An Efficient Coding Technique for Stochastic Processes

In the framework of coding theory, under the assumption of a Markov process (Xt) on a finite alphabet A, the compressed representation of the data will be composed of a description of the model used to code the data and the encoded data. Given the model, the Huffman’s algorithm is optimal for the number of bits needed to encode the data. On the other hand, modeling (Xt) through a Partition Markov Model (PMM) promotes a reduction in the number of transition probabilities needed to define the model. This paper shows how the use of Huffman code with a PMM reduces the number of bits needed in this process. We prove the estimation of a PMM allows for estimating the entropy of (Xt), providing an estimator of the minimum expected codeword length per symbol. We show the efficiency of the new methodology on a simulation study and, through a real problem of compression of DNA sequences of SARS-CoV-2, obtaining in the real data at least a reduction of 10.4%.

Efficient Coding of the Embedded Signal in Steganographic Systems with Multiple Access

Today, steganographic systems with multiple access are of considerable importance. In such sys-tems, the orthogonal Walsh-Hadamard transform is most often used for multiplexing and divid-ing channels, which leads to the need for efficient coding of the Walsh-Hadamard transform coefficients for the convenience of their subsequent embedding. The purpose of the research is to develop a theoretical basis for efficient coding of the embedded signal in steganographic sys-tems with multiple access with an arbitrary number of users N, based on MC-CDMA technology. This purpose was fulfilled by forming the theoretical basis for constructing effective codes de-signed to encode the embedded signal in steganographic systems with multiple access. The most important results obtained are the proposed and proven relations that determine both the possible values of the Walsh-Hadamard transform coefficients, for a given value of the number of divid-ed channels, and the probability of occurrence of the given values of the Walsh-Hadamard transform coefficients, which allow the construction of effective codes to represent the embed-ded signal. In the case of the number of divided channels N=4, we propose to use a constant amplitude code that provides a smaller value of the average codeword length in comparison with the Huffman code, while the constructed code has correcting capabilities. The significance of the obtained results is determined by the possibility of using the developed theoretical basis when constructing effective codes for encoding the embedded signal in steganographic systems with multiple access at an arbitrary value of the number of divided channels N.

Feasibility Study of Using Huffman Code Calculator in Learning Achievement of Data Compression

In the world of education there is already a curriculum that must be carried out with learning outcomes that must be achieved by students, as well as lecturers who also have duties as facilitators in these achievements. With the Learning Outcomes, it makes students have the ability or competence in accordance with the requirements to meet the predefined study program profiles. One of the competencies that graduates of the Broadband Multimedia field must achieve is in the field of data processing including data compression. The most widely used data compression technique is the Huffman code. Some research on the Huffman code has been done a lot, and someone has made the Calculator application. The calculator is used to determine the code for each character. The code for each character is not fixed, depending on the frequency of appearance in a text. The more often the character appears, the shorter the code. In this study, it has proven that the feasibility of the Huffman Calculator as a tool for Learning Outcomes can be done where data compression with language variables, in this case English and Bahasa Indonesia to the compression ratio, produces the same compression ratio, which ranges from 1.51 to 1.64 for Bahasa Indonesia while English is 1.56 to 1.83, with the average entropy for English 4.35 and Bahasa Indonesia 4.41. Keywords: competence , data compression, huffman code, learning outcomes.

On Two-Stage Guessing

Stationary memoryless sources produce two correlated random sequences Xn and Yn. A guesser seeks to recover Xn in two stages, by first guessing Yn and then Xn. The contributions of this work are twofold: (1) We characterize the least achievable exponential growth rate (in n) of any positive ρ-th moment of the total number of guesses when Yn is obtained by applying a deterministic function f component-wise to Xn. We prove that, depending on f, the least exponential growth rate in the two-stage setup is lower than when guessing Xn directly. We further propose a simple Huffman code-based construction of a function f that is a viable candidate for the minimization of the least exponential growth rate in the two-stage guessing setup. (2) We characterize the least achievable exponential growth rate of the ρ-th moment of the total number of guesses required to recover Xn when Stage 1 need not end with a correct guess of Yn and without assumptions on the stationary memoryless sources producing Xn and Yn.

Pixel P Air-Wise Fragile Image Watermarking Based on HC-Based Absolute Moment Block Truncation Coding

In this paper, we first designed Huffman code (HC)-based absolute moment block truncation coding (AMBTC). Then, we applied Huffman code (HC)-based absolute moment block truncation coding (AMBTC) to design a pixel pair-wise fragile image watermarking method. Pixel pair-wise tampering detection and content recovery mechanisms were collaboratively applied in the proposed scheme to enhance readability even when images have been tampered with. Representative features are derived from our proposed HC-based AMBTC compression codes of the original image, and then serve as authentication code and recovery information at the same time during tamper detection and recovery operations. Recovery information is embedded into two LSB of the original image with a turtle shell-based data hiding method and a pre-determined matrix. Therefore, each non-overlapping pixel-pair carries four bits of recovery information. When the recipient suspects that the received image may have been tampered with, the compressed image can be used to locate tampered pixels, and then the recovery information can be used to restore the tampered pixels.

Digital Link—B

Chapter 7 explained the detection and hypothesis testing problems, Huffman codes and the situation where errors are independent and Gaussian. In this chapter, we prove the optimality of the Huffman code in Sect. 8.1 and the Neyman–Pearson Theorem in Sect. 8.2. Section 8.3 discusses the theory of jointly Gaussian random variables that is used to analyze the modulation schemes of Sect. 7.5 . Section 8.4 uses the results on jointly Gaussian random variables to explain hypothesis tests that arise when analyzing data. That section discusses the chi-squared test and the F-test. Section 8.5 is devoted to the LDPC codes that are widely used in high-speed communication links. These codes augment a group of bits to be transmitted over a noisy channel with additional bits computed from those in the group. When it receives the bits, when the augmented bits are not consistent, the receiver attempts to determine the bits that are most likely to have been corrupted by noise.

Steganography Technique with Huffman Code

The growth of modern communication technologies imposes a particular means of security mechanisms in particular in case of data networks. In order to protect sensitive data while these are en route, applications call up different methods. Here we are trying to code the message by Huffman coding technique and applying the Steganography using differencing and substitution mechanisms with encryption to the original message which can give multi label security. Here we are trying to communicate in two phases such as (1) Encrypt the message by Huffman code and (2) applying the In Steganography. We divide the image into multiple blocks which are non-overlapped in nature and the block size is 3×3 pixel that will consider as matrix. For every value from the matrix can be represented in eight bit where two bit will use as least significant bit (LSB) substitution and quotient value differencing (QVD) is applied for other bits. We are trying to process in three levels: (i) Huffman tree through message is encrypted which is secret (ii) LSB substitution at lower bit planes and (iii) QVD at higher bit planes.

A New Scheme for Removing Duplicate Files from Smart Mobile Devices

The continuous development of the information technology and mobile communication world and the potentials available in the smart devices make these devices widely used in daily life. The mobile applications with the internet are distinguished simple, essay to use in any time/anywhere, communication between relatives and friends in different places in the world. The social application networks make these devices received several of the duplicate files daily which lead to many drawbacks such inefficient use of storage, low performance of CPU, RAM, and increasing consumption battery. In this paper, we present a good scheme to remove from the duplicate files, and we focus on image files as a common case in social apps. Our work overcomes on the above-mentioned issues and focuses to use hash function and Huffman code to build unique code for each image. Our experiments improve the performance from 1046770, 1995808 ns to 950000, and 1981154 ns in Galaxy and HUAWEI, respectively. In the storage side, the proposed scheme saves storage space from 1.9 GB, 1.24 GB to 2 GB, and 1.54 GB, respectively.