Computer Science – Information Theory
Scientific paper
2009-10-07
Computer Science
Information Theory
17 pages, 1 figure. Presented at Allerton 2009
Scientific paper
It is well known that there is a one-to-one correspondence between the entropy vector of a collection of n random variables and a certain group-characterizable vector obtained from a finite group and n of its subgroups. However, if one restricts attention to abelian groups then not all entropy vectors can be obtained. This is an explanation for the fact shown by Dougherty et al that linear network codes cannot achieve capacity in general network coding problems (since linear network codes form an abelian group). All abelian group-characterizable vectors, and by fiat all entropy vectors generated by linear network codes, satisfy a linear inequality called the Ingleton inequality. In this paper, we study the problem of finding nonabelian finite groups that yield characterizable vectors which violate the Ingleton inequality. Using a refined computer search, we find the symmetric group S_5 to be the smallest group that violates the Ingleton inequality. Careful study of the structure of this group, and its subgroups, reveals that it belongs to the Ingleton-violating family PGL(2,p) with primes p > 3, i.e., the projective group of 2 by 2 nonsingular matrices with entries in F_p. This family of groups is therefore a good candidate for constructing network codes more powerful than linear network codes.
Hassibi Babak
Mao Wei
No associations
LandOfFree
Violating the Ingleton Inequality with Finite Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Violating the Ingleton Inequality with Finite Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Violating the Ingleton Inequality with Finite Groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-36951