误事件的概率的加权和。假设接收器选择“操作区域”,并且如果代码索引向量在操作区域内,则打算解码消息。在有限码字长度的假设下,得到了操作区域和广义误差性能度量之间折衷的可验证界。

英文摘要:

This paper presents generalized channel coding theorems for a time-slotted distributed communication system where a transmitter-receiver pair is communicating in parallel with other transmitters. Assume that the channel code of each transmitter is chosen arbitrarily in each time slot. The coding choice of a transmitter is denoted by a code index parameter, which is known neither to other transmitters nor to the receiver. Fundamental performance limitation of the system is characterized using an achievable region defined in the space of the code index vectors. As the codeword length is taken to infinity, for all code index vectors inside the region, the receiver will decode the message reliably, while for all code index vectors outside the region, the receiver will report a collision reliably. A generalized system error performance measure is defined as the weighted sum of probabilities of different types of communication error events. Assume that the receiver chooses an "operation region" and intends to decode the message if the code index vector is inside the operation region. Achievable bounds on the tradeoff between the operation region and the generalize error performance measure are obtained under the assumption of a finite codeword length.

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