Least Squares Superposition Codes of Moderate Dictionary Size Are Reliable at Rates up to Capacity

被引：81

作者：

Joseph, Antony ^{[1
]}

Barron, Andrew R. ^{[1
]}

机构：

[1] Yale Univ, Dept Stat, New Haven, CT 06520 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2012年 / 58卷 / 05期

关键词：

Achieving capacity; compressed sensing; exponential error bounds; Gaussian channel; maximum likelihood estimation; subset selection; INFORMATION-THEORETIC LIMITS; PARITY-CHECK CODES; SIGNAL RECOVERY; SPARSITY RECOVERY; MODEL SELECTION; REPRESENTATIONS; APPROXIMATION; CONSISTENCY; REGRESSION; ALGORITHM;

D O I：

10.1109/TIT.2012.2184847

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

For the additive white Gaussian noise channel with average codeword power constraint, coding methods are analyzed in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design, with the possible messages indexed by the choice of subset. Decoding is by least squares (maximum likelihood), tailored to the assumed form of codewords being linear combinations of elements of the design. Communication is shown to be reliable with error probability exponentially small for all rates up to the Shannon capacity.

引用

页码：2541 / 2557

页数：17

共 72 条

[31] Forney G. Jr, 1966, CONCATENATED CODES, V37
[32] Modulation and coding for linear Gaussian channels
Forney, GD
Ungerboeck, G
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (06) : 2384 - 2415
[33] Fuchs JJ, 2004, INT CONF ACOUST SPEE, P533
[34] On sparse representations in arbitrary redundant bases
Fuchs, JJ
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (06) : 1341 - 1344
[35] Gallager R. G., 1968, Information Theory and Reliable Communication, V2
[36] Gilbert AC, 2005, 2005 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), VOLS 1 AND 2, P1000
[37] Joint permutor analysis and design for multiple turbo codes
He, Ching
Lentmaier, Michael
Costello, Daniel J., Jr.
Zigangirov, Kamil Sh.
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (09) : 4068 - 4083
[38] PROBABILITY-INEQUALITIES FOR SUMS OF BOUNDED RANDOM-VARIABLES
HOEFFDING, W
[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1963, 58 (301) : 13 - +
[39] False Discovery Rate Control With Groups
Hu, James X.
Zhao, Hongyu
Zhou, Harrison H.
[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2010, 105 (491) : 1215 - 1227
[40] Huang C., 2008, RISK PENALIZED LEAST

← 1 2 3 4 5 6 7 8 →