Compressed sensing and linear codes over real numbers

Zhang, Fan; Pfister, Henry D.

doi:10.1109/ita.2008.4601055

Cited by 41 publications

(44 citation statements)

References 24 publications

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“…We present the average reduction in the total storage size for a differential system with L = 10, assuming identical PMFs on the sparsity levels for every version, i.e., P Γj (γ j ) = P Γ (γ) for each 2 ≤ j ≤ 10. The average percentage reduction in the total storage size and total I/O reads number are computed similarly to (18), and are illustrated in Fig. 10.…”

Section: Experimental Results For L >mentioning

confidence: 99%

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Differential Erasure Codes for Efficient Archival of Versioned Data in Cloud Storage Systems

Harshan

Datta

Oggier

2016

Transactions on Large-Scale Data- And Knowledge-Centered Systems XXX

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In this paper, we study the problem of storing an archive of versioned data in a reliable and efficient manner in distributed storage systems. We propose a new storage technique called differential erasure coding (DEC) where the differences (deltas) between subsequent versions are stored rather than the whole objects, akin to a typical delta encoding technique. However, unlike delta encoding techniques, DEC opportunistically exploits the sparsity (i.e., when the differences between two successive versions have few non-zero entries) in the updates to store the deltas using compressed sensing techniques applied with erasure coding. We first show that DEC provides significant savings in the storage size for versioned data whenever the update patterns are characterized by in-place alterations. Subsequently, we propose a practical DEC framework so as to reap storage size benefits against not just in-place alterations but also real-world update patterns such as insertions and deletions that alter the overall data sizes. We conduct experiments with several synthetic workloads to demonstrate that the practical variant of DEC provides significant reductions in storage overhead (up to 60% depending on the workload) compared to baseline storage system which incorporates concepts from Rsync, a delta encoding technique to store and synchronize data across a network.

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Section: Experimental Results For L >mentioning

confidence: 99%

“…The following proposition [18] gives a sufficient condition on Φ to uniquely recover z from z using a syndrome decoder.…”

Section: System Model For Version Managementmentioning

confidence: 99%

Differential Erasure Codes for Efficient Archival of Versioned Data in Cloud Storage Systems

Harshan

Datta

Oggier

2016

Transactions on Large-Scale Data- And Knowledge-Centered Systems XXX

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“…From the syndrome r, it is desired to find the exact error pattern w by using the calculated syndrome r and the parity-check matrix H. The error correction capability of this code C mainly relies on its minimum distance, which is the minimum Hamming weight (the number of nonzero elements) of any codeword. The tight connection between CS and coding theory was reported in [11] and [12].…”

Section: Connection To Syndrome Decodingmentioning

confidence: 86%

Performance Evaluation of Finite Sparse Signals for Compressed Sensing Frameworks

Seong

2018

IEICE Trans. Inf. & Syst.

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SUMMARY In this paper, we consider to develop a recovery algorithm of a sparse signal for a compressed sensing (CS) framework over finite fields. A basic framework of CS for discrete signals rather than continuous signals is established from the linear measurement step to the reconstruction. With predetermined priori distribution of a sparse signal, we reconstruct it by using a message passing algorithm, and evaluate the performance obtained from simulation. We compare our simulation results with the theoretic bounds obtained from probability analysis.

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“…Recently, it is observed that CS is closely related to the well-known channel code called low-density parity-check (LDPC) codes [3,4]. In particular, when the measurement matrix in CS is chosen to be the parity-check matrix of an LDPC code, the CS reconstruction algorithm proposed by Baron et al [5] is almost identical to Luby's LDPC decoding algorithm [6].…”

Section: Introductionmentioning

confidence: 99%

Compressive cooperation for gaussian half-duplex relay channel

Liu

Luo

2012

J Wireless Com Network

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Motivated by the compressive sensing (CS) theory and its close relationship with low-density parity-check code, we propose compressive transmission which utilizes CS as the channel code and directly transmits multi-level CS random projections through amplitude modulation. This article focuses on the compressive cooperation strategies in a relay channel. Four decode-and-forward (DF) strategies, namely receiver diversity, code diversity, successive decoding and concatenated decoding, are analyzed and their achievable rates in a three-terminal half-duplex Gaussian relay channel are quantified. The comparison among the four schemes is made through both numerical calculation and simulation experiments. In addition, we compare compressive cooperation with a separate source channel coding scheme for transmitting sparse sources. Results show that compressive cooperation has great potential in both transmission efficiency and its adaptation capability to channel variations.

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Compressed sensing and linear codes over real numbers

Cited by 41 publications

References 24 publications

Differential Erasure Codes for Efficient Archival of Versioned Data in Cloud Storage Systems

Differential Erasure Codes for Efficient Archival of Versioned Data in Cloud Storage Systems

Performance Evaluation of Finite Sparse Signals for Compressed Sensing Frameworks

Compressive cooperation for gaussian half-duplex relay channel

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