TY - GEN

T1 - The dispersion of infinite constellations

AU - Ingber, Amir

AU - Zamir, Ram

AU - Feder, Meir

PY - 2011

Y1 - 2011

N2 - In the setting of a Gaussian channel without power constraints, proposed by Poltyrev, the codewords are points in an n-dimensional Euclidean space (an infinite constellation) and their optimal density is considered. Poltyrev's "capacity" is the highest achievable normalized log density (NLD) with vanishing error probability. This capacity as well as error exponents for this setting are known. In this work we consider the optimal NLD for a fixed, nonzero error probability, as a function of the codeword length (dimension) n. We show that as n grows, the gap to capacity is inversely proportional (up to the first order) to the square-root of n where the proportion constant is given by the inverse Q-function of the allowed error probability, times the square root of 1/2. In an analogy to similar result in channel coding, the dispersion of infinite constellations is 1/2 nat2 per channel use. We show that this optimal convergence rate can be achieved using lattices, therefore the result holds for the maximal error probability as well. Connections to the error exponent of the power constrained Gaussian channel and to the volume-to-noise ratio as a figure of merit are discussed.

AB - In the setting of a Gaussian channel without power constraints, proposed by Poltyrev, the codewords are points in an n-dimensional Euclidean space (an infinite constellation) and their optimal density is considered. Poltyrev's "capacity" is the highest achievable normalized log density (NLD) with vanishing error probability. This capacity as well as error exponents for this setting are known. In this work we consider the optimal NLD for a fixed, nonzero error probability, as a function of the codeword length (dimension) n. We show that as n grows, the gap to capacity is inversely proportional (up to the first order) to the square-root of n where the proportion constant is given by the inverse Q-function of the allowed error probability, times the square root of 1/2. In an analogy to similar result in channel coding, the dispersion of infinite constellations is 1/2 nat2 per channel use. We show that this optimal convergence rate can be achieved using lattices, therefore the result holds for the maximal error probability as well. Connections to the error exponent of the power constrained Gaussian channel and to the volume-to-noise ratio as a figure of merit are discussed.

UR - http://www.scopus.com/inward/record.url?scp=80054824110&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2011.6033771

DO - 10.1109/ISIT.2011.6033771

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:80054824110

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1407

EP - 1411

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

Y2 - 31 July 2011 through 5 August 2011

ER -