Run-Length Properties of a Reed-Muller RM(1,m) Code with Applications in Channels with at Most One Synchronization Error

机译：Reed-Muller RM（1，m）码的运行长度特性及其在最多具有一个同步误差的通道中的应用

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In this paper we analyze the performance of a Reed-Muller(1,m) code in channels where at most one synchronization error, viewed as either a repetition or a deletion of a bit, occurs. We first establish several useful properties of the run-lengths of a Reed-Muller(1,m) code. Based on the transformation of a code in which a repetition operation becomes an insertion of a zero operation, we conclude that a Reed-Muller(1,m) code is immune to a sampling error that causes a single repetition of a bit. By analyzing the image of the code under this same transformation, and utilizing the previously established properties of a Reed-Muller(1,m) code, we are able to enumerate all pairs of sequences of this code that can result in the same received sequence when a sampling error causes a deletion of a bit. In addition, we propose a simple way to prune the code so that the resulting linear subcode is immune to a single deletion.

机译：在本文中，我们分析了Reed-Muller（1，m）码在最多出现一个同步错误（被视为重复或删除位）的通道中的性能。我们首先建立Reed-Muller（1，m）代码游程长度的几个有用属性。根据其中重复操作变为零操作插入的代码转换，我们得出结论，Reed-Muller（1，m）代码不受引起单个位重复的采样错误的影响。通过分析相同转换下的代码映像，并利用先前建立的Reed-Muller（1，m）代码的属性，我们可以枚举该代码的所有序列对，这些序列对可以导致相同的接收序列当采样错误导致位删除时。此外，我们提出了一种修剪代码的简单方法，以使生成的线性子代码不受单个删除的影响。

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《Annual Allerton Conference on Communication, Control, and Computing; 20040929-1001; Monticello,IL(US)》|2004年|P.270-279|共10页
会议地点 MonticelloIL(US)
作者
Lara Dolecek; Venkat Anantharam;
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Dept. of Electrical Engineering and Computer Sciences University of California, Berkeley Berkeley, CA, 94720;

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正文语种 eng
中图分类通信;
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1. Using Reed–Muller ${hbox{RM}},(1, m)$ Codes Over Channels With Synchronization and Substitution Errors [J] . Dolecek L., Anantharam V. IEEE Transactions on Information Theory . 2007,第4期

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2. Using Reed–Muller ${hbox{RM}},(1, m)$ Codes Over Channels With Synchronization and Substitution Errors [J] . Lara Dolecek, Venkat Anantharam IEEE Transactions on Information Theory . 2007,第期

机译：在具有同步和替换错误的通道上使用Reed–Muller $ {hbox {RM}} ,,（1，m）$代码
3. A survey of error-correcting codes for channels with symbol synchronization errors [J] . Communications Surveys & Tutorials, IEEE . 2010,第1期

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4. Run-Length Properties of a Reed-Muller RM(1,m) Code with Applications in Channels with at Most One Synchronization Error [C] . Lara Dolecek, Venkat Anantharam, University of Illinois at Urbana-Champaign, Annual Allerton Conference on Communication, Control, and Computing . 2004

机译：REED-MULLER RM（1，M）代码的运行长度属性，其中包含最多一个同步错误的通道中的应用程序
5. Design & analysis for practical LDPC-coded systems from broadcast channel to low error-floor applications. [D] . Kyung, Gyu Bum. 2011

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7. Some general results of coding theory with applications to the study of codes for the correction of synchronization errors [O] . Calabi L., Hartnett W.E. 1969

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8. Some General Results of Coding Theory with Applications to the Study of Codes for the Correction of Synchronization Errors [R] . Calabi, L., Hartnett, W. E. 1968

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Run-Length Properties of a Reed-Muller RM(1,m) Code with Applications in Channels with at Most One Synchronization Error

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