Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm
نویسندگان
چکیده
We prove that Alekhnovich’s algorithm can be used for row reduction of skew polynomial matrices. This yields an O(ln log(n)) decoding algorithm for l-Interleaved Gabidulin codes of length n, where ω is the matrix multiplication exponent, improving in the exponent of n compared to previous results.
منابع مشابه
On Transform–domain Decoding of Gabidulin Codes
Gabidulin codes are the rank metric analogues of Reed–Solomon codes and found many applications including network coding. Interleaving or the direct sum of Gabidulin codes allows both decreasing the redundancy and increasing the error correcting capability for network coding. In this paper, for Gabidulin codes we propose a transform–domain algorithm correcting both errors and erasures. We show ...
متن کاملDecoding of Block and Convolutional Codes in Rank Metric DISSERTATION
Rank-metric codes recently attract a lot of attention due to their possible application to network coding, cryptography, space-time coding and distributed storage. An optimal-cardinality algebraic code construction in rank metric was introduced some decades ago by Delsarte, Gabidulin and Roth. This Reed–Solomon-like code class is based on the evaluation of linearized polynomials and is nowadays...
متن کاملDecoding of block and convolutional codes in rank metric
R ank-metric codes recently attract a lot of attention due to their possible application to network coding, cryptography, space-time coding and distributed storage. An optimal-cardinality algebraic code construction in rank metric was introduced some decades ago by Delsarte, Gabidulin and Roth. This Reed–Solomon-like code class is based on the evaluation of linearized polynomials and is nowaday...
متن کاملList and unique error-erasure decoding of interleaved Gabidulin codes with interpolation techniques
A new interpolation-based decoding principle for interleaved Gabidulin codes is presented. The approach consists of two steps: First, a multi-variate linearized polynomial is constructed which interpolates the coefficients of the received word and second, the roots of this polynomial have to be found. Due to the specific structure of the interpolation polynomial, both steps (interpolation and r...
متن کاملRow reduction applied to decoding of rank-metric and subspace codes
We show that error and erasure decoding of `-Interleaved Gabidulin codes, as well as list-` decoding of Mahdavifar–Vardy codes can be solved by row reducing skew polynomial matrices. Inspired by row reduction of F[x] matrices, we develop a general and flexible approach of transforming matrices over skew polynomial rings into certain normal forms. We apply this to solve generalised shift registe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 57 شماره
صفحات -
تاریخ انتشار 2017