Threshold saturation of spatially coupled sparse superposition codes for all memoryless channels
Threshold saturation of spatially coupled sparse superposition codes for all memoryless channels
复制标题
所有无记忆通道的空间耦合稀疏叠加码的阈值饱和
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
N. Macris
中科院分区：
文献类型：
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作者：
Jean Barbier;M. Dia;N. Macris
最近我们证明了在加性白色高斯噪声信道上空间耦合稀疏叠加码的门限饱和性[1]。在这里，我们将我们的分析推广到更广泛的背景。我们表明，对于任何无记忆信道，空间耦合允许广义近似消息传递（GAMP）解码达到潜在的（或贝叶斯最优）阈值的代码集成。此外，在大输入字母表大小限制下：i）底层（或非耦合）码系综的GAMP算法阈值被简单地表示为Fisher信息; ii）潜在阈值倾向于香农容量。虽然我们专注于编码与我们以前的结果的一致性，框架和方法是非常普遍的，并举行了广泛的一类广义估计问题的随机线性混合。
We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel [1]. Here we generalize our analysis to a much broader setting. We show for any memoryless channel that spatial coupling allows generalized approximate message-passing (GAMP) decoding to reach the potential (or Bayes optimal) threshold of the code ensemble. Moreover in the large input alphabet size limit: i) the GAMP algorithmic threshold of the underlying (or uncoupled) code ensemble is simply expressed as a Fisher information; ii) the potential threshold tends to Shannon's capacity. Although we focus on coding for sake of coherence with our previous results, the framework and methods are very general and hold for a wide class of generalized estimation problems with random linear mixing.