Rotationally invariant nonlinear trellis codes for two-dimensional modulation

Author

Pietrobon, S.S. ; Ungerboeck, G. ; Perez, L.C. ; Costello, D.J., Jr.

Author_Institution

Australia Space Centre for Signal Process., Univ. of South Australia, The Levels, SA, Australia

Volume

40

Issue

6

fYear

1994

Firstpage

1773

Lastpage

1791

Abstract

A general parity-check equation is presented that defines rotationally invariant trellis codes of rate k/(k+1) for two-dimensional signal sets. This parity-check equation is used to find rate k/(k+1) codes for 4PSK, 8PSK, 16PSK, and QAM signal sets by systematic code searches. The MPSK codes exhibit smaller free Euclidean distances than nonrotationally invariant linear codes with the same number of states. However, since the nonlinear codes have a smaller number of nearest neighbors, their performance at moderate signal to noise ratios is close to that of the best linear codes. The rotationally invariant QAM codes with 8, 32, 64, and 256 states achieve the same free Euclidean distance as the best linear codes. Transparency of user information under phase rotations is accomplished either by conventional differential encoding and decoding, or by integrating this function directly into the code trellis.<>

Keywords

decoding; encoding; phase shift keying; quadrature amplitude modulation; trellis codes; 16PSK; 4PSK; 8PSK; MPSK codes; QAM codes; TCM; code searches; code trellis; differential decoding; differential encoding; free Euclidean distances; nonlinear trellis codes; parity-check equation; phase rotations; rotationally invariant trellis codes; signal to noise ratios; two-dimensional signal sets; Convolutional codes; Decoding; Encoding; Euclidean distance; Linear code; Nearest neighbor searches; Nonlinear equations; Parity check codes; Quadrature amplitude modulation; Signal to noise ratio;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.340454

Filename

340454