A Novel High-Speed Systematic Encoder for Long Binary Cyclic Codes

Long codes encoders have some limitations in high speed data transmission, making them not adequate to some applications' requirements. In this paper, a novel systematic encoding algorithm for cyclic codes shows a satisfactory time saving percentage over traditional algorithms, especially for long codes (n ≥ 2
¹⁴
-1). Time computational complexity of max{O(t √k),O(t
²
log n) log(t log n) log (log (t log n)))} has been estimated for the proposed encoder. Although the proposed encoder is applicable to any cyclic code, comparisons to conventional encoders (systematic and non-systematic) are carried out for long BCH codes. MATLAB simulated results prove superior time saving percentage over traditional encoders, especially for extremely long codes even with large error correction capability.