Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. I
Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. I
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DOI：
10.1109/9780470544242.ch23
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
N. Sloane;A. Wyner
中科院分区：
文献类型：
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作者：
N. Sloane;A. Wyner
给出了在有噪声的离散无记忆信道上通过使用块编码可以实现的最小差错概率的新下界。像以前的上界一样，这些下界随着块长度N的增加而指数减小。指数中N的系数是速率的凸函数。从一定的传输速率到信道容量，上下限的指数重合。在这个特定的速率下，上界和下界的指数不同，尽管当速率接近零时，它们接近相同的极限。文中给出了实例，并发展了与编码理论有关的各种附带结果和技术。本文分为两个部分：第一部分总结了主要结果，并详细讨论了高传输率的情况；第二部分将在后续问题中讨论低传输率的情况。
New lower bounds are presented for the minimum error probability that can be achieved through the use of block coding on noisy discrete memoryless channels. Like previous upper bounds, these lower bounds decrease exponentially with the block length N . The coefficient of N in the exponent is a convex function of the rate. From a certain rate of transmission up to channel capacity, the exponents of the upper and lower bounds coincide. Below this particular rate, the exponents of the upper and lower bounds differ, although they approach the same limit as the rate approaches zero. Examples are given and various incidental results and techniques relating to coding theory are developed. The paper is presented in two parts: the first, appearing here, summarizes the major results and treats the case of high transmission rates in detail; the second, to appear in the subsequent issue, treats the case of low transmission rates.