Reducing the Overhead of BCH Codes: New Double Error Correction Codes

[EN] The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-known class of powerful error correction cyclic codes. BCH codes can correct multiple errors with minimal redundancy. Primitive BCH codes only exist for some word lengths, which do not frequently match those employed in digital systems. This paper focuses on double error correction (DEC) codes for word lengths that are in powers of two (8, 16, 32, and 64), which are commonly used in memories. We also focus on hardware implementations of the encoder and decoder circuits for very fast operations. This work proposes new low redundancy and reduced overhead (LRRO) DEC codes, with the same redundancy as the equivalent BCH DEC codes, but whose encoder, and decoder circuits present a lower overhead (in terms of propagation delay, silicon area usage and power consumption). We used a methodology to search parity check matrices, based on error patterns, in order to design the new codes. We implemented and synthesized them, and compared their results with those obtained for the BCH codes. Our implementation of the decoder circuits achieved reductions between 2.8% and 8.7% in the propagation delay, between 1.3% and 3.0% in the silicon area, and between 15.7% and 26.9% in the power consumption. Therefore, we propose LRRO codes as an alternative for protecting information against multiple errors. This research was supported in part by the Spanish Government, project TIN2016-81075-R, by Primeros Proyectos de Investigacion (PAID-06-18), Vicerrectorado de Investigacion, Innovacion y Transferencia de la Universitat Politecnica de Valencia (UPV), project 20190032, and by the Institute of Information and Communication Technologies (ITACA). Saiz-Adalid, L.; Gracia-Morán, J.; Gil Tomás, DA.; Baraza Calvo, JC.; Gil, P. (2020). Reducing the Overhead of BCH Codes: New Double Error Correction Codes. Electronics. 9(11):1-14. https://doi.org/10.3390/electronics9111897 Fujiwara, E. (2005). Code Design for Dependable Systems. doi:10.1002/0471792748 Xinmiao, Z. (2017). VLSI Architectures for Modern Error-Correcting Codes. doi:10.1201/b18673 Bose, R. C., & Ray-Chaudhuri, D. K. (1960). On a class of error correcting binary group codes. Information and Control, 3(1), 68-79. doi:10.1016/s0019-9958(60)90287-4 Chen, P., Zhang, C., Jiang, H., Wang, Z., & Yue, S. (2015). High performance low complexity BCH error correction circuit for SSD controllers. 2015 IEEE International Conference on Electron Devices and Solid-State Circuits (EDSSC)