By Topic

Representing group codes as permutation codes

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Biglieri, Ezio ; Dipt. di Elettronica, Politecnico di Milano, Italy ; Karlof, J. ; Viterbo, E.

Given an abstract group 𝒢, an N-dimensional orthogonal matrix representation G of 𝒢, and an “initial vector” x∈R N, Slepian defined the group code generated by the representation G to be the set of vectors Gx. If G is a group of permutation matrices, the set Gx is called a “permutation code”. For permutation codes a “stack algorithm” decoder exists that, in the presence of low noise, produces the maximum-likelihood estimate of the transmitted vector by using far fewer computations than the standard decoder. In this correspondence, a new concept of equivalence of codes of different dimensions is presented which is weaker than the usual definition of equivalent codes. We show that every group code is (weakly) equivalent to a permutation code and we discuss the minimal degree of this permutation code

Published in:

Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 6 )