Interleaved Reed-Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed-Solomon codes. Usually, these codewords are decoded independently by classical algebraic decoding methods. However, by collaborative algebraic decoding approaches, such interleaved schemes allow the correction of error patterns beyond half the minimum distance, provided that the errors in the received signal occur in bursts. In this work, collaborative decoding of interleaved Reed-Solomon codes by multi-sequence shift-register synthesis is considered and analyzed. Based on the framework of interleaved Reed-Solomon codes, concatenated code designs are investigated, which are obtained by interleaving several Reed-Solomon codes, and concatenating them with an inner block code.

In this paper, we present a new soft-decision decoding algorithm for Reed-Muller codes. It is based on the GMC decoding algorithm proposed by Schnabl and Bossert [1] which interprets Reed-Muller codes as generalized multiple concatenated codes. We extend the GMC algorithm to list-decoding (L-GMC). As a result, a SDML decoding algorithm for the first order Reed-Muller codes is obtained. Moreover, the performance achieved with L-GMC for Reed-Muller codes of higher order is considerably better compared to GMC. In particular, for the Reed-Muller codes of length ¢ ¡ ¤ £ , quasi SDML decoding performance is obtained at a computational complexity that is by far less than optimum decoding using the syndrome trellis [2]. Simulations will also show that for Reed-Muller codes up to a length 1024, the performance of L-GMC decoding is more than 1dB superior to conventional GMC decoding.

No abstract

Vector sets with optimal coherence according to the Welch bound cannot exist for all pairs of dimension and cardinality. If such an optimal vector set exists, it is an equiangular tight frame and represents the solution to a Grassmannian line packing problem. Best Complex Antipodal Spherical Codes (BCASCs) are the best vector sets with respect to the coherence. By extending methods used to find best spherical codes in the real-valued Euclidean space, the proposed approach aims to find BCASCs, and thereby, a complex-valued vector set with minimal coherence. There are many applications demanding vector sets with low coherence. Examples are not limited to several techniques in wireless communication or to the field of compressed sensing. Within this contribution, existing analytical and numerical approaches for coherence optimization of complex-valued vector spaces are summarized and compared to the proposed approach. The numerically obtained coherence values improve previously reported results. The drawback of increased computational effort is addressed and a faster approximation is proposed which may be an alternative for time critical cases.

In this paper, a new approach for decoding lowrate Reed-Solomon codes beyond half the minimum distance is considered and analyzed. Unlike the Sudan algorithm published in 1997, this new approach is based on multi-sequence shiftregister synthesis, which makes it easy to understand and simple to implement. The computational complexity of this shift-register based algorithm is of the same order as the complexity of the well-known Berlekamp-Massey algorithm. Moreover, the error correcting radius coincides with the error correcting radius of the original Sudan algorithm, and the practical decoding performance observed on a q-ary symmetric channel (QSC) is virtually identical to the decoding performance of the Sudan algorithm. Bounds for the failure and error probability as well as for the QSC decoding performance of the new algorithm are derived, and the performance is illustrated by means of examples.Index Terms-Reed-Solomon codes, decoding beyond half the minimum distance, Interleaved Reed-Solomon codes, multisequence shift-register synthesis,

No abstract

No abstract

We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for codebased cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.