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- Chao-Bing Song, Shu-Tao Xia, Xin-Ji Liu
- ArXiv
- 2013

—In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing with the well-known ℓ1-minimization. Restricted isometry property (RIP) and restricted isometry constant (RIC) of… (More)

- Chao-Bing Song, Shu-Tao Xia, Xin-Ji Liu
- IEEE Signal Processing Letters
- 2014

In the context of compressed sensing (CS), subspace pursuit (SP) is an important iterative greedy recovery algorithm which could reduce the recovery complexity greatly comparing with l<sub>1</sub>-minimization. Restricted isometry property (RIP) and restricted isometry constant (RIC) of measurement matrices which ensure the convergence of iterative… (More)

- Xin-Ji Liu, Shu-Tao Xia
- 2013 IEEE International Symposium on Information…
- 2013

Recently, Dimakis, Smarandache, and Vontobel indicated that the parity-check matrices of good LDPC codes can be used as provably good measurement matrices for compressed sensing (CS) under basis pursuit (BP). In this paper, we consider the parity-check matrix H(r, q) of the array codes, one of the most important kind of structured LDPC codes. The spark,… (More)

- Xin-Ji Liu, Shu-Tao Xia
- ArXiv
- 2014

- Shu-Tao Xia, Xin-Ji Liu, Yong Jiang, Hai-Tao Zheng
- IEEE Transactions on Signal Processing
- 2015

Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as provably good measurement matrices for compressed sensing… (More)

- Yanbo Lu, Jie Hao, Xin-Ji Liu, Shu-Tao Xia
- 2015 International Symposium on Network Coding…
- 2015

As the rapid growth of data, many storage systems have used erasure codes instead of replication to reduce the storage cost under the same level of reliability. Maximum-Distance- Separable (MDS) codes have been the most widely adopted, due to their optimal storage efficiency. It is well understood that the application of codes in storage systems, where the… (More)

- Xin-Ji Liu, Shu-Tao Xia
- 2013 IEEE International Symposium on Information…
- 2013

Binary 0-1 measurement matrices, especially those from coding theory, were introduced to compressed sensing (CS) recently. Good measurement matrices with preferred properties, e.g., the restricted isometry property (RIP) and nullspace property (NSP), have no known general ways to be efficiently checked. Khajehnejad et al. made use of girth to certify the… (More)

- Shu-Tao Xia, Xin-Ji Liu, Yong Jiang, Hai-Tao Zheng
- ArXiv
- 2013

—For a measurement matrix in compressed sensing, its spark (or the smallest number of columns that are linearly dependent) is an important performance parameter. The matrix with spark greater than 2k guarantees the exact recovery of k-sparse signals under an l0-optimization, and the one with large spark may perform well under approximate algorithms of the… (More)

- Xin-Ji Liu, Shu-Tao Xia, Tao Dai
- 2015 IEEE International Conference on Acoustics…
- 2015

We introduce a general framework to deterministically construct binary measurement matrices for compressed sensing. The proposed matrices are composed of (circulant) permutation submatrix blocks and zero submatrix blocks, thus making their hardware realization convenient and easy. Firstly, using the famous Johnson bound for binary constant weight codes, we… (More)

- Yong Jiang, Shu-Tao Xia, Xin-Ji Liu, Fang-Wei Fu
- 2013 IEEE International Symposium on Information…
- 2013

On a binary erasure channel (BEC) with erasing probability e, the performance of a binary linear code is determined by the incorrigible sets of the code. The incorrigible set distribution (ISD) {I<sub>i</sub>}<sub>i=0</sub><sup>n</sup> enumerates the number of incorrigible sets with size i of the code. The probability of unsuccessful decoding under optimal… (More)