RS (255, 249) Codec Based on All Primitive Polynomials Over GF(\(2^8\))

  • Jagannath Samanta
  • Jaydeb Bhaumik
  • Soma Barman
  • Sk. G. S. Hossain
  • Mandira Sahu
  • Subrata Dutta
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 470)

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.

Keywords

Galois field Primitive polynomial Reed–Solomon code Phase-shift keying RiBM algorithm and FPGA 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Jagannath Samanta
    • 1
  • Jaydeb Bhaumik
    • 1
  • Soma Barman
    • 2
  • Sk. G. S. Hossain
    • 3
  • Mandira Sahu
    • 1
  • Subrata Dutta
    • 1
  1. 1.Haldia Institute of TechnologyHaldiaIndia
  2. 2.Institute of Radio Physics and ElectronicsUniversity of CalcuttaKolkataIndia
  3. 3.Department Of CSEAliah UniversityNewtownIndia

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