QR codes have revolutionized the industry because of its larger storage capacity and high damage resistance than the traditional barcodes. Color QR code is the future as it provides much higher encoding capacity that the typical B/W QR codes. We propose a color QR code decoding algorithm for mobile applications by considering the color profile of Red, Green and Blue channels respectively. We have developed a prototype by including various image processing techniques and the open source Zxing library. This paper presents an Android based color QR code decoder implementation and performance evaluation. Experimental results show the high success rate of the methodology implemented.
QR codes have revolutionized the industry because of its larger storage capacity and high damage resistance than the traditional barcodes. Color QR code is the future as it provides much higher encoding capacity that the typical B/W QR codes. We propose a color QR code decoding algorithm for mobile applications by considering the color profile of Red, Green and Blue channels respectively. We have developed a prototype by including various image processing techniques and the open source Zxing library. This paper presents an Android based color QR code decoder implementation and performance evaluation. Experimental results show the high success rate of the methodology implemented.
The LDPC codes are Shannon Limit codes that can achieve low bit error rates for SNR applications. The features of LDPC Codes are reduction in the decoding time, latency and as well as no error-floors at high SNRs. The proposed algorithms are SBF, MSA, and MLDD. The various decoding algorithms have been compared for these codes. The parameters are describing the which algorithm further helps in selecting the better decoder used for Medical and Signal Processing Applications. These codes are also used in Generating the Barcodes depends on the size of the Parity Check matrix.
Color codes present distinct advantages for fault-tolerant quantum computing, such as high encoding rates and the transversal implementation of Clifford gates. However, existing matching-based decoders for the color codes such as the restricted decoder (Kubica and Delfosse, 2023), suffer from limited decoding performance. Inspired by the global decoding insight of the unified decoder (Benhemou et al., 2023), this paper introduces a correlated decoder for the 4.8.8 color code, which improves upon the conventional restricted decoder by leveraging correlations between restricted lattices, and is derived by mapping the correlated matching decoder for the surface code onto the color code lattice. Analytical and numerical results show that the correlated decoder achieves higher thresholds than the restricted and unified decoders, while matching the performance of the unified decoder at very low physical error rates. Under the code capacity and phenomenological noise models, the estimated thresholds for the color code against bit-flip error are 10.38% and 3.13%, respectively. Furthermore, by applying the surface-color code mapping, the thresholds of 16.62% and 3.52% are obtained for the surface code against depolarizing noise.
The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a recovery operation with a high success rate. In this work, we implement a decoder that finds the recovery operation with the highest success probability by mapping the decoding problem to a spin system and using Population Annealing to estimate the free energy of the different error classes. We study the decoder performance on a 4.8.8 color code lattice under different noise models, including code capacity with bit-flip and depolarizing noise, and phenomenological noise, which considers noisy measurements, with performance reaching near-optimal thresholds for bit-flip and depolarizing noise, and the highest reported threshold for phenomenological noise. This decoding algorithm can be applied to a wide variety of stabilizer codes, including surface codes and quantum Low-Density Parity Check (qLDPC) codes.
In this paper, the performance of quadratic residue (QR) codes of lengths within 100 is given and analyzed when the hard decoding, soft decoding, and linear programming decoding algorithms are utilized. We develop a simple method to estimate the soft decoding performance, which avoids extensive simulations. Also, a simulation-based algorithm is proposed to obtain the maximum likelihood decoding performance of QR codes of lengths within 100. Moreover, four important theorems are proposed to predict the performance of the hard decoding and the maximum-likelihood decoding in which they can explore some internal properties of QR codes. It is shown that such four theorems can be applied to the QR codes with lengths less than 100 for predicting the decoding performance. In contrast, they can be straightforwardly generalized to longer QR codes. The result is never seen in the literature, to our knowledge. Simulation results show that the estimated hard decoding performance is very accurate in the whole signal-to-noise ratio (SNR) regimes, whereas the derived upper bounds of the maximum likelihood decoding are only tight for moderate to high SNR regions. For each of the considered QR codes, the soft decoding is approximately 1.5 dB better than the hard decoding. By using powerful redundant parity-check cuts, the linear programming-based decoding algorithm, i.e., the ACG-ALP decoding algorithm performs very well for any QR code. Sometimes, it is even superior to the Chase-based soft decoding algorithm significantly, and hence is only a few tenths of dB away from the maximum likelihood decoding.
Solving for quantum error correction remains one of the key challenges of quantum computing. Traditional decoding methods are limited by computing power and data scale, which restrict the decoding efficiency of color codes. There are many decoding methods that have been suggested to solve this problem. Machine learning is considered one of the most suitable solutions for decoding task of color code. We project the color code onto the surface code, use the deep Q network to iteratively train the decoding process of the color code and obtain the relationship between the inversion error rate and the logical error rate of the trained model and the performance of error correction. Our results show that through unsupervised learning, when iterative training is at least 300 times, a self-trained model can improve the error correction accuracy to 96.5%, and the error correction speed is about 13.8% higher than that of the traditional algorithm. We numerically show that our decoding method can achieve a fast prediction speed after training and a better error correction threshold.
Abstract Quantum image processing, which merges classical image processing techniques with quantum computing, provides exceptional storage capacity and unparalleled parallel computing power. In this study, we present a quantum color image watermarking scheme that employs quantum error correction codes to address issues such as pixel loss and image distortion during watermark embedding and extraction. By utilizing the least significant bit method to embed the color values of the watermark image into those of the carrier image, we improve the scheme’s robustness. We also address the error correction capabilities of channel coding for phase-flip errors and follow the majority principle, resulting in more accurate extraction of the watermark image’s color and enhancing the watermarking scheme’s reliability and integrity. Our experimental simulations demonstrate that the proposed watermarking scheme boasts high security, strong robustness, and excellent concealment.