Constructions of Optimal Optical Orthogonal Codes with Weights Set 5,7 via Cyclic Packing

Double-weight optical orthogonal codes are variable-weight optical orthogonal codes (OOCs), which have been widely applied in optical networks and systems. Some works have been devoted to optimal n , W , 1 , Q -OOCs with max w : w ∈ W ≤ 6 . So far, there is no explicit construction of optimal n , W , 1 , Q -OOCs with W = 5,7 . It is known that heavier-weight codewords have better code performance than lighter-weight codewords. So, in this paper, we use cyclic packing to construct two infinite classes of optimal OOCs with weights set 5,7 explicitly, for any prime p ≡ 3 mod 4 and p ≥ 7 . In addition, for 1 ≤ t < p − 1 / 2 , by breaking t blocks of size 7 into 3 of 31 p , 5,7 , 1 , 1 / 2 , 1 / 2 -OOCs and 41 p , 5,7 , 1 , 2 / 3 , 1 / 3 -OOCs, we obtain new infinite classes of optimal 31 p , 3,5,7 , 1 , 7 t / p − 1 + 6 t , p − 1 / 2 p − 1 + 6 t , p − 1 − 2 t / 2 p − 1 + 6 t -OOCs and 41 p , 3,5,7 , 1 , 14 t / 3 p − 1 + 4 t , 2 p − 1 / 3 p − 1 + 4 t , p − 1 − 2 t / 3 p − 1 + 4 t -OOCs, respectively.

The geometry of Hermitian self-orthogonal codes

We prove that if $$n >k^2$$ n > k 2 then a k-dimensional linear code of length n over $${\mathbb F}_{q^2}$$ F q 2 has a truncation which is linearly equivalent to a Hermitian self-orthogonal linear code. In the contrary case we prove that truncations of linear codes to codes equivalent to Hermitian self-orthogonal linear codes occur when the columns of a generator matrix of the code do not impose independent conditions on the space of Hermitian forms. In the case that there are more than n common zeros to the set of Hermitian forms which are zero on the columns of a generator matrix of the code, the additional zeros give the extension of the code to a code that has a truncation which is equivalent to a Hermitian self-orthogonal code.

NEW CONCATENATION SCHEMES BASED ON THE MULTITHRESHOLD DECODERS OF CONVOLUTIONAL SELF-ORTHOGONAL CODES FOR GAUSSIAN CHANNELS

New serial concatenation schemes based on the multithreshold decoders and di- vergent principle for the convolutional self-orthogonal codes under Gaussian channels are proposed. Using both binary and symbolic decoders on the second decoding stage of the convolutional codes are considered. Simulation results are indicated the higher performance characteristics of the proposed cascade schemes on majority decoders in comparison with clas- sical schemes based on the Viterbi algorithm and Reed-Solomon codes. A moderate increase in decoding delay during concatenation is revealed. It is determined by the absence of the need to use traditional two-dimensional concatenated structures.

A Full-Polarization Radar Image Reconstruction Method with Orthogonal Coding Apertures

Imaging radar is widely applied in both military and civil fields, including remote sensing. In recent years, polarization information has attracted more and more attention in the imaging radar. The orthogonality between different channels is always the core problem for the full-polarization imaging radar. To solve this problem, an image reconstruction method using orthogonal coding apertures technique is proposed for full-polarization imaging radar in this paper. Firstly, the signal model of the orthogonal coding apertures is proposed. This model realizes the ideal time-domain orthogonality between switching two channels by the apertures with two trains of orthogonal codes. Then, a multichannel joint reconstruction method based on compressed sensing is proposed for the imaging processing, which is named the coded aperture simultaneous orthogonal matching pursuit (CAS-OMP) algorithm. The proposed algorithm combines the information of all polarization channels so as to ensure the consistency of the scattering point position obtained by each polarization channel and also improves the reconstruction accuracy. Finally, the simulation experiments using both the simple scaled model of the satellite and measured data of an unmanned aerial vehicle (UAV) are conducted, and the effectiveness of the proposed method is verified.