Commutative group codes for the Gaussian channel
- 1 March 1973
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 19 (2) , 215-219
- https://doi.org/10.1109/tit.1973.1054982
Abstract
A class of codes for the Gaussian channel is analyzed. The code class is a subclass of the group codes for the Gaussian channel described by Slepian. Using the vector model for the Gaussian channel, the code vectors are obtained by transformations of an initial vector. The class of codes in which the transformations form a commutative group is called the class of commutative group codes. The performance of the codes is evaluated using the union bound on the error probability as a performance measure. The union bound is shown to be closely related to the moments of the scalar product between the code vectors. Commutative group codes are described. It is shown that linear algebraic codes may be represented as commutative group codes. The code class is also shown to include simplex and biorthogonal codes in all dimensions.Keywords
This publication has 2 references indexed in Scilit:
- Group codes for the Gaussian channel (Abstr.)IEEE Transactions on Information Theory, 1968
- A class of codes for polyphase signals on a bandlimited Gaussian channelIEEE Transactions on Information Theory, 1965