Density evolution, thresholds and the stability condition for non-binary LDPC codes
Density evolution, thresholds and the stability condition for non-binary LDPC codes
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DOI：
10.1049/ip-com:20050230
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发表时间：
2005-12-01
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影响因子：
--
通讯作者：
Urbanke, R
中科院分区：
文献类型：
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作者：
Rathi, V;Urbanke, R
当二进制擦除通道上发生传输时，非二元低密度平价检查（LDPC）的密度演变方程将被得出。引入了相对于二进制场上的通用线性组定义的集合。对于这些集合，密度演化方程可以紧凑。通用线性组的密度演化有助于理解针对有限场定义的代码的密度演化。针对各种LDPC合奏的不同字母大小计算阈值。令人惊讶的是，阈值不是字母大小的单调函数。陈述了任何二进制无内存对称通道上非二元LDPC合奏的稳定性条件。根据出口曲线和区域定理的各种非二进制集合的地图阈值上的上限。
The density evolution equations for non-binary low-density parity-check (LDPC) ensembles when transmission takes place over the binary erasure channel are derived. Ensembles defined with respect to the general linear group over the binary field are introduced. For these ensembles the density evolution equations can be written compactly. The density evolution for the general linear group helps in understanding the density evolution for codes defined with respect to finite fields. Thresholds are computed for different alphabet sizes for various LDPC ensembles. Surprisingly, the threshold is not a monotonic function of the alphabet size. The stability condition for non-binary LDPC ensembles over any binary memoryless symmetric channel is stated. Upper bounds on the MAP thresholds for various non-binary ensembles based on EXIT curves and the area theorem are given.