Abstract
Reed–Solomon (RS) codes are generally employed to detect and correct errors in digital transmission and storage systems. The primitive polynomial has a great role to design any RS codes. In this chapter, a RS (255, 249) codec has been designed and implemented based on sixteen primitive polynomials over GF(\(2^8\)) field. The details of theoretical and FPGA synthesis results of the RS (255, 249) codec are presented here. The area in terms of lookup tables and delay of RS (255, 249) codec have been observed for sixteen primitive polynomials. The RS (255, 249) codec based on primitive polynomial, PP3 = \(x^{8} +x^{5} +x^{3} +x^{2} +1\), has consumed lowest area compared to all other primitive polynomials. This codec architecture can be employed in M-ary phase-shift keying modulation scheme and ultra-wideband application.
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References
S. Lin, D.J. Costello, Error Control Coding: Fundamentals and Applications. Prentice-Hall (1983)
S.B. Wicker, V.K. Bhargava, Reed Solomon Codes and Their Applications. IEEE Press (1994)
J. Baek, M.H. Sunwoo, Low hardware complexity key equation solver chip for ReedSolomon decoders, in Proceedings of IEEE Asian Solid-State Circuits Conference (Jeju, Korea, 2007), p. 5154
I.S. Reed, M.T. Shih, T.K. Truong, VLSI design of inverse-free Berlekamp Massey algorithm, in Proceedings of the Institution of Electrical Engineers, vol. 138 (1991), pp. 295–298
H.C. Chang, C.B. Shung, New serial architecture for the Berlekamp Massey algorithm. IEEE Trans. Commun. 47(4), 441–443 (1999)
J.H. Jeng, T.K. Truong, On decoding of both errors and erasures of a Reed-Solomon code using an inverse-free Berlekamp-Massey algorithm. IEEE Trans. Commun. 47(10), 1488–1494 (1999)
D.V. Sarwate, N.R. Shanbhag, High-speed architectures for Reed-Solomon decoder. IEEE Trans. VLSI Syst. 9(5), 641–655 (2001)
Y.W. Chang, T.K. Truong, J.H. Jeng, VLSI architecture of modified Euclidean algorithm for reed-Solomon code. Inform. Sci. 155(1), 139–150 (2003)
A. Kumar, S. Sawitzki, High Throughput and Low power Reed Solomon Decoder for Ultra Wide Band, in Proceedings of Intelligent Algorithms in Ambient and Biomedical Computing, vol. 7 (2006), pp. 299–316
I.S. Jin, Design and implementation of efficient Reed-Solomon decoder for intelligent home networking, in Proceedings of Conference (FGCN), CCIS 265 (2011), pp. 261–268
J. Samanta, J. Bhaumik, S. Barman, FPGA based area efficient RS (23, 17) codec. Microsyst. Technol. 23(3), 639–650 (2017)
M.B. Dissanayake, Y. Deng, A. Nallanathan, E.M.N. Ekanayake, M. Elkashlan, Reed Solomon codes for molecular communication with full absorption receiver. IEEE Commun. Lett. (2017)
(255, 249) Reed Solomon Decoder, Algorithm data sheet. Blue Rum Consulting Limited (2009)
G. Heidari, WiMedia UWB: Technology of Choice for Wireless USB and Bluetooth. Wiley (2008). ISBN: 978-0-470-51834-2
R.D. Cideciyan, E. Eleftheriou, Concatenated Reed-Solomon/convolutional coding scheme for data transmission in CDMA cellular systems, in IEEE Vehicular Technology Conference (1994), pp. 1369–1373
Kar Peo Yar, Design and analysis of short packet and concatenated coded communication systems, Ph.D. Thesis, The University of Michigan, 2007
S.N. Ramlan, R. Mohamad, N. Arbain, Implementation of M-ary Phase Shift Keying (PSK) base band modem on Texas instrument digital signal processor TMS320C6713, in Proceedings in IEEE International Conference on Computer Applications and Industrial Electronics (ICCAIE) (2011), pp. 627–632
M. Wan, N. Zhang, Searching IP Blocks: Application Specific Components, https://people.eecs.berkeley.edu/~newton/Classes/EE290sp99/pages/hw2/asc.htm
D. Bhattacharya, D. Mukhopadhyay, D. Roy, Chowdhury, A cellular automata based approach for generation of large primitive polynomial and its application to RS-Coded MPSK modulation. Lecture Notes in Computer Science vol. 4173 (2006), pp. 204–214
T. Hansen, G.L. Mullen, Primitive polynomials over finite fields. Math. Comput. 59(200), 639–643 (1992)
W. Han, The distribution of coefficient of primitive polynomials over finite fields. Cryptogr. Comput. Number Theory 20, 43–57 (2001)
C. Xiaojun, G. Jun, L. Zhihui, RS encoder design based on FPGA, in Proceedings of 2nd IEEE, ICACC 2010, vol. 1 (2010), pp. 419-421
R. Huynh, G.E. Ning, Y. Huazhong, A low power error detection in the syndrome calculator block for Reed-Solomon codes: RS(204, 188). J. Tsinghua Sci. Technol. 14(4), 474–477 (2009)
J.I. Park, K. Lee, C.S. Choi, H. Lee, High-speed low-complexity Reed-Solomon decoder using pipelined Berlekamp-Massey algorithm and its folded architecture. J. Semicond. Technol. Sci. 10(3), 193–202 (2010)
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Samanta, J., Bhaumik, J., Barman, S., Hossain, S.G.S., Sahu, M., Dutta, S. (2017). RS (255, 249) Codec Based on All Primitive Polynomials Over GF(\(2^8\)). In: Bhaumik, J., Chakrabarti, I., De, B.P., Bag, B., Mukherjee, S. (eds) Communication, Devices, and Computing. ICCDC 2017. Lecture Notes in Electrical Engineering, vol 470. Springer, Singapore. https://doi.org/10.1007/978-981-10-8585-7_7
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