An Improved Bound on the List Error Probability and List Distance Properties
An Improved Bound on the List Error Probability and List Distance Properties
复制标题
列表错误概率和列表距离属性的改进界限
DOI：
10.1109/tit.2007.911176
复制
发表时间：
2008
影响因子：
2.5
通讯作者：
M. Loncar
中科院分区：
文献类型：
--
作者：
I. Bocharova;R. Johannesson;B. Kudryashov;M. Loncar
研究了加性白色高斯噪声信道下二进制分组码的列表译码问题。列表解码器的输出是最可能码字的列表，即，在欧几里得度量意义上最接近接收信号的信号点。当发送的码字不在此列表上时，发生解码错误。它示出的列表错误概率是完全由所谓的列表配置矩阵，这是从形成列表的信号向量获得的Gram矩阵描述。最坏情况列表配置矩阵确定代码的最小列表距离，这是列表解码的情况下的最小距离的推广。研究了列表配置矩阵的一些性质，并建立了它们与列表距离的关系。进一步利用这些结果，以获得一个新的上限列表错误概率，这是严格的比以前已知的界限。这个界是通过结合技术获得的切向联盟界与一个改进的边界上的错误概率为一个给定的列表。最后用实例说明了结果。
List decoding of binary block codes for the additive white Gaussian noise (AWGN) channel is considered. The output of a list decoder is a list of the most likely codewords, that is, the signal points closest to the received signal in the Euclidean-metric sense. A decoding error occurs when the transmitted codeword is not on this list. It is shown that the list error probability is fully described by the so-called list configuration matrix, which is the Gram matrix obtained from the signal vectors forming the list. The worst case list configuration matrix determines the minimum list distance of the code, which is a generalization of the minimum distance to the case of list decoding. Some properties of the list configuration matrix are studied and their connections to the list distance are established. These results are further exploited to obtain a new upper bound on the list error probability, which is tighter than the previously known bounds. This bound is derived by combining the techniques for obtaining the tangential union bound with an improved bound on the error probability for a given list. The results are illustrated by examples.