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

Abstract

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 ≥ 214 − 1). Time computational complexity of max{O(t √ k),O(t2 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