The encoding complexity of a general (en,ek) quasicyclic code is O(e 2 (n − k)k). This paper presents a novel lowcomplexity encoding algorithm for quasi-cyclic (QC) codes based on matrix transformation. First, a message vector is encoded into a transformed codeword in the transform domain. Then, the transmitted codeword is obtained from the transformed codeword by the inverse Galois Fourier transform. For binary QC codes, a simple and fast mapping is required to post-process the transformed codeword such that the transmitted codeword is binary as well. The complexity of our proposed encoding algorithm is O(e(n−k)k) symbol operations for non-binary codes and O(e(n − k)k log 2 e) bit operations for binary codes. These complexities are much lower than their traditional counterpart O(e 2 (n−k)k). For example, our complexity of encoding a 64-ary (4095,2160) QC code is only 1.59% of that of traditional encoding, and our complexities of encoding the binary (4095, 2160) and (8176, 7154) QC codes are respectively 9.52% and 1.77% of those of traditional encoding. We also study the application of our low-complexity encoding algorithm to one of the most important subclasses of QC codes, namely QC-LDPC codes, especially when their parity-check matrices are rank deficient.
Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX A robust method and strategy for efficient full field-ofview and depth separation optical imaging through scattering media regardless of the three-dimensional (3D) optical memory effect are proposed. In this method, the problem of imaging de-aliasing, decomposition, and separation of speckle patterns are solved taking advantages of the spatial decorrelation characteristics of speckles by employing randomly modulated illumination strategy and independent component analysis methods. Full field-of-view imaging of multi-targets locate at diverse spatial positions behind a scattering layer are realized and observed experimentally, for the first time, to the best of our knowledge. The method and strategy provide a potentially useful means for incoherent imaging through scattering in a wide class of fields such as optical microscopy, biomedical imaging, and astronomical imaging.
A theoretical model of one-dimensional (ID) hierarchical metacomposite with internal resonators was proposed to generate negative effective mass over specific frequency ranges. Different from the single-resonator microstructure, the current hierarchical metamaterial with multilevel resonators was constructed by a series of springs and rigid bodies. The general formula of the current hierarchical metamaterial model was induced to reveal the relationship between the effective mass and the forcing frequency. It is found that the hierarchical metamaterial with multilevel resonators generates multifrequency band gaps with negative effective masses. The number of the band gaps equals to the order of the hierarchy. The total bandwidth for the negative effective mass increases with the hierarchy, meanwhile increasing the mass ratio can also obviously increase the band width generating negative effective mass.
We demonstrate a novel method for fabricating glass microlens (arrays) with single step on conventional lens surface. In this method, the glass microlens can be achieved by only one step with sol gel glass material. The microlens aperture and focus length can be controlled easily and uniformly. The fabricated sample shows good focusing property. This work will be useful to improve the performance of compound eyes optical system such as camera, telescope, 3D integral imaging and so on.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.