Analysis of LT Codes over Finite Fields under Optimal Erasure Decoding

Author

Schotsch, Birgit ; Garrammone, Giuliano ; Vary, Peter

Author_Institution

Inst. of Commun. Syst. & Data Process., RWTH Aachen Univ., Aachen, Germany

Volume

17

Issue

9

fYear

2013

fDate

Sep-13

Firstpage

1826

Lastpage

1829

Abstract

The erasure correction performance of Luby transform (LT) code ensembles over higher order Galois fields is analysed under optimal, ie maximum likelihood (ML) erasure decoding. We provide the complete set of four bounds on the erasure probability after decoding on word as well as on symbol level. Especially the upper bounds are extremely close to the simulated residual erasure rates after decoding and can thus be used for code design instead of time-consuming simulations.

Keywords

Galois fields; maximum likelihood decoding; transform coding; Galois fields; LT codes analysis; Luby transform code; code design; erasure correction performance; finite fields; fountain codes; maximum likelihood decoding; maximum likelihood erasure decoding; optimal erasure decoding; random matrices; residual erasure rates; symbol level; Generators; Maximum likelihood decoding; Monte Carlo methods; Receivers; Upper bound; Vectors; Fountain codes; finite fields; maximum likelihood decoding; random matrices;

fLanguage

English

Journal_Title

Communications Letters, IEEE

Publisher

ieee

ISSN

1089-7798

Type

jour

DOI

10.1109/LCOMM.2013.072313.131212

Filename

6574309