Computer Science – Information Theory
Scientific paper
2009-03-15
Computer Science
Information Theory
20 pages, submitted to IEEE Transactions on Information Theory
Scientific paper
Constant-dimension codes (CDCs) have been investigated for noncoherent error correction in random network coding. The maximum cardinality of CDCs with given minimum distance and how to construct optimal CDCs are both open problems, although CDCs obtained by lifting Gabidulin codes, referred to as KK codes, are nearly optimal. In this paper, we first construct a new class of CDCs based on KK codes, referred to as augmented KK codes, whose cardinalities are greater than previously proposed CDCs. We then propose a low-complexity decoding algorithm for our augmented KK codes using that for KK codes. Our decoding algorithm corrects more errors than a bounded subspace distance decoder by taking advantage of the structure of our augmented KK codes. In the rest of the paper we investigate the covering properties of CDCs. We first derive bounds on the minimum cardinality of a CDC with a given covering radius and then determine the asymptotic behavior of this quantity. Moreover, we show that liftings of rank metric codes have the highest possible covering radius, and hence liftings of rank metric codes are not optimal packing CDCs. Finally, we construct good covering CDCs by permuting liftings of rank metric codes.
Gadouleau Maximilien
Yan Zhiyuan
No associations
LandOfFree
Construction and Covering Properties of Constant-Dimension Codes 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 Construction and Covering Properties of Constant-Dimension Codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Construction and Covering Properties of Constant-Dimension Codes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-223476