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/electronics9111897S114911Fujiwara, E. 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DEC ECC design to improve memory reliability in Sub-100nm technologies. 2008 15th IEEE International Conference on Electronics, Circuits and Systems. doi:10.1109/icecs.2008.4674921Saiz-Adalid, L.-J., Gracia-Moran, J., Gil-Tomas, D., Baraza-Calvo, J.-C., & Gil-Vicente, P.-J. (2019). Ultrafast Codes for Multiple Adjacent Error Correction and Double Error Detection. IEEE Access, 7, 151131-151143. doi:10.1109/access.2019.2947315Saiz-Adalid, L.-J., Gil-Vicente, P.-J., Ruiz-García, J.-C., Gil-Tomás, D., Baraza, J.-C., & Gracia-Morán, J. (2013). Flexible Unequal Error Control Codes with Selectable Error Detection and Correction Levels. Computer Safety, Reliability, and Security, 178-189. doi:10.1007/978-3-642-40793-2_17Saiz-Adalid, L.-J., Reviriego, P., Gil, P., Pontarelli, S., & Maestro, J. A. (2015). MCU Tolerance in SRAMs Through Low-Redundancy Triple Adjacent Error Correction. 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Multiple Cell Upsets Correction for OLS Codes

ABSTRACT: An Error Correction code with Parity check matrix is implemented which is other type of the One Step Majority Logic Decodable (OS-MLD) called as Orthogonal Latin Squares (OLS) codes. It is a concurrent error detection technique for OLS codes encoders and syndrome computation because of the fact that when ECCs are used, the encoder and decoder circuits can also suffer errors.These OLS codes are used to correct the memories and caches. This can be achieved due to their modularity such that the error correction capabilities can be easily adapted to the error rate or to the mode of the operation.OLS codes typically require more parity bits than other codes to correct the same number of errors. However, due to their modularity and the simple low delay decoding implementation these are widely used in Error Correction. All the errors that affect a single circuit node are detected by the parity prediction scheme. The area and latency values are monitored

Design, Implementation and Evaluation of a Low Redundant Error Correction Code

[EN] The continuous raise in the integration scale of CMOS technology has provoked an augment in the fault rate. Particularly, computer memory is affected by Single Cell Upsets (SCU) and Multiple Cell Upsets (MCU). A common method to tolerate errors in this element is the use of Error Correction Codes (ECC). The addition of an ECC introduces a series of overheads: silicon area, power consumption and delay overheads of encoding and decoding circuits, as well as several extra bits added to allow detecting and/or correcting errors. ECC can be designed with different parameters in mind: low redundancy, low delay, error coverage, etc. The idea of this paper is to study the effects produced when adding an ECC to a microprocessor with respect to overheads. Usually, ECC with different characteristics are continuously proposed. However, a great quantity of these proposals only present the ECC, not showing its behavior when using them in a microprocessor. In this work, we present the design of an ECC whose main characteristic is a low number of code bits (low redundancy). Then, we study the overhead this ECC introduces. Firstly, we show a study of silicon area, delay and power consumption of encoder and decoder circuits, and secondly, how the addition of this ECC affects to a RISC microprocessor.© 2021 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Gracia-Morán, J.; Saiz-Adalid, L.; Baraza-Calvo, J.; Gil Tomás, DA.; Gil, P. (2021). Design, Implementation and Evaluation of a Low Redundant Error Correction Code. IEEE Latin America Transactions. 19(11):1903-1911. https://doi.org/10.1109/TLA.2021.947562419031911191