A bounded-distance decoding algorithm for lattices obtained from a generalized code formula

Author

Silva, Mauro A O da Costa e ; Palazzo, Reginaldo, Jr.

Author_Institution

Dept. of Electr. Eng., Sao Paulo Univ., Brazil

Volume

40

Issue

6

fYear

1994

fDate

11/1/1994 12:00:00 AM

Firstpage

2075

Lastpage

2082

Abstract

A multistage decoding algorithm is given for lattices obtained from a multilevel code formula. The algorithm is shown to have the same effective error-correcting radius as maximum-likelihood decoding, so that the performance loss is essentially determined by the increase in the effective error coefficient, for which an expression is given. The code formula generalizes some previous multilevel constructions to constructions of known single-level binary lattices with many levels, and then to decoders for them with the proposed algorithm. The trade-off between complexity reduction and performance loss is evaluated for several known lattices and two new ones, indicating that the approach is effective provided the binary codes involved in the code formula are not too short. All codes used in our constructions are binary Reed-Muller codes

Keywords

Reed-Muller codes; binary sequences; decoding; Reed-Muller codes; binary codes; bounded-distance decoding algorithm; complexity reduction; decoders; error coefficient; error-correcting radius; generalized code formula; lattices; maximum-likelihood decoding; multilevel construction; multistage decoding algorithm; performance loss; single-level binary lattices; Block codes; Costs; Error correction; Lattices; Maximum likelihood decoding; Maximum likelihood detection; Partitioning algorithms; Performance loss; Sufficient conditions; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.340485

Filename

340485