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Decoding High-Order Interleaved Rank-Metric Codes

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh
2021 2021 IEEE International Symposium on Information Theory (ISIT)  
This paper presents an algorithm for decoding homogeneous interleaved codes of high interleaving order in the rank metric.  ...  In contrast to previously-known decoding algorithms, the new decoder works for any rank-metric code, not only Gabidulin codes.  ...  Metzner-Kapturowski Algorithm for Decoding High-Order Interleaved Codes in the Hamming Metric In [1] , Metzner and Kapturowski proposed a Hamming-metric decoding algorithm for interleaved codes with high  ... 
doi:10.1109/isit45174.2021.9518085 fatcat:ser3zcr2qjefhnwdohrzsbrwdi

Decoding High-Order Interleaved Rank-Metric Codes [article]

Sven Puchinger, Julian Renner, Antonia Wachter-Zeh
2019 arXiv   pre-print
This paper presents an algorithm for decoding homogeneous interleaved codes of high interleaving order in the rank metric.  ...  In contrast to previously-known decoding algorithms, the new decoder works for any rank-metric code, not only Gabidulin codes.  ...  Metzner-Kapturowski Algorithm for Decoding High-Order Interleaved Codes in the Hamming Metric In [1] , Metzner and Kapturowski proposed a Hamming-metric decoding algorithm for interleaved codes with high  ... 
arXiv:1904.08774v1 fatcat:zbedy7fyyzfzpbjyiihrqk7ql4

Interleaving Loidreau's Rank-Metric Cryptosystem [article]

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh
2019 arXiv   pre-print
We propose and analyze an interleaved variant of Loidreau's rank-metric cryptosystem based on rank multipliers.  ...  Finding secure instances requires near-MRD rank-metric codes which are not investigated in the literature.  ...  For a high interleaving order ℓ ≥ w, the algorithm proposed in [30] is able to solve the Interleaved Search RSD Problem with high probability in polynomial time.  ... 
arXiv:1901.10413v2 fatcat:5ojzkj4cljelpeugx2qlttizu4

Rank-Metric Codes and Their Applications [article]

Hannes Bartz, Lukas Holzbaur, Hedongliang Liu, Sven Puchinger, Julian Renner, Antonia Wachter-Zeh
2022 arXiv   pre-print
The rank metric measures the distance between two matrices by the rank of their difference.  ...  In distributed data storage, codes in the rank metric have been used repeatedly to construct codes with locality, and in coded caching, they have been employed for the placement of coded symbols.  ...  Thus, decoding (any) linear interleaved rank-metric code of high interleaving order is an easy problem. • For w ≤ ⌊ u u+1 (n − k)⌋, the Interleaved Gabidulin Code Search RSD Problem (Problem 3.1.8) can  ... 
arXiv:2203.12384v1 fatcat:brysqya7ynem5i25adxfwf5vl4

Repairing the Faure-Loidreau Public-Key Cryptosystem [article]

Antonia Wachter-Zeh and Sven Puchinger and Julian Renner
2018 arXiv   pre-print
A repair of the Faure-Loidreau (FL) public-key code-based cryptosystem is proposed. The FL cryptosystem is based on the hardness of list decoding Gabidulin codes which are special rank-metric codes.  ...  We prove that the recent structural attack on the system by Gaborit et al. is equivalent to decoding an interleaved Gabidulin code.  ...  Since the structure of this code only permits decoding like a random rank-metric code, it can be decoded with the syndrome decoding attack from [15] whose complexity is in the order of (n − k) 3 m 3  ... 
arXiv:1801.03688v2 fatcat:hba3jwr35ra7xfpsvg66rdtofm

Right-hand side decoding of Gabidulin code and applications [article]

Maxime Bombar, Alain Couvreur
2022 arXiv   pre-print
We discuss the decoding of Gabidulin and interleaved Gabidulin codes.  ...  Finally, we show that this algorithm turns out to provide a very clear and natural approach for the decoding of interleaved Gabidulin codes.  ...  Gabidulin codes are the rank-metric analogue of Reed-Solomon codes and are somehow optimal because they reach the rank-metric Singleton bound and come with efficient decoders up to the unique decoding  ... 
arXiv:2112.07322v2 fatcat:shvpiysf2zdbzixjpw2igmdcti

Multistage Iterative Decoding With Complexity Reduction for Concatenated Space–Time Codes

A. Reial, S.G. Wilson
2005 IEEE Transactions on Communications  
This iterative decoder architecture allows an encoder employing decoupled coding and modulation to reach the performance of coded modulation systems.  ...  Space-time encoders exploiting concatenated coding structures are efficient in attaining the high rates available to largedimensional multiple-transmitter, multiple-receiver wireless systems under fading  ...  taking advantage of the available high diversity orders.  ... 
doi:10.1109/tcomm.2005.852848 fatcat:7goy4hqhozfghf2vgl76jydaae

Bit-interleaved space-frequency coded Modulation for OFDM systems

D. Rende, T.F. Wong
2005 IEEE Transactions on Wireless Communications  
A block precoding method is proposed to further improve the diversity order. An efficient sphere decoding algorithm is also developed, for reducing the decoding complexity of the proposed scheme.  ...  We present an orthogonal frequency-division multiplexing (OFDM) system with bit-interleaved space-frequency coded modulation for frequency-selective fading channels employing multiple transmit and receive  ...  Therefore, space-time codes with high trellis complexities are needed for channels with large frequency-selectivity orders.  ... 
doi:10.1109/twc.2005.853816 fatcat:vhwl2mnc7reyvncbmvoyokalp4

LIGA: A Cryptosystem Based on the Hardness of Rank-Metric List and Interleaved Decoding [article]

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh
2020 arXiv   pre-print
We propose the new rank-metric code-based cryptosystem LIGA which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes.  ...  and interleaved decoding of Gabidulin codes.  ...  Also, we are thankful to Michael Schelling for his observation that decryption of the FL system can be seen as error-erasure decoding.  ... 
arXiv:1812.04892v2 fatcat:mz3o2goz3zdnno6dcfgcy2fuye

A Public-Key Cryptosystem from Interleaved Goppa Codes [article]

Molka Elleuch, Antonia Wachter-Zeh, Alexander Zeh
2018 arXiv   pre-print
In this paper, a code-based public-key cryptosystem based on interleaved Goppa codes is presented.  ...  For example, for security level 128 bits, we obtain a key size of 696 Kbits whereas the classical McEliece scheme based on Goppa codes using list decoding requires a key size of 1935 Kbits.  ...  From a high-level point of view, decoding a "random" interleaved code is an easy problem for larger interleaving orders and if the burst errors has full rank.  ... 
arXiv:1809.03024v1 fatcat:mqoahhi7inbsfa4vbarxbyhnka

On Error Decoding of Locally Repairable and Partial MDS Codes [article]

Lukas Holzbaur, Sven Puchinger, Antonia Wachter-Zeh
2019 arXiv   pre-print
We consider error decoding of locally repairable codes (LRC) and partial MDS (PMDS) codes through interleaved decoding.  ...  For PMDS codes we show that there is a wide range of parameters for which interleaved decoding can increase their decoding radius beyond the minimum distance with the probability of successful decoding  ...  beyond their minimum distance with high probability by the decoding algorithm for high-order interleaved codes by Metzner and Kapturowski [11] .  ... 
arXiv:1904.05623v2 fatcat:omrqlztrxnc2nb2nyytkdw2xhe

Reduced-complexity collaborative decoding of interleaved Reed-Solomon and Gabidulin codes

Hans Kurzweil, Mathis Seidl, Johannes B. Huber
2011 2011 IEEE International Symposium on Information Theory Proceedings  
An alternative method for collaborative decoding of interleaved Reed-Solomon codes as well as Gabidulin codes for the case of high interleaving degree is proposed.  ...  As an example of application, simulation results are presented for a concatenated coding scheme using polar codes as inner codes.  ...  A NOTE ON GABIDULIN CODES Gabidulin codes [7] are a class of linear rank metric codes which play an important role in random linear network coding [8] .  ... 
doi:10.1109/isit.2011.6034030 dblp:conf/isit/KurzweilSH11 fatcat:xgvxwmuqs5hdnhd3yxapimw6cm

LIGA: a cryptosystem based on the hardness of rank-metric list and interleaved decoding

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh
2021 Designs, Codes and Cryptography  
AbstractWe propose the new rank-metric code-based cryptosystem which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes. is an improved variant of the Faure–Loidreau  ...  and interleaved decoding of Gabidulin codes.  ...  Interleaved rank-metric codes Interleaved Gabidulin Codes are a code class for which efficient decoders are known that are able to correct w.h.p. random errors of rank larger than d−1 2 .  ... 
doi:10.1007/s10623-021-00861-z fatcat:ugo3dwngfrb7rpnqwiuckzpe5i

List and unique error-erasure decoding of interleaved Gabidulin codes with interpolation techniques

Antonia Wachter-Zeh, Alexander Zeh
2014 Designs, Codes and Cryptography  
A new interpolation-based decoding principle for interleaved Gabidulin codes is presented.  ...  This decoding principle can be applied as a list decoding algorithm (where the list size is not necessarily bounded polynomially) as well as an efficient probabilistic unique decoding algorithm.  ...  (Interleaved) Gabidulin Codes Gabidulin codes [3, 6, 26] are special MRD codes and are considered as rank-metric analogs of Reed-Solomon codes.  ... 
doi:10.1007/s10623-014-9953-5 fatcat:rdn5tpvy3nhrxfqmakuk4huktm

List and Unique Error-Erasure Decoding of Interleaved Gabidulin Codes with Interpolation Techniques [article]

Antonia Wachter-Zeh, Alexander Zeh
2014 arXiv   pre-print
A new interpolation-based decoding principle for interleaved Gabidulin codes is presented.  ...  This decoding principle can be applied as a list decoding algorithm (where the list size is not necessarily bounded polynomially) as well as an efficient probabilistic unique decoding algorithm.  ...  (Interleaved) Gabidulin Codes Gabidulin codes [3, 6, 26] are special MRD codes and are considered as rank-metric analogs of Reed-Solomon codes.  ... 
arXiv:1404.6048v1 fatcat:kkw57tfr55fztfc2e4da44o4rq
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