Abstract
A Lattice triangular expansion matrix is presented based on the classical Hadamard matrices, which is defined over the fields of finite characteristic. Also, the modular Lattice and Pentagon expansion matrices are structured from triangular 7x7 matrix, each of the expansion matrices are modular the sides of the shape p. The issue for the existence (necessary conditions) of odd and even order matrices of that kind is addressed. The modular Lattice code is highly efficient since it requires only additions, multiplications by constant modulo p. The modular 6 Lattice triangular expanded constellation is even possible efficiency to gain advantage from the channel selection and maximum likelihood (ML) decoding in the interference Lattice alignment (IA) system.
Highlights
The generalized reverse jacket transforms (GRJT) as multi-phase or multilevel generalizations of the WHT and the even-length DFT were introduced in [1]
A Lattice triangular expansion matrix is presented based on the classical Hadamard matrices, which is defined over the fields of finite characteristic
The modular Lattice and Pentagon expansion matrices are structured from triangular 7 7 matrix, each of the expansion matrices are modular the sides of the shape p
Summary
The generalized reverse jacket transforms (GRJT) as multi-phase or multilevel generalizations of the WHT and the even-length DFT were introduced in [1]. It can be proven that matrices having the abovementioned properties with entries from the field of complex numbers do exist only for even orders [2] It seems the problem of the existence of similar transforms on distinct odd dimension spaces sounds natural. For the two-user interference channel, one of the best known achievable regions is that introduced by Han and Kobayashi [5]. This achievable region can be naturally generalized to more than two-users. In [6], it is shown that a layered lattice coding scheme can result in an improved set of achievable rates than an i.i.d. Gaussian Han & Kobayashi region.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
