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Introduction
Published in Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski, Computer Arithmetics for Nanoelectronics, 2018
Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski
The BCH code is a generalization of the Hamming code, that allows multiple error correction. BCH codes are important because at a block length of a few hundred, they outperform all other block codes with the same blocklength and code rate. The most commonly used BCH codes employ a binary alphabet and a codeword length of n=2r-1, where r=3,4,….
Signature-Based Media Authentication
Published in Borko Furht, Darko Kirovski, Multimedia Encryption and Authentication Techniques and Applications, 2006
Error Correction Coding. An (N, K, D) code [40] is a code of N-bit codewords, where K is the number of message digits (the extracted feature set in this chapter) and D is the minimum distance between codewords. N–K=P is the number of parity check digits (i.e., checksum or check information). It should be noted that an ECC with rate K/N can correct up to T=(D – 1)/2 errors. Here, we are only interested in binary BCH ECC (i.e., Bose–Chaudhuri–Hochquenghem code). BCH code is a multilevel, cyclic, error-correcting, variable-length digital code used to correct errors of up to approximately 25% of the total number of digits. Like other linear ECC codes, the first K-bit digits in its N-bit codeword are exactly the same as its original K-bit message bits. This is the main motivation for selecting the BCH code: in the procedure of content signing, the output (codeword) from the ECC encoder can still be separated into two parts: the original message and its corresponding PCBs. We can then embed the PCB into the image as a watermark. In the procedure of content authentication, the authenticity can be verified by checking the syndrome of the merged codeword (message comes from the feature set extracted from the image to be verified and PCB comes from the watermark extracted from the same image).
Signature-Based Media Authentication
Published in Borko Furht, Darko Kirovski, Multimedia Security Handbook, 2004
Error Correction Coding. A (N, K, D) code [40] is a code of N-bit codewords, where K is the number of message digits (the extracted feature set in this chapter) and D is the minimum distance between codewords. N – K = P is the number of parity check digits (i.e., checksum or check information). It should be noted that an ECC with rate K/N can correct up to T=(D−1)/2 errors. Here, we are only interested in binary BCH ECC (i.e., Bose–Chaudhuri–Hochquenghem Code). BCH code is a multilevel, cyclic, error-correcting, variable-length digital code used to correct errors of up to approximately 25% of the total number of digits. Like other linear ECC codes, the first K-bit digits in its N-bit codeword are exactly the same as its original K-bit message bits. This is the main motivation for selecting the BCH code: In the procedure of content signing, the output (codeword) from the ECC encoder can still be separated into two parts: the original message and its corresponding PCBs. We can then embed the PCB into the image as a watermark. In the procedure of content authentication, the authenticity can be verified by checking the syndrome of the merged codeword (message comes from the feature set extracted from the image to be verified and PCB comes from the watermark extracted from the same image).
Neural network detector with sparse codes for spin transfer torque magnetic random access memory
Published in Cogent Engineering, 2023
Spintronics-based memories have potential errors due to the sensitivity of the spin states to external perturbations. Hamming codes or BCH codes (Jiang et al., 2022; Zhang et al., 2023) are commonly used to correct such errors. Moreover, other error-correcting codes have been researched to enhance the performance of non-volatile memories (K. Cai & Schouhamer Immink, 2017; Everspin Technologies MR4A16B Features, 2021). It has been reported that conventional error-correction codes (ECCs), such as Hamming and BCH codes, offer the same error-correcting capability for both bit-flipping directions (Wen et al., 2013). Modulation codes are already widely used in next-generation data storage systems (C. D. Nguyen, 2020; C. D. Nguyen et al., 2021; Shao et al., 2018). They are regarded as one of the best approaches to overcoming the AWE and unknown offset challenges.
Performance analysis of concatenated BCH and convolutional coded OFDM system
Published in International Journal of Electronics, 2020
Ozan Yavasoglu, Nursel Akcam, Tayfun Okan
BCH codes are block codes that operate on multiple bits rather than individual bits. A BCH(n,k) code is used to encode k message bits and produce a coded n bit data (). In this study binary BCH codes are used, where message bits or coded bits are consisted of 0’s and 1’s. These codes are cyclic codes over Galois Field (GF(2)). If is a primitive element in GF(), then the generator polynomial g(x) of the BCH code of length is the lowest degree polynomial over GF(2) which has as its roots (Sato, Ohtsuki, Kashima, & Jarot, 2007).