Abelian Group Codes for Channel Coding and Source Coding
Abelian Group Codes for Channel Coding and Source Coding
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DOI：
10.1109/tit.2015.2407874
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发表时间：
2015-05-01
影响因子：
2.5
通讯作者：
Pradhan, S. Sandeep
中科院分区：
文献类型：
--
作者：
Sahebi, Aria Ghasemian;Pradhan, S. Sandeep
本文研究了任意离散（有限字母表）无记忆信道的信道编码问题以及任意离散（有限字母表）无记忆信源的有损信源编码问题的阿贝尔群码的渐近性能。对于信道编码问题，我们发现容量的特点是在一个单字母的信息理论的形式。当底层组是字段时，这简化为通道的对称容量。对于信源编码的问题，我们推导出可实现的率失真函数，其特征在于在一个单字母的信息理论的形式。当底层群是场时，它简化为对称率失真函数。我们给出几个说明性的例子。由于所考虑的源和通道的非对称性，我们的分析使用了信息论和群论工具的协同作用。
In this paper, we study the asymptotic performance of Abelian group codes for the channel coding problem for arbitrary discrete (finite alphabet) memoryless channels as well as the lossy source coding problem for arbitrary discrete (finite alphabet) memoryless sources. For the channel coding problem, we find the capacity characterized in a single-letter information-theoretic form. This simplifies to the symmetric capacity of the channel when the underlying group is a field. For the source coding problem, we derive the achievable rate-distortion function that is characterized in a single-letter information-theoretic form. When the underlying group is a field, it simplifies to the symmetric rate-distortion function. We give several illustrative examples. Due to the nonsymmetric nature of the sources and channels considered, our analysis uses a synergy of information-theoretic and group-theoretic tools.