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

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 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

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 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 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 Asymmetric Error Control Codes for Short-Range Optical Networks

In most communication networks, error probabilities 1 → 0 and 0 → 1 are equally likely to occur. However, in short-range optical networks (SRONs), such as local and access networks, this is not the case. In these networks, photons may fade or fail to be detected, but new photons cannot be generated. Hence, if the receiver operates correctly, only asymmetric (1 → 0) errors can occur. Motivated by this fact, the authors of this chapter have constructed four classes of integer codes capable of correcting various types of asymmetric errors. The most attractive feature of all these codes is their ability to be implemented "for free" (in software). This is achieved by using integer and lookup table operations, which are supported by all processors. The aim of this chapter is to overview four classes of integer asymmetric codes and to illustrate their potential for use in modern SRONs. Topics covered include: fundamentals in the design of integer codes, necessary and sufficient conditions for constructing integer asymmetric codes and the processor-based strategy for implementation of these codes

Loop transversal codes

This dissertation discusses the performance of loop transversal codes (LT codes), linear error correcting block codes constructed with attention to the syndrome function rather than to the code itself. LT codes are compared to lexicodes. Binary lexicodes which are linear are shown to be identical to those LT codes which are constructed by a greedy syndrome construction algorithm. Proofs by Conway and Sloane, and Brualdi and Pless, that binary lexicodes and greedy codes in the white-noise case are linear are generalized to the binary non-white-noise case. Using this result, we prove that those binary LT codes which are constructed by the greedy syndrome construction algorithm for a given set of errors (white or non-white noise) are always identical to the lexicode designed to correct the same set of errors. The proof of this generalization uses a metric d[subscript]E which is a generalization of the Hamming metric for any set of errors E such that 0 ⊂ E and E is closed under negation. This metric has the property that, if E is the set of errors corrected by a code C, then decoding is identical to minimum distance decoding under the metric d[subscript]E.;Those LT codes which are constructed by the greedy algorithm are shown to be maximal among linear codes, and in the case that the set of errors is closed under scalar multiplication, LT codes so constructed are shown to be maximal among all codes, linear and non-linear.;Data for ternary LT codes are shown to compare well--in both white-noise and non-white-noise cases--to the best linear codes known and also to lexicodes, which in non-binary cases are not generally linear. The ternary LT code constructed by the greedy algorithm for random single and double errors produces the (perfect) ternary (11, 6, 5) Golay code, a (43, 34, 5) code (1 dimension better than previously known for n = 43 and d = 5), a (44, 35, 5) code, and a (45, 36, 5) code, each 2 dimensions better than any previously known

Security Enhanced Symmetric Key Encryption Employing an Integer Code for the Erasure Channel

An instance of the framework for cryptographic security enhancement of symmetric-key encryption employing a dedicated error correction encoding is addressed. The main components of the proposal are: (i) a dedicated error correction coding and (ii) the use of a dedicated simulator of the noisy channel. The proposed error correction coding is designed for the binary erasure channel where at most one bit is erased in each codeword byte. The proposed encryption has been evaluated in the traditional scenario where we consider the advantage of an attacker to correctly decide to which of two known messages the given ciphertext corresponds. The evaluation shows that the proposed encryption provides a reduction of the considered attacker’s advantage in comparison with the initial encryption setting. The implementation complexity of the proposed encryption is considered, and it implies a suitable trade-off between increased security and increased implementation complexity