Embedded Rank Distance Codes for ISI Channels

Codes for Unknown ISI Channels

The traditional method of sending a training signal to identify a channel, followed by data, may be viewed as a simple code for the unknown channel. Results in blind sequence detection suggest that performance similar to this traditional approach can be obtained without training. However, for short packets and/or time-recursive algorithms, signi cant error oors exist due to the existence of seq...

Skew codes of prescribed distance or rank

In this paper we propose two methods to produce block codes of prescribed rank or distance. Following [4, 5] we work with skew polynomial rings of automorphism type and the codes we investigate are ideals in quotients of this ring. There is a strong connection with linear difference operators and with linearized polynomials (or q-polynomials) reviewed in the first section. 1 Galois theory of di...

Performance and Distance Spectrum Calculation of TCM Over ISI Channels

Isometries for rank distance and permutation group of Gabidulin codes

The rank distance was introduced in 1985 by E. Gabidulin [1]. He determined a lower bound for the minimum rank distance of a code. Moreover, he constructed a class of codes which meet this bound: the so-called Gabidulin codes. In this paper, we first characterize the linear isometries for the rank distance. Then we determine the isometry group and the permutation group of Gabidulin codes of ful...

Maximum distance separable codes for b-symbol read channels

Recently, Yaakobi et al. introduced codes for b-symbol read channels, where the read operation is performed as a consecutive sequence of b > 2 symbols. In this paper, we establish a Singleton-type bound on b-symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum bdistance. Based on...