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Peak-to-mean power control and error correction for OFDM transmission using Golay sequences and Reed-Muller codes

J.A. Davis, J. Jedwab
1997 Electronics Letters  
In this correspondence we derive lower bounds on the maximum number of codewords in a class of frameproof codes and traceability schemes, and give constructions for both with more codewords than the best  ...  Abstract-In this correspondence we derive lower bounds on the maximum number of codewords in a class of frame-proof codes and traceability schemes, and give constructions for both with more codewords than  ...  Known Bounds on Error-Correcting Codes In this section, we recall some known results from coding theory.  ... 
doi:10.1049/el:19970205 fatcat:z6jt742rsnhsbfdh2hct6nvvge

Serial concatenation of reed muller and LDPC codes with low error floor

Xin Xiao, Mona Nasseri, Bane Vasic, Shu Lin
2017 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
In this paper, we propose a concatenated coding scheme involving an outer Reed-Muller (RM) code and an inner Finite Field low-density parity check (LDPC) code of medium length and high rate.  ...  It lowers the error floor of inner Finite Field LDPC code. This concatenation scheme offers flexibility in design and it is easy to implement.  ...  Reed Muller code Reed Muller Codes are one class of linear block codes that can correct multiple errors.  ... 
doi:10.1109/allerton.2017.8262804 dblp:conf/allerton/XiaoNVL17 fatcat:xvbw2lg7cbcv7le3n2gg5goi3u

Accelerating Soft-Decision Reed-Muller Decoding Using a Graphics Processing Unit

Md. Sharif Uddin, Cheol Hong Kim, Jong-Myon Kim
2014 Asia-pacific Journal of Multimedia services convergent with Art Humanities and Sociology  
To solve this problem, this paper proposes a graphics processing unit (GPU)-based parallel error control approach using Reed-Muller R(r, m) coding for real-time wireless communication systems.  ...  The Reed-Muller code is one of the efficient algorithms for multiple bit error correction, however, its high-computation requirement inherent in the decoding process prohibits its use in practical applications  ...  It is one of linear error-correcting codes. The Reed-Muller code was invented by D. E. Muller and I. S.  ... 
doi:10.14257/ajmahs.2014.12.10 fatcat:7ezipzbs3rfmjdivczgv4xz7q4

Correcting capacity of soft-decision decoder of ternary Reed – Muller second-order codes with a large number of errors
Корректирующая способность декодера мягких решений троичных кодов Рида - Маллера второго порядка при большом числе ошибок

Nadegda Mogilevskaya--
2015 Вестник Донского государственного технического университета  
codes, softdecision decoder, mathematical model of communication channel, experimental research of the code correcting capability, error control out of the half minimum code distance.  ...  on-Don, Russian Federation F3 F3 The research objective is to study the correcting capacity of a new soft decoder of Reed-Muller codes.  ...  codes, softdecision decoder, mathematical model of communication channel, experimental research of the code correcting capability, error control out of the half minimum code distance.  ... 
doi:10.12737/10395 fatcat:cb4abio7x5befjez2adaq4nldy

Fault-Tolerant Conversion between the Steane and Reed-Muller Quantum Codes

Jonas T. Anderson, Guillaume Duclos-Cianci, David Poulin
2014 Physical Review Letters  
The 15-qubit Reed-Muller code also does not admit a universal fault-tolerant gate set but possesses fault-tolerant T and control-control-Z gates.  ...  One interpretation of our result is that both codes correspond to the same subsystem code in different gauges. Our scheme extends to the entire family of quantum Reed-Muller codes.  ...  Clifford group transformations are realized in Steane's 7-qubit code [19] , while the T ¼ Z 1=4 gate and/or the control-control-Z gate are realized using the 15-qubit Reed-Muller code [15] ; either of  ... 
doi:10.1103/physrevlett.113.080501 pmid:25192082 fatcat:mxt2atun6ne3bck6cdm7ovkz7m

Page 7543 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
7543 2000j:94034 94B05 Paterson, Kenneth G. (4-HPL; Bristol) Generalized Reed-Muller codes and power control in OFDM modulation. (English summary) IEEE Trans. Inform.  ...  In this paper, a powerful theory linking Golay complementary sets of polyphase sequences and Reed-Muller codes is developed.  ... 

Page 3628 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
on the covering radii of the Reed-Muller codes.  ...  Summary: “Let R(r,m) be the rth-order Reed-Muller code of length 2”, and let p(r,m) be its covering radius.  ... 

A Performance Comparison Of Golay And Reed-Muller Coded Ofdm Signal For Peak-To-Average Power Ratio Reduction

Sanjay Singh, M Sathish Kumar, H. S Mruthyunjaya
2009 Zenodo  
Moreover, for the optimum PAPR reduction performance, code configuration for Golay and Reed-Muller codes has been identified.  ...  In this paper we have compared the PAPR reduction performance of Golay and Reed-Muller coded OFDM signal.  ...  By employing error control coding techniques it gives dual advantage of error control as well as PAPR reduction. Next two sections deals with Golay and Reed-Muller codes.  ... 
doi:10.5281/zenodo.1335381 fatcat:bscktm4o6zbcffppnfabuo7afa

Page 1825 of Mathematical Reviews Vol. 52, Issue 5 [page]

1976 Mathematical Reviews  
subcodes of the binary Reed-Muller codes and can be very simply instrumented, (3) a new class of constacyclic codes that are subcodes of the p-ary Reed-Muller codes, (4) two new classes of binary convolutional  ...  This property is then used as the key to a variety of code constructions, including: (1) a simplified derivation of binary Reed-Muller codes [I. S. Reed, Trans. I.R.E.  ... 

On the Super Codes of the First Order Reed-Muller Code Based on m-Sequence Pairs

Ying Xu, Yuejun Wei, Yuhang Yang, Wen Chen
2011 2011 IEEE 73rd Vehicular Technology Conference (VTC Spring)  
The super codes of the first order Reed-Muller code are widely used in the practical wireless communication systems, such as WCDMA and LTE.  ...  In addition, the constructed super codes outperform the conventional codes in terms of decoding error rate.  ...  INTRODUCTION The super codes of the first order Reed-Muller are a conventional error-correcting code, which can provide excellent performance when the code length is short.  ... 
doi:10.1109/vetecs.2011.5956255 dblp:conf/vtc/XuWYC11 fatcat:njljt6me4rgv5bti6o6sxer3ga

Page 2958 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
Summary: “Recursive representations of the matrices of two vari- ations of Reed-Muller transforms that are used for first-order Reed-Muller codes and certain Hamming codes are presented, and coding and  ...  The recursive construction of the binary Reed-Muller codes [F. J. MacWilliams and N. J. A.  ... 

Quantum Reed-Muller codes

A.M. Steane
1999 IEEE Transactions on Information Theory  
A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n, k, d]  ...  with a few comments on the usefulness of the quantum Reed-Muller codes.  ...  In equation (5) , take G 1 = G 2 = 2 r , k RM (t, r), 2 t+1 Reed-Muller code, (6) where k RM (t, r) = 2 r − t i=0 C(r, i). (7) Take D x such that G 1 and D x together generate the Reed-Muller code of  ... 
doi:10.1109/18.771249 fatcat:2zoavomj2namxfvyijz3mekgzu

Error Correction at Malicious Nodes using Reed-Muller Codes

Ratnakumari Challa, Devaraju Isuru, Kanusu Srinivasa
2016 International Journal of Computer Applications  
To handle message tampering at articulation points, this system performs error correction using Reed-Muller decoding algorithm.  ...  This paper proposes a model where Reed-Muller codes are used to find the locations of the malicious nodes and calculate the probability that a node is malicious.  ...  The malicious nodes can also be detected by using error control codes. Reed-Muller codes are used as error control codes to determine the locations [2] of the malicious nodes in the network.  ... 
doi:10.5120/ijca2016911721 fatcat:o2dzrheljfeizaltq6yc4r7v2q

A brief history of the development of error correcting codes

I.S. Reed
2000 Computers and Mathematics with Applications  
Also details are given about the origins of both the Reed-Muller and Reed-Solomon codes. (~)  ...  It describes the history in which the author was a participant in some of the early developments of error-correcting codes and computers.  ...  Somewhat after the time of my work on Reed-Muller codes, Neal came to me one day and said, "Irv, I want you to teach me about error-correcting codes."  ... 
doi:10.1016/s0898-1221(00)00112-7 fatcat:qcpmplrixnh3zepk4tx32pz5we

Quantum Reed-Muller Codes [article]

Andrew Steane
1996 arXiv   pre-print
A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n,k,d]] = [[2^r, 2^r - C(r,t) - 2 sum_i=0^t-1 C(r,i), 2^t + 2^t-1 ]].  ...  conclude with a few comments on the usefulness of the quantum Reed-Muller codes.  ...  In equation (8) , take G 1 = G 2 = 2 r , k RM (t, r), 2 t+1 Reed-Muller code, (9) where k RM (t, r) = 2 r − t i=0 C(r, i). (10) Take D x such that G 1 and D x together generate the Reed-Muller code of  ... 
arXiv:quant-ph/9608026v2 fatcat:vm26jtgjvvb6bg2k5bnb3n3lsm
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