TY - JOUR
T1 - Non-random coding error bounds for lattices
AU - Domb, Yuval
AU - Feder, Meir
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - An upper bound on the error probability of specific lattices, based on their distance spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers. In many ways, the new bound greatly resembles the Shulman-Feder bound for linear codes. Based on the new bound, error-exponent and channel-dispersion expressions are derived for specific lattice sequences (of increasing dimension) over the AWGN channel. Measuring a sequence's gap to capacity, using the new asymptotics, is demonstrated. Additional finite dimension results, encountered along the way, are presented.
AB - An upper bound on the error probability of specific lattices, based on their distance spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers. In many ways, the new bound greatly resembles the Shulman-Feder bound for linear codes. Based on the new bound, error-exponent and channel-dispersion expressions are derived for specific lattice sequences (of increasing dimension) over the AWGN channel. Measuring a sequence's gap to capacity, using the new asymptotics, is demonstrated. Additional finite dimension results, encountered along the way, are presented.
KW - Error exponent
KW - Error probability bounds
KW - Maximum-likelihood decoding
KW - Specific lattices
UR - http://www.scopus.com/inward/record.url?scp=84959206092&partnerID=8YFLogxK
U2 - 10.1109/TIT.2015.2496352
DO - 10.1109/TIT.2015.2496352
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84959206092
SN - 0018-9448
VL - 62
SP - 108
EP - 120
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 1
M1 - 7312993
ER -