Minimum-Rate Spectrum-Blind Sampling Based on Sparse-Graph Codes.
IEEE Trans. Signal Process.（2023）
摘要
We study the problem of
spectrum-blind
sampling, that is, sampling signals with sparse spectra whose frequency support is unknown. The minimum sampling rate for this class of signals has been established as twice the measure of its frequency support; however, constructive schemes that achieve this minimum rate are not known to exist, to the best of our knowledge. We propose a novel
constructive
sampling framework by leveraging tools from
modern coding theory
, which has been largely untapped in the field of sampling. We make interesting connections between the problem of spectrum-blind sampling, and that of designing erasure-correcting codes based on sparse graphs. Our key idea is to cleverly exploit the aliasing artifacts induced by subsampling, introducing linear mixing of spectral components in the form of parity constraints for
sparse-graph codes
. We achieve this by subsampling the input signal after filtering it using a carefully designed ‘sparse-graph coded filter bank’, where the pass-band patterns are designed to match the parity-check constraints of a sparse-graph code. We show that the signal reconstruction under this scheme is equivalent to the fast “peeling“ decoding of sparse-graph codes. We further show that the achievable sampling rate is determined by the
rate
of the codes used in the filter bank. As a result, based on insights derived from the design of capacity-achieving sparse-graph codes, we can
simultaneously
approach the minimum sampling rate for spectrum-blind sampling and low computational complexity based on fast peeling-based decoding with operations per unit of time scaling
linearly
with the sampling rate.
更多查看译文
关键词
Sampling methods,error correction codes,filtering
AI 理解论文
溯源树
样例
生成溯源树，研究论文发展脉络
Chat Paper
正在生成论文摘要