Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation
Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation
复制标题
DOI：
10.1109/tit.2013.2280915
复制
发表时间：
2013-12-01
影响因子：
2.5
通讯作者：
Urbanke, Ruediger L.
中科院分区：
文献类型：
--
作者：
Kudekar, Shrinivas;Richardson, Tom;Urbanke, Ruediger L.
我们研究空间耦合的代码集成。对于在二进制擦除信道上的传输，最近表明，空间耦合将集合的置信传播阈值增加到基本上底层组件集合的最大先验阈值。这就解释了为什么最初由Felstrom和Zigangirov引入的卷积LDPC集成在这个信道上表现如此出色。我们证明了等价的结果适用于一般的二进制输入无记忆输出对称信道的传输。更确切地说，给定期望的错误概率和容量间隙，我们可以构建一个空间耦合的系综，该系综在置信传播解码下普遍满足这类信道上的这些约束。事实上，这个集合中的大多数码都具有这种性质。量词universal指的是对所有信道都好的单个系综/码，但我们假设该信道在接收器处是已知的。关键的技术结果是证明，在置信传播解码下，空间耦合的合奏基本上实现了底层的非耦合合奏的面积阈值。最后，我们讨论一些有趣的开放问题。
We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a priori threshold of the underlying component ensemble. This explains why convolutional LDPC ensembles, originally introduced by Felstrom and Zigangirov, perform so well over this channel. We show that the equivalent result holds true for transmission over general binary-input memoryless output-symmetric channels. More precisely, given a desired error probability and a gap to capacity, we can construct a spatially coupled ensemble that fulfills these constraints universally on this class of channels under belief propagation decoding. In fact, most codes in this ensemble have this property. The quantifier universal refers to the single ensemble/code that is good for all channels but we assume that the channel is known at the receiver. The key technical result is a proof that, under belief-propagation decoding, spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble. We conclude by discussing some interesting open problems.