Simultaneous Partial Inverses and Decoding Interleaved Reed–Solomon Codes
نویسندگان
چکیده
منابع مشابه
Simultaneous Partial Inverses and Decoding Interleaved Reed-Solomon Codes
This paper introduces the simultaneous partialinverse problem for polynomials and develops its application to decoding interleaved Reed-Solomon codes and subfield-evaluation codes beyond half the minimum distance. The simultaneous partial-inverse problem has a unique solution (up to a scale factor), which can be computed by an efficient new algorithm, for which we also offer some variations. De...
متن کاملDecoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm
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.
متن کاملImproved Decoding of Interleaved AG Codes
We analyze a generalization of a recent algorithm of Bleichenbacher et al. for decoding interleaved codes on the Q-ary symmetric channel for large Q. We will show that for any m and any the new algorithms can decode up to a fraction of at least βm βm+1 (1−R−2Q−1/2m)− errors, where β = ln(qm−1) ln(qm) , and that the error probability of the decoder is upper bounded by O(1/q ), where n is the blo...
متن کاملDecoding Interleaved Gabidulin Codes and Ciphertext-Security for GPT variants
In this paper we view interleaved Gabidulin codes and describe how to correct errors up to a rank equal to the amount of redundancy of the code with high probability. We give a detailed proof for our estimation of the probability of correct decoding. In a second part, we view the application to variants of the GPT cryptosystem. For GGPT this leads to an efficient attack on the remaining secure ...
متن کاملDecoding interleaved Reed-Solomon codes over noisy channels
We consider error-correction over the Non-Binary Symmetric Channel (NBSC) which is a natural probabilistic extension of the Binary Symmetric Channel (BSC). We propose a new decoding algorithm for interleaved Reed-Solomon Codes that attempts to correct all “interleaved” codewords simultaneously. In particular, interleaved encoding gives rise to multi-dimensional curves and more specifically to a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2018
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2018.2868701