Two 16-state, rate R=2/4 trellis codes whose free distances meet the Heller bound

Author

Johannesson, Rolf ; Wittenmark, Emma

Author_Institution

Dept. of Inf. Technol., Lund Univ., Sweden

Volume

44

Issue

4

fYear

1998

fDate

7/1/1998 12:00:00 AM

Firstpage

1602

Lastpage

1604

Abstract

For rate R=1/2 convolutional codes with 16 states there exists a gap between Heller´s (1968) upper bound on the free distance and its optimal value. This article reports on the construction of 16-state, binary, rate R=2/4 nonlinear trellis and convolutional codes having d _free=8; a free distance that meets the Heller upper bound. The nonlinear trellis code is constructed from a 16-state, rate R=1/2 convolutional code over Z₄ using the Gray map to obtain a binary code. Both convolutional codes are obtained by computer search. Systematic feedback encoders for both codes are potential candidates for use in combination with iterative decoding. Regarded as modulation codes for 4-PSK, these codes have free squared Euclidean distance d_{E, free}²=16

Keywords

binary sequences; convolutional codes; decoding; feedback; iterative methods; modulation coding; phase shift keying; trellis codes; 16-state trellis codes; 4-PSK; Gray map; Heller upper bound; binary code; code rate; computer search; convolutional codes; free distance; free squared Euclidean distance; iterative decoding; modulation codes; nonlinear trellis codes; systematic feedback encoders; Binary codes; Convolutional codes; Error correction codes; Euclidean distance; Feedback; Iterative decoding; Modulation coding; Quadrature phase shift keying; Signal to noise ratio; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.681337

Filename

681337