TY - GEN
T1 - Uniformity properties of Construction C
AU - Bollauf, Maiara F.
AU - Zamir, Ram
N1 - Publisher Copyright: © 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - Construction C (also known as Forney's multi-level code formula) forms a Euclidean code for the additive white Gaussian noise (AWGN) channel from L binary code components. If the component codes are linear, then the minimum distance is the same for all the points, although the kissing number may vary. In fact, while in the single level (L = 1) case it reduces to lattice Construction A, a multi-level Construction C is in general not a lattice. We show that the two-level (L = 2) case is special: a two-level Construction C satisfies Forney's definition for a geometrically uniform constellation. Specifically, every point sees the same configuration of neighbors, up to a reflection of the coordinates in which the lower level code is equal to 1. In contrast, for three levels and up (L ≥ 3), we construct examples where the distance spectrum varies between the points, hence the constellation is not geometrically uniform.
AB - Construction C (also known as Forney's multi-level code formula) forms a Euclidean code for the additive white Gaussian noise (AWGN) channel from L binary code components. If the component codes are linear, then the minimum distance is the same for all the points, although the kissing number may vary. In fact, while in the single level (L = 1) case it reduces to lattice Construction A, a multi-level Construction C is in general not a lattice. We show that the two-level (L = 2) case is special: a two-level Construction C satisfies Forney's definition for a geometrically uniform constellation. Specifically, every point sees the same configuration of neighbors, up to a reflection of the coordinates in which the lower level code is equal to 1. In contrast, for three levels and up (L ≥ 3), we construct examples where the distance spectrum varies between the points, hence the constellation is not geometrically uniform.
KW - Construction A, C, D
KW - Construction by Code-Formula
KW - Lattice construction
KW - distance spectrum
KW - geometrically uniform constellation
KW - linear codes
UR - http://www.scopus.com/inward/record.url?scp=84985990685&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/ISIT.2016.7541552
DO - https://doi.org/10.1109/ISIT.2016.7541552
M3 - منشور من مؤتمر
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1516
EP - 1520
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -