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 -