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Two-dimensional optical orthogonal codes have important applications in optical code division multiple access networks. In this paper, a generic construction of two-dimensional optical orthogonal codes with at most one pulse per wavelength (AM-OPPW 2D OOCs) is proposed. As a result, some optimal AM-OPPW 2D OOCs with new parameters can be yielded. The new AM-OPPW 2D OOC may support more subscribers and heavier asynchronous traffic compared with known constructions.

We investigate further the existence question regarding optimal (v, 4, 2, 1) optical orthogonal codes begun in Momihara and Buratti (IEEE Trans Inform Theory 55:514–523, 2009). We give some non-existence results for infinitely many values of v ≡ ± 3 (mod 9) and several explicit constructions for infinite classes of perfect optical orthogonal codes.

Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault injection attacks. Non-binary LCD codes in characteristic 2 can be transformed into binary LCD codes by expansion. On the other hand, being optimal codes, maximum distance separable codes (abbreviated MDS) are of much interest from many viewpoints due to their theoretical and practical properties. However, little work has been done on LCD MDS codes. In particular, determining the existence of q-ary [n, k] LCD MDS codes for various lengths n and dimensions k is a basic and interesting problem. In this paper, we firstly study the problem of the existence of q-ary [n, k] LCD MDS codes and solve it for the Euclidean case. More specifically, we show that for q>3 there exists a q-ary [n, k] Euclidean LCD MDS code, where 0≤k≤n≤q+1 , or, q=2m , n=q+2 and k=3orq-1 . Secondly, we investigate several constructions of new Euclidean and Hermitian LCD MDS codes. Our main techniques in constructing Euclidean and Hermitian LCD MDS codes use some linear codes with small dimension or codimension, self-orthogonal codes and generalized Reed-Solomon codes.

Future 4G systems require transmission of richer multimedia services which inevitably implies an increase in data rate. Orthogonal frequency and code division multiplexing (OFCDM) technique has shown promising results in achieving a high data rate while simultaneously combating multipath fading. OFCDM is an amalgamation of orthogonal frequency division multiplexing and two-dimensional (2D) spreading. 2D spreading helps to achieve diversity gains in both time and frequency domains. The present OFCDM systems employ 1D orthogonal variable spreading factor (OVSF) codes to achieve the required 2D spreading in code multiplexed channels. However, 2D OVSF codes have better correlation properties in comparison to 1D OVSF codes. Motivated by this principle, the authors propose a spreading scheme for OFCDM systems using 2D OVSF codes. The spreading scheme is designed to increase the system throughput and reduce multi-code interference. Here, the authors study the OFCDM system performance using the proposed spreading scheme in a multipath fast fading channel with varying spreading factors in both time and frequency domains. The results are compared with the existing OFCDM systems using 1D OVSF codes.

Let t ≥ 2 be an integer, and let p1, ⋯, pt be distinct primes. By using algebraic properties, the present paper gives a sufficient and necessary condition for the existence of non-trivial self-orthogonal cyclic codes over the ring Zp1p2⋯pt and the corresponding explicit enumerating formula. And it proves that there does not exist any self-dual cyclic code over Zp1p2⋯pt .

Convolutional doubly orthogonal (CDO) codes constitute a recent group of binary error correcting codes for additive white gaussian noise channel, achieving very good error performance at moderate values of Eb/N0 under the threshold decoding algorithm. Inspired by the low-density parity-check codes over the finite fields, this study extends the construction and decoding of single shift register CDO codes from binary field to the finite fields GF(q) for q > 2, referred to as the q-ary CDO codes. The threshold decoding algorithm is modified to accommodate the decoding requirement for this set of codes. Superior error performance has been observed for q-ary CDO codes over their binary counterparts, especially in the error floor region.

In this study, the authors study a fibre-optic local area network deploying optical code division multiple access technique with differential M-ary pulse position modulation (DPPM). The authors present the performance analysis of DPPM signalling using a double optical hardlimiter receiver structure considering the impairment caused by interference of other users. The analysis assumes a set of bit asynchronous transmitters employing generalised optical orthogonal codes for their DPPM signalling (GOOC-DPPM). Using mathematical analysis and simulations, the authors have demonstrated that GOOC-DPPM improves both frame error probability and the maximum achievable network throughput compared with M-ary PPM modulation scheme. It is also indicated that using generalised OOC codes instead of strict OOC codes in DPPM modulation can increase the number of users who can simultaneously transmit data in the network. The authors have analysed the stability of GOOC-DPPM in a multi-user system and demonstrated its stability. Moreover, the performance of the proposed scheme is evaluated when its important design parameters such as code length, code weight and multiplicity index of the modulation are changed. The findings led the authors to provide some guidelines for proper selection of these parameters to be used for efficient system design.

The improved multi-stage clustering (IMSC)-based blind equalisation algorithm proposed by Mitra and colleagues in 2011 gave rise to significant improvements in terms of performance metrics as compared with its state-of-the-art counterparts. However, the present authors' research studies show that IMSC performance degrades significantly for multiple access interference (MAI) in code-division multiplexing access (CDMA) systems. To mitigate MAI, code filtering by orthogonal Hadamard codes is a popular practice to minimise the interference. Code-filtering techniques have been used in the past in which a de-correlating transform (inverse of an orthonormal Hadamard matrix) has been incorporated into the cost function of the parent algorithm (which can be any traditional equalisation algorithm). A hybrid equalisation scheme is suggested which combines IMSC and code-filtering, so as to mitigate interference in CDMA environments. The code-filtered IMSC shows better performance than any of the previously proposed algorithms.

Currently, microwave correlation imaging (MCI) is regarded as an important method to address the forward‐looking imaging problem in radar. The key step of this method is to form a spatio‐temporal two‐dimensional random radiation field through various means. However, the current methods do not consider the polarization domain, which is an important dimension of electromagnetic signals. The existing research mainly focuses on using polarized antenna elements, without incorporating polarization information into the imaging system. To fill this gap, this letter proposes the polarization microwave correlation imaging (PMCI) based on the orthogonal complement space, which performs instantaneous polarization measurements (IPM) while correlating imaging of the target. Through simulation analysis, this method can further improve the quality and anti‐interference ability of MCI. Moreover, under the condition of low time‐frequency product, the peak sidelobe level (PSL) and isolation of this method are approximately 3.5 dB and 12.5 dB higher than those of traditional instantaneous polarization measurement methods (TIPM). This letter proposes a polarization microwave correlation imaging method based on the orthogonal complement space. It utilizes the orthogonal complement space of the HV antenna radiation field to cross‐multiply the echo information, enabling simultaneous correlation imaging and instantaneous polarization measurement of the target.

AbstractThe article deals with the problem of masking hidden messages under natural noise in highly undetectable stegosystems ±1HUGO and ⊕HUGO. To ensure high resistance of stegosystems to hacking, a preliminary discrete chaotic transformation of a hidden message is performed using the Arnold cat algorithm. Further, in their research, the authors effectively apply noise-resistant coding for the covering object and stego using a self-orthogonal noise-resistant code. To model the data transmission channel, a model of a binary synchronous communication channel with interference is used. The article also presents the results of simulation modeling, confirming the high resistance of the proposed stegosystems to hacking.