Integer Codes Correcting Single Errors and Detecting Burst Errors Within a Byte

Correcting single and detecting adjacent errors has become important in memory systems using high density DRAM chips. The reason is that, in these systems, the strike of a single energetic particle can upset one or more adjacent bits. In this article, we present a simple solution for this problem based on integer codes capable of correcting single errors and detecting l -bit burst errors confined to a b -bit byte ( 1<l<b ). Unlike the classical approach, the proposed one does not rely on the use of dedicated encoding/decoding hardware. Instead, it uses the processor as both encoder and decoder. The effectiveness of such solution is demonstrated on a theoretical model of an eight-core processor. The obtained results show that it has the potential to be used in future DDR5 systems.This is the peer-reviewed version of the paper: Radonjic, A., 2020. Integer Codes Correcting Single Errors and Detecting Burst Errors Within a Byte. IEEE Transactions on Device and Materials Reliability 20, 748–753. [https://doi.org/10.1109/TDMR.2020.3033511]© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising 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.Published version: [https://hdl.handle.net/21.15107/rcub_dais_9998

Integer Codes Correcting Double Errors and Triple-Adjacent Errors Within a Byte

This article presents a class of integer codes that are suitable for use in optical computer networks in which the data are transmitted serially. The presented codes are constructed with the help of a computer and have three desirable properties. First, they use integer and lookup table operations, which make them suitable for software implementation. Second, depending on the application requirements, the proposed codes can be used as low-rate error correction (EC) codes or as high-rate error detection (ED) codes. In the EC mode, which is suited for realtime applications, the receiver can correct all single and double errors, as well as all triple-adjacent (TA) errors within one b-bit byte. On the other hand, if the integrity of data is of high importance, the receiver may operate in the ED mode. In that case, it is able to detect all quadruple errors, all double TA errors within one b-bit byte, and all double TA errors within two b-bit bytes. Finally, it is important to note that the presented codes can be interleaved without delay and without using any additional hardware. Owing to this, it is possible to construct simple codes capable of detecting/correcting multiple TA and random errors.This is the peer-reviewed version of the paper: Radonjic, A., 2020. Integer Codes Correcting Double Errors and Triple-Adjacent Errors Within a Byte. IEEE Transactions on Very Large Scale Integration (VLSI) Systems 28, 1901–1908. [https://doi.org/10.1109/TVLSI.2020.2998364]© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising 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.Published version: [https://hdl.handle.net/21.15107/rcub_dais_9991

Integer codes correcting sparse byte errors

In public optical networks, the data are scrambled with a xu + 1 self-synchronous scramblers (SSSs). The reason for this is to avoid long strings of ones or zeros, which might affect the receiver synchronization. Unfortunately, the use of SSSs is always related to the problem of duplication of channel errors. More precisely, each error occurring during the transmission will be duplicated u bits later. In this paper, we present a low-cost solution to this problem based on integer codes capable of correcting sparse byte errors.Radonjic, A., Vujicic, V., 2019. Integer codes correcting sparse byte errors. Cryptogr. Commun. 11, 1069–1077. [https://doi.org/10.1007/s12095-019-0350-9

Integer Codes Correcting High-Density Byte Asymmetric Errors

In optical networks without optical amplifiers, the number of received photons never exceeds the number of sent ones. Hence, upon transmission, only asymmetric (1 → 0) errors can occur. Motivated by this fact, in this letter, we present a class of integer codes capable of correcting high-density asymmetric errors within a b-bit byte. Unlike classical codes, these codes use integer and lookup table operations. As a result, they can be implemented “for free,” i.e., without modifying the network hardware.This is the peer-reviewed manuscript of the article: Radonjic, A., Vujicic, V., 2017. Integer Codes Correcting High-Density Byte Asymmetric Errors. IEEE Communications Letters 21, 694–697. [https://doi.org/10.1109/LCOMM.2016.2644661

Integer codes correcting burst asymmetric within a byte and double asymmetric errors

This paper presents a class of integer codes capable of correcting l-bit burst asymmetric errors within a b-bit byte (1 ≤ l < b) and double asymmetric errors within a codeword. The presented codes are constructed with the help of a computer and have the potential to be used in unamplified optical networks. In addition, the paper derives the upper bound on code length and shows that the proposed codes are efficient in terms of redundancy.This is the peer reviewed version of the following article: Radonjic, A., Vujicic, V., 2019. Integer codes correcting burst asymmetric within a byte and double asymmetric errors. Cryptogr. Commun. [https://doi.org/10.1007/s12095-019-00388-0]The original version of this article unfortunately contained a mistake in the main title. Instead of “Integer codes correcting burst asymmetric within a byte and double asymmetric errors” the title should read “Integer codes correcting burst asymmetric errors within a byte and double asymmetric errors”. The correction: [https://doi.org/10.1007/s12095-019-00398-y]Published version: [https://hdl.handle.net/21.15107/rcub_dais_10030

Integer Codes Correcting Spotty Byte Asymmetric Errors

In short-range optical networks, channel errors occur due to energy losses. Upon transmission, they mostly manifest themselves as spotty byte asymmetric errors. In this letter, we present a class of codes that can correct these errors. The presented codes use integer and lookup table operations, which make them suitable for software implementation. In addition, if needed, the proposed codes can be interleaved without delay and without using any additional hardware

Integer Codes Correcting Burst Asymmetric Errors Within a Byte

This paper presents two types of integer codes capable of correcting burst asymmetric errors within a byte. The presented codes are constructed with the help of a computer and are very efficient in terms of redundancy. The results of a computer search have shown that, for practical data lengths up to 4096 bits, the presented codes use up to two check-bits less than the best burst asymmetric error correcting codes. Besides this, it is shown that the presented codes are suitable for implementation on modern processors

Erratum to “Integer Codes Correcting Burst and Random Asymmetric Errors within a Byte” [J. Franklin Inst. 355 (2018) 981–996] (S0016003218302722) (10.1016/j.jfranklin.2018.04.034))

An equation appearing on page 992 of the article is incorrect. The incorrect equation appearing thus: [Formula presented] Should in fact appear thus: [Formula presented] Also, a sentence appearing on page 922 is incorrect. The following statement: [Formula presented] Should read thus: …one code with code rate 0.9922 has theoretical throughput above 32 Gbps. Thus, it could be candidate for use in ONWOAs operating at 32 Gbps (e.g. 32G Fibre Channel network). © 2018The contribution corrects an equation from the paper: Maharajan, C., Raja, R., Cao, J., Rajchakit, G., 2018. Novel global robust exponential stability criterion for uncertain inertial-type BAM neural networks with discrete and distributed time-varying delays via Lagrange sense. Journal of the Franklin Institute 355, 4727–4754. [https://doi.org/10.1016/j.jfranklin.2018.04.034

Logarithmic time encoding and decoding of integer error control codes

One of the most important characteristics of all error control codes (ECCs) is the complexity of the encoding/decoding algorithms. Today, there are many ECCs that can correct multiple bit errors, but at the price of high encoding/decoding complexity. Among the rare exceptions are integer ECCs (IECCs), whose serial encoding/decoding algorithms run in O(n) time, where n is the codeword length. In this article, we show that IECCs can be encoded/decoded even faster, that is, that their parallel encoding/decoding algorithms have O(log2n) time complexity

Naturally weighted measurement data in power grid – measurement data in Fourier domain

The latest development of stochastic digital measurement method allows extremely simple measurement of Fourier coefficients and, thus, the harmonic amplitudes: the natural weights of the measurement data in Fourier domain. The significance of each measurement data is defined by its weight, which allows the optimization of data recording, data analysis and artificial neural network training in a power grid