Related papers: Complex Orthogonal Designs with Forbidden $2 \time…
Complex orthogonal designs (CODs) are used to construct space-time block codes. COD $\mathcal{O}_z$ with parameter $[p, n, k]$ is a $p\times n$ matrix, where nonzero entries are filled by $\pm z_i$ or $\pm z^*_i$, $i = 1, 2,..., k$, such…
Complex orthogonal design (COD) with parameter $[p, n, k]$ is a combinatorial design used in space-time block codes (STBCs). For STBC, $n$ is the number of antennas, $k/p$ is the rate, and $p$ is the decoding delay. A class of rate $1/2$…
Orthogonal designs are fundamental mathematical notions used in the construction of space time block codes for wireless transmissions. Designs have two important parameters, the rate and the decoding delay; the main problem of the theory is…
Square COD (complex orthogonal design) with size $[n, n, k]$ is an $n \times n$ matrix $\mathcal{O}_z$, where each entry is a complex linear combination of $z_i$ and their conjugations $z_i^*$, $i=1,\ldots, k$, such that $\mathcal{O}_z^H…
Complex orthogonal designs (CODs) play a crucial role in the construction of space-time block codes. Their real analog, real orthogonal designs (or equivalently, sum of squares composition formula) have a long history. Adams et al. (2011)…
Complex Orthogonal Design (COD) codes are known to have the lowest detection complexity among Space-Time Block Codes (STBCs). However, the rate of square COD codes decreases exponentially with the number of transmit antennas. The…
The maximal rate for non-square Complex Orthogonal Designs (CODs) with $n$ transmit antennas is ${1/2}+\frac{1}{n}$ if $n$ is even and ${1/2}+\frac{1}{n+1}$ if $n$ is odd, which are close to 1/2 for large values of $n.$ A class of maximal…
Space-time block codes (STBCs) from non-square complex orthogonal designs are bandwidth efficient when compared with those from square real/complex orthogonal designs. Though there exists rate-1 ROD for any number of transmit antennas,…
Nine new 2-D OOCs are presented here, all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature. Each of these constructions…
We generalized to higher dimensions the notions of optical orthogonal codes. We establish uper bounds on the capacity of general $ n $-dimensional OOCs, and on specific types of ideal codes (codes with zero off-peak autocorrelation). The…
The maximal rate of a non-square complex orthogonal design for $n$ transmit antennas is $1/2+\frac{1}{n}$ if $n$ is even and $1/2+\frac{1}{n+1}$ if $n$ is odd and the codes have been constructed for all $n$ by Liang (IEEE Trans. Inform.…
Space-Time Block Codes from square complex orthogonal designs (SCOD) have been extensively studied and most of the existing SCODs contain large number of zero. The zeros in the designs result in high peak-to-average power ratio (PAPR) and…
To combine the high power efficiency of Continuous Phase Modulation (CPM) with either high spectral efficiency or enhanced performance in low Signal to Noise conditions, some authors have proposed to introduce CPM in a MIMO frame, by using…
In this paper, we further investigate the constructions on three-dimensional $(u\times v\times w,k,1)$ optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM-OPP $3$-D $(u\times v\times…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
Codes considered as structures within unit schemes greatly extends the availability of linear block and convolutional codes and allows the construction of these codes to required length, rate, distance and type. Properties of a code emanate…
It is well known that Space-Time Block Codes (STBCs) from orthogonal designs (ODs) are single-symbol decodable/symbol-by-symbol decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
It is well known that the Space-time Block Codes (STBCs) from Complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD). The weight matrices of the square CODs are all unitary and obtainable from the…
The study of optical orthogonal codes has been motivated by an application in an optical code-division multiple access system. This paper focuses on optimal two-dimensional optical orthogonal codes with autocorrelation and cross-correlation…