CONSTRUCTION OF NESTED REAL IDEAL LATTICES
FOR INTERFERENCE CHANNEL CODING
C.C. Trinca Watanabe1, J.-C. Belfiore2,
E.D. De Carvalho2, J. Vieira Filho4, R.A. Watanabe5 1Department of Communications (DECOM)
Campinas State University
Campinas-SP, 13083-852, BRAZIL 2Department of Communications and Electronics
Télécom ParisTech, Paris, 75013, FRANCE 3Department of Mathematics
São Paulo State University
Ilha Solteira-SP, 15385-000, BRAZIL 4Telecommunications Engineering
São Paulo State University
São João da Boa Vista-SP, 13876-750, BRAZIL 5Institute of Mathematics, Statistics
and Scientific Computation (IMECC)
Campinas State University
Campinas-SP, 13083-852, BRAZIL
In this work we develop a new algebraic methodology which quantizes real-valued channels in order to realize interference alignment (IA) onto a real ideal lattice. Also we make use of the minimum mean square error (MMSE) criterion to estimate real-valued channels contaminated by additive Gaussian noise.
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References
[1] J. Tang and S. Lambotharan, Interference alignment techniques for MIMO
multi-cell interfering broadcast channels, IEEE Trans. on Communications,
61 (2013), 164-175.
[2] A.R. Calderbank and N.J.A. Sloane, New trellis codes based on lattices
and cosets, IEEE Trans. on Information Theory, 33 (1987), 177-195.
[3] G.D. Forney, Coset Codes - Part I: Introduction and Geometrical Classification,
IEEE Trans. on Information Theory, 34(5) (1998), 1123-1151.
[4] R. Zamir, Lattices are everywhere, In: Proc. of the 4th Annual Workshop
on Information Theory and its Applications (ITA) (2009).
[5] C.C. Trinca Watanabe, J.-C. Belfiore, E.D. de Carvalho, J. Vieira
Filho, R. Palazzo Jr. and R.A. Watanabe, Construction of complex
nested ideal lattices for complex-valued channel quantization, International
Journal of Applied Mathematics, 31, No 4 (2018), 549-585; DOI:
10.12732/ijam.v31i4.4.
[6] A.A. de Andrade, C. Alves and T.C. Bertoldi, Rotated lattices via the
cyclotomic field Q(ξ2r ), International Journal of Applied Mathematics, 19,
No. 3 (2006), 321-331.
[7] C.C. Trinca, A contribution to the study of channel coding in wireless
communication systems, Ilha Solteira - S˜ao Paulo, Brazil: Universidade
Estadual Paulista “J´ulio de Mesquita Filho” (UNESP), 2013.
[8] C.C. Trinca Watanabe, J.-C. Belfiore, E.D. de Carvalho and J. Vieira
Filho, E−8-lattice via the cyclotomic field Q(ξ24), International Journal of
Applied Mathematics, 31, No 1 (2018), 63-71; DOI: 10.12732/ijam.v31i1.6.
[9] J. Leech and N.J.A. Sloane, Sphere packings and error correcting codes,
Canadian J. of Mathematics, 23 (1971), 718-745.
[10] E. Bayer-Fluckiger, F. Oggier and E. Viterbo, Algebraic lattice constellations:
bounds on performance, IEEE Trans. on Information Theory, 52,
No 1 (2006), 319-327.
[11] C.C. Trinca, J.-C. Belfiore, E.D. de Carvalho and J. Vieira Filho, Construction
of coset codes in order to realize interference alignment, The
8th Intern. Multi-Conference on Complexity, Informatics and Cybernetics:
IMCIC 2017, (2017).
[12] K. Conrad, Dirichlet’s unit theorem, Retrieved from
http://www.math.uconn.edu/∼kconrad/blurbs/gradnumthy/unittheorem.pdf.
[13] A.K. Lenstra, H.W. Lenstra Jr. and L. Lov´asz, Fatoring polynomials with
rational coefficients, Mathematische Annalen, 261 (1982), 515-534.
[14] U. Fincke and M. Pohst, Improved methods for calculating vectors of short
length in a lattice, including a complexity analysis, Mathematics of Computation,
44, No 170 (1985), 463-471.
[15] B. Nazer and M. Gastpar, Compute-and-forward: Harnessing interference
through structured codes, IEEE Trans. on Information Theory, 57, No 10
(2011), 6463-6486.
[16] R.A. Watanabe and C.C. Trinca, Application of the support function and
the steiner point on the study of interference alignment channel, 2017 IEEE
Intern. Conf. on Fyzzy Systems (FUZZ-IEEE), (2017).
[17] C.C. Trinca, J-C. Belfiore, E.D. de Carvalho and J. Vieira Filho, Coding
for the Gaussian interference channel, In: XXXI Simp´osio Brasileiro de
Telecomunica¸c˜oes (SBrT) (2013).