A construction of MDS array codes
نویسندگان
چکیده
In this paper a new construction of MDS array codes is introduced. In order to obtain a code with this property, the parity-check matrix is constructed just using a superregular matrix by blocks composed by powers of the companion matrix of a primitive polynomial. Also a decoding algorithm for these codes is introduced.
منابع مشابه
Asymptotically MDS Array BP-XOR Codes
Belief propagation or message passing on binary erasure channels (BEC) is a low complexity decoding algorithm that allows the recovery of message symbols based on bipartite graph prunning process. Recently, array XOR codes have attracted attention for storage systems due to their burst error recovery performance and easy arithmetic based on Exclusive OR (XOR)-only logic operations. Array BP-XOR...
متن کاملConstacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
متن کاملLDPC Codes for Two-Dimensional Arrays
Binary codes over two-dimensional arrays are very useful in data storage, where each array column represents a storage device or unit that may suffer failure. In this paper we propose a new framework for probabilistic construction of codes on two-dimensional arrays. Instead of a pure combinatorial erasure model used in traditional array codes, we propose a mixed combinatorial-probabilistic mode...
متن کاملConstructions of MDS-convolutional codes
Maximum-distance separable (MDS) convolutional codes are characterized through the property that the free distance attains the generalized singleton bound. The existence of MDS convolutional codes was established by two of the authors by using methods from algebraic geometry. This correspondence provides an elementary construction of MDS convolutional codes for each rate k/n and each degree δ. ...
متن کاملCauchy MDS Array Codes With Efficient Decoding Method
Array codes have been widely used in communication and storage systems. To reduce computational complexity, one important property of the array codes is that only XOR operation is used in the encoding and decoding process. In this work, we present a novel family of maximal-distance separable (MDS) array codes based on Cauchy matrix, which can correct up to any number of failures. We also propos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013