Exponential sums and constrained error-correcting codes

1992 ◽  
pp. 16-22 ◽  
Author(s):  
Alexander Barg
Keyword(s):  
Exponential Sums ◽  
Error Correcting Codes

An Enhanced Two Stage MMSE Equalizer for Coded FBMC/OQAM Systems

2019 ◽  
Vol 10 (1) ◽  
pp. 69-82 ◽  
Author(s):  
Mohammad Rizk Assaf ◽  
Abdel-Nasser Assimi
Keyword(s):  
Error Propagation ◽  
Channel Model ◽  
Error Correcting Codes ◽  
Two Stage ◽  
Probability Of Error ◽  
Second Stage ◽  
Different Types ◽  
Mmse Equalizer ◽  
And Performance ◽  
Ici Cancellation

In this article, the authors investigate the enhanced two stage MMSE (TS-MMSE) equalizer in bit-interleaved coded FBMC/OQAM system which gives a tradeoff between complexity and performance, since error correcting codes limits error propagation, so this allows the equalizer to remove not only ICI but also ISI in the second stage. The proposed equalizer has shown less design complexity compared to the other MMSE equalizers. The obtained results show that the probability of error is improved where SNR gain reaches 2 dB measured at BER compared with ICI cancellation for different types of modulation schemes and ITU Vehicular B channel model. Some simulation results are provided to illustrate the effectiveness of the proposed equalizer.

A robust and high capacity data hiding method for JPEG compressed images with SVD-based block selection and advanced error correcting techniques

2021 ◽  
pp. 1-11
Author(s):  
Kusan Biswas
Keyword(s):  
Data Hiding ◽  
High Capacity ◽  
Error Correcting Codes ◽  
Human Vision ◽  
Data Embedding ◽  
Compressed Images ◽  
Matrix Encoding ◽  
Dct Coefficients ◽  
Capacity Data ◽  
Value Decomposition

In this paper, we propose a frequency domain data hiding method for the JPEG compressed images. The proposed method embeds data in the DCT coefficients of the selected 8 × 8 blocks. According to the theories of Human Visual Systems  (HVS), human vision is less sensitive to perturbation of pixel values in the uneven areas of the image. In this paper we propose a Singular Value Decomposition based image roughness measure (SVD-IRM) using which we select the coarse 8 × 8 blocks as data embedding destinations. Moreover, to make the embedded data more robust against re-compression attack and error due to transmission over noisy channels, we employ Turbo error correcting codes. The actual data embedding is done using a proposed variant of matrix encoding that is capable of embedding three bits by modifying only one bit in block of seven carrier features. We have carried out experiments to validate the performance and it is found that the proposed method achieves better payload capacity and visual quality and is more robust than some of the recent state-of-the-art methods proposed in the literature.

scholarly journals Algorithms for q-ary error-correcting codes with limited magnitude and feedback

2021 ◽  
Vol 344 (2) ◽  
pp. 112199
Author(s):  
Christian Deppe ◽  
Vladimir Lebedev
Keyword(s):  
Error Correcting Codes

scholarly journals A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenpeng Zhang ◽  
Xingxing Lv
Keyword(s):  
Exponential Sums ◽  
Exponential Sum ◽  
Gauss Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

scholarly journals Robust Secret Image Sharing Resistant to Noise in Shares

2021 ◽  
Vol 17 (1) ◽  
pp. 1-22
Author(s):  
Xuehu Yan ◽  
Lintao Liu ◽  
Longlong Li ◽  
Yuliang Lu
Keyword(s):  
Chinese Remainder Theorem ◽  
Recovery Phase ◽  
Error Correcting Codes ◽  
Secret Image Sharing ◽  
Data Loss ◽  
Least Significant Bit ◽  
Recovery Method ◽  
Secret Image ◽  
Image Sharing ◽  
Salt And Pepper

A secret image is split into   shares in the generation phase of secret image sharing (SIS) for a  threshold. In the recovery phase, the secret image is recovered when any   or more shares are collected, and each collected share is generally assumed to be lossless in conventional SIS during storage and transmission. However, noise will arise during real-world storage and transmission; thus, shares will experience data loss, which will also lead to data loss in the secret image being recovered. Secret image recovery in the case of lossy shares is an important issue that must be addressed in practice, which is the overall subject of this article. An SIS scheme that can recover the secret image from lossy shares is proposed in this article. First, robust SIS and its definition are introduced. Next, a robust SIS scheme for a  threshold without pixel expansion is proposed based on the Chinese remainder theorem (CRT) and error-correcting codes (ECC). By screening the random numbers, the share generation phase of the proposed robust SIS is designed to implement the error correction capability without increasing the share size. Particularly in the case of collecting noisy shares, our recovery method is to some degree robust to some noise types, such as least significant bit (LSB) noise, JPEG compression, and salt-and-pepper noise. A theoretical proof is presented, and experimental results are examined to evaluate the effectiveness of our proposed method.

[[2n,n]] Additive quantum error correcting codes

2008 ◽  
Vol 25 (4) ◽  
pp. 519-522
Author(s):  
Yongjun Du ◽  
Yuefei Ma
Keyword(s):  
Error Correcting Codes ◽  
Quantum Error
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