Algebraic Optimization of Binary Spatially Coupled Measurement Matrices for Interval Passing
Algebraic Optimization of Binary Spatially Coupled Measurement Matrices for Interval Passing
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DOI：
10.1109/itw.2018.8613339
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
Salman Habib;J. Kliewer
中科院分区：
文献类型：
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作者：
Salman Habib;J. Kliewer
我们考虑二进制空间耦合（SC）的低密度测量矩阵的稀疏信号的低复杂度重建通过间隔通过算法（IPA）。已知IPA由于二进制稀疏测量矩阵的坦纳图中存在有害子结构（所谓的termatiko集）而失效。在这项工作中，我们构造基于阵列（AB）SC稀疏测量矩阵，通过代数提升图，使termatiko集的数量最小化的坦纳图。为此，我们表明，最关键的termatiko集的情况下，可以通过消除所有长度为12周期与坦纳图，通过代数提升。因此，与未耦合的AB LDPC测量矩阵相比，具有SC测量矩阵的基于IPA的重构能够为显著密集的信号向量提供几乎无误差的重构。
We consider binary spatially coupled (SC) low density measurement matrices for low complexity reconstruction of sparse signals via the interval passing algorithm (IPA). The IPA is known to fail due to the presence of harmful sub-structures in the Tanner graph of a binary sparse measurement matrix, so called termatiko sets. In this work we construct array-based (AB) SC sparse measurement matrices via algebraic lifts of graphs, such that the number of termatiko sets in the Tanner graph is minimized. To this end, we show for the column-weight-three case that the most critical termatiko sets can be removed by eliminating all length-12 cycles associated with the Tanner graph, via algebraic lifting. As a consequence, IPA-based reconstruction with SC measurement matrices is able to provide an almost error free reconstruction for significantly denser signal vectors compared to uncoupled AB LDPC measurement matrices.