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Repair of RS codes with optimal access and error correction
2020 IEEE International Symposium on Information Theory (ISIT), 2020We address two aspects of the repair problem of Reed-Solomon codes. First, we propose a new repair scheme for the RS codes constructed in [Tamo-Ye-Barg, IEEE Trans. Inf. Theory, May 2019] which in addition to optimal repair bandwidth is also robust to erroneous information provided by the helper nodes.
Zitan Chen, Min Ye 0005, Alexander Barg
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2019
This chapter begins presenting the original approach to Reed–Solomon (RS) codes exhibiting the generator matrix of the code. This is followed by an equivalent method that selects codewords “screening” words by the parity-check matrix. The familiar ideas of addition and multiplication of complex numbers are utilized to construct Galois fields using ...
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This chapter begins presenting the original approach to Reed–Solomon (RS) codes exhibiting the generator matrix of the code. This is followed by an equivalent method that selects codewords “screening” words by the parity-check matrix. The familiar ideas of addition and multiplication of complex numbers are utilized to construct Galois fields using ...
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A decoding algorithm for DEC RS codes
Proceedings of IEEE. IEEE Region 10 Conference. TENCON 99. 'Multimedia Technology for Asia-Pacific Information Infrastructure' (Cat. No.99CH37030), 2003A step-by-step decoding algorithm is proposed for double-error-correcting (DEC) Reed-Solomon (RS) codes of length n=2/sup m/-1. Since the decoding algorithm can directly find the error value at the highest-order position in a received vector without determining the error location polynomial, the decoding procedure is very simple and regular, and ...
null Erl-Huei Lu +2 more
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Optimal RS-like LRC codes of arbitrary length
Applicable Algebra in Engineering, Communication and Computing, 2020RS-like locally recoverable (LRC) codes have a construction based on the classical construction of Reed-Solomon (RS) codes, where codewords are obtained as evaluations of suitably chosen polynomials. These codes were previously introduced under the assumption that the length \(n\) of the code is divisible by \(r+1,\) where \(r\) is the locality of the ...
Charul Rajput, Maheshanand Bhaintwal
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More on the Minimum and Stopping Distances of RS-LDPC Codes
IEEE Communications Letters, 2020Based on the extended Reed-Solomon (RS) code that has two information symbols over the field ${\mathbb F}_{q}$ , we can construct a binary regular matrix ${ {\boldsymbol{\textstyle H}}}(\gamma,\rho)$ , where $q:=2^{r}$ for some positive integer $r$ , $\gamma $ and $\rho $ are two positive integers such that $\gamma ...
Haiyang Liu, Xiaopeng Jiao
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Iterative coding and decoding algorithm of RS digital fountain code
2008 11th IEEE Singapore International Conference on Communication Systems, 2008Combining forward error correcting and automatic repeat request is a commonly used method in digital communication system. But in broadcast communication system, this method will compromise the communication efficiency and cause longer transmission delay due to the need of retransmitting data. This problem, however, can be effectively solved by the use
null Weijia Lei +3 more
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On the performance of LDPC-RS product codes for mobile DTV
IEEE international Symposium on Broadband Multimedia Systems and Broadcasting, 2012This paper proposes an LDPC-RS product codes for the future terrestrial DTV system, which has to face an increasing demand of high spectrum efficiency and reliability. Particularly, we develop an adaptive decoding algorithm that can switch dynamically according to the SNR of received signals.
Yaqi Li +6 more
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2019
Abstract This chapter addresses the myth of ‘decentralized governance’ of public blockchains, arguing that certain people who create, operate, or reshape them function much like fiduciaries of those who rely on these data structures. It compares the role of leading software developers and Frankel’s conception of a ‘fiduciary’ and finds ...
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Abstract This chapter addresses the myth of ‘decentralized governance’ of public blockchains, arguing that certain people who create, operate, or reshape them function much like fiduciaries of those who rely on these data structures. It compares the role of leading software developers and Frankel’s conception of a ‘fiduciary’ and finds ...
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Implementation Architectures and Applications of RS Codes
1999Some basic concepts of the RS codes and various encoding and decoding algorithms are discussed in Chapter 6. In this chapter, certain implementation architectures for RS codes are examined and compared. Also to further demonstrate the power of RS codes certain important applications of are introduced in this chapter.
Irving S. Reed, Xuemin Chen
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Explicit constructions of MDS array codes and RS codes with optimal repair bandwidth
2016 IEEE International Symposium on Information Theory (ISIT), 2016Given any r and n, we present an explicit construction of high-rate maximum distance separable (MDS) array codes that can optimally repair any d failed nodes from any h helper nodes for all h, 1 ≤ h ≤ r and d, k ≤ d ≤ n − h simultaneously. These codes can be constructed over any base field F as long as |F| ≥ sn; where s = lcm(1, 2, …, r). The encoding,
Min Ye 0005, Alexander Barg
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