Title :
Codes over Gaussian integers
Author_Institution :
Res. Inst., Deutsche Bundespost Telekom, Darmstadt, Germany
fDate :
1/1/1994 12:00:00 AM
Abstract :
The author shows how block codes over Gaussian integers can be used for coding over two-dimensional signal space. He introduces a two-dimensional modular distance called the Mannheim distance and proposes using codes designed for this distance. Some simple constructions of such codes are given, among them icyclic codes which belong to the class of constacyclic codes. As a special case icyclic codes include perfect one Mannheim error correcting codes. For most of the codes considered efficient decoders are given and their performance on the Gaussian channel is investigated
Keywords :
amplitude modulation; block codes; cyclic codes; decoding; error correction codes; telecommunication channels; Gaussian channel; Gaussian integers; Mannheim distance; Mannheim error correcting codes; QAM signal constellations; block codes; constacyclic codes; decoders; icyclic codes; performance; quadrature amplitude modulation; two-dimensional modular distance; two-dimensional signal space; Block codes; Constellation diagram; Decoding; Error correction codes; Galois fields; Gaussian channels; Gaussian processes; Hamming distance; Phase shift keying; Quadrature amplitude modulation;
Journal_Title :
Information Theory, IEEE Transactions on
