Properties of low augmentation level T-codes

In coding theory, we study various properties of codes for application in data compression, cryptography, error correction and network coding. The study of codes is introduced in information theory, electrical engineering, mathematics and computer sciences for the transmission of data through reliable and efficient methods. We have to consider how coding of messages can be done efficiently so that maximum number of messages can be sent over a noiseless channel in a given time. Thus, minimum value of mean codeword length subject to a given constraint on codeword lengths has to be founded. In this paper, average code word length is proposed. Corresponding to newly defined average code word length a relationship with a result of generalized fuzzy information measures is introduced. Some Noiseless coding theorems connected with fuzzy information measure are also analyzed.

A novel clustered multi-dictionary code compression method is proposed to effectively reduce the memory size which program code stored. According to the repeat times of distinct codes, the code set is clustered into several clusters. Each cluster is compressed with different dictionary and the codeword length is the same for the same dictionary. Shorter codeword is used for the dictionary whose size is smaller. Experimental results of MiBench benchmark compiled for ARM and MIPS show that the compression efficiency of this method is superior to the traditional multi-level dictionary-based code compression. The latency of instruction fetch is almost not increased, decode logic overhead is tiny and acceptable. Furthermore, the storage-bandwidth is increased.

The aim of source coding is to remove as much redundancy as possible to achieve only the information in a file. This chapter shows that with the requirement of unique decompression, it is possible to achieve the average codeword length arbitrarily close to the entropy, but not less. A simple algorithm is given to construct a code, the Huffman code, that is optimal in terms of codeword length for a source with independent and identically distributed symbols. With Kraft inequality, a mathematical foundation needed to consider an optimization function for the codeword lengths is obtained. One standard method for minimization of a function with some side criterion is the Lagrange multiplication method. The idea of arithmetic coding is to consider the probabilities for vectors and to build a code with codeword length that grows as the logarithm of the probability for the vector, but without the exponential growth in complexity.

In coding theory, we study various properties of codes for application in data compression, cryptography, error correction, and network coding. The study of codes is introduced in Information Theory, electrical engineering, mathematics, and computer sciences for the transmission of data through reliable and efficient methods. We have to consider how coding of messages can be done efficiently so that the maximum number of messages can be sent over a noiseless channel in a given time. Thus, the minimum value of mean codeword length subject to a given constraint on codeword lengths has to be founded. In this paper, we have introduced mean codeword length of orderαand typeβfor 1:1 codes and analyzed the relationship between average codeword length and fuzzy information measures for binary 1:1 codes. Further, noiseless coding theorem associated with fuzzy information measure has been established.

By the problem, called a representation of the integers, is meant the encoding of the positive integers without a known upper bound, for which unique decoding can be provided. From the viewpoint of information theory, this problem has been discussed theoretically in its relation to the universality, asymptotic optimality, and computation theory. The result in those approaches has been applied to the data compression scheme for the type of data referring to the past as well as the URR and other floating-pointnumber representations with variable exponential length. This paper discusses representation of the integers problem from the viewpoint of the codeword-length function, which is the function to represent the length of the codeword. As a result, a general construction method is presented which has the desirable property and can uniquely encode all representations. Several methods are given from this approach, which can construct not only the traditional representations of the integers but also the first representations of the integers which has not been considered. It is noted first that two construction methods of codeword length, which are independent of the encoding, are considered. One is based on the combination of the codeword-length functions, and the other is based on the codeword-length distribution. More precisely, it is shown that not only are the traditional representations derived, but also the representations that have not been considered in the past. Using detailed examples, it is shown that the computational complexity of the encoding and decoding depends on the codeword-length function.

The characterization of wideband radio channels requires knowledge of such parameters as the average delay, the delay spread, and their coherence bandwidth. These are also descriptors that provide relevant information to system design engineers. Channel sounding is a technique for developing this information for a specific communication's path and frequency range. The GTE Laboratories sounder is a computer-controlled, mobile, channel probe that uses a sliding correlator architecture to measure transmission loss and delay spread. The transmitter sends out a pseudorandom waveform with a predetermined chip interval and code word length. It is these two parameters that determine the minimum time resolution and maximum delay spread that is measurable. At the receiver, a replica of the transmitted pseudorandom waveform is correlated with the in-phase and quadrature-phase components of the received signal. The output of the correlator is integrated and sampled. This process is conducted for each chip in the pseudorandom code period in order to obtain a valid measurement of the entire delay-spread function. It is this delay spread that is one of the key parameters used to characterize channel performance, as it has the most significant effect on the channel error rate. >

An information source generates independent and identically distributed status update messages from an observed random phenomenon which takes n distinct values based on a given probability mass function (PMF). These update packets are encoded at the transmitter node to be sent to a receiver node which wants to track the observed random variable with as little age as possible. The transmitter node implements a selective k encoding policy such that rather than encoding all possible n realizations, the transmitter node encodes the most probable k realizations. We consider three different policies regarding the remaining n-k less probable realizations: highest k selective encoding which disregards whenever a realization from the remaining n-k values occurs; randomized selective encoding which encodes and sends the remaining n-k realizations with a certain probability to further inform the receiver node at the expense of longer codewords for the selected k realizations; and highest k selective encoding with an empty symbol which sends a designated empty symbol when one of the remaining n-k realizations occurs. For all of these three encoding schemes, we find the average age and determine the age-optimal real codeword lengths, including the codeword length for the empty symbol in the case of the latter scheme, such that the average age at the receiver node is minimized. Through numerical evaluations for arbitrary PMFs, we show that these selective encoding policies result in a lower average age than encoding every realization, and find the corresponding age-optimal k values. Since we focus on real-valued codeword lengths in this paper, the resulting age value obtained in each case studied here serves as a lower bound to what can be attained by integer-valued codeword lengths in that case.

BackgroundSeeking health information on the internet is a popular trend. Xigua Video, a short video platform in China, ranks among the most accessed websites in the country and hosts an increasing number of videos with medical information. However, the nature of these videos is frequently unscientific, misleading, or even harmful.ObjectiveLittle is known about Xigua Video as a source of information on breast cancer. Thus, the study aimed to investigate the contents, quality, and reliability of breast cancer–related content on Xigua Video.MethodsOn February 4, 2020, a Xigua Video search was performed using the keyword “breast cancer.” Videos were categorized by 2 doctors based on whether the video content provided useful or misleading information. Furthermore, the reliability and quality of the videos were assessed using the 5-point DISCERN tool and 5-point global quality score criteria.ResultsOut of the 170 videos selected for the study, 64 (37.6%) were classified as useful, whereas 106 (62.4%) provided misleading information. A total of 41.8% videos (71/170) were generated by individuals compared to 19.4% videos (33/170) contributed by health care professionals. The topics mainly covered etiology, anatomy, symptoms, preventions, treatments, and prognosis. The top topic was “treatments” (119/170, 70%). The reliability scores and global quality scores of the videos in the useful information group were high (P<.001). No differences were observed between the 2 groups in terms of video length, duration in months, and comments. The number of total views was higher for the misleading information group (819,478.5 vs 647,940) but did not reach a level of statistical significance (P=.112). The uploading sources of the videos were mainly health care professionals, health information websites, medical advertisements, and individuals. Statistical differences were found between the uploading source groups in terms of reliability scores and global quality scores (P<.001). In terms of total views, video length, duration, and comments, no statistical differences were indicated among the said groups. However, a statistical difference was noted between the useful and misleading information video groups with respect to the uploading sources (P<.001).ConclusionsA large number of Xigua videos pertaining to breast cancer contain misleading information. There is a need for accurate health information to be provided on Xigua Video and other social media; health care professionals should address this challenge.

A new hybrid coding technique is introduced which is based on the Discrete Cosine Transform, interframe DPCM, conditional replenishment, detection of significant subareas in the transform domain, adaptive quantization, adaptive Huffman coding and postbuffer control. This coder concept is the result of a comparison of several coding methods including uniform/nonuniform quantization, constant/variable word length coding and prebuffer/post-buffer control schemes. An important feature of the presented coder is the selection of transform coefficients within each block which are grouped in subareas for adaptive entropy coding. The components of the coder are described and its excellent performance is demonstrated by means of SNR-measurements and a typical videoconference sequence.

Variable length codes (VLC) have found widespread use for efficient encoding of symbols with unequal probabilities in many practical situations. However, bit errors can cause a loss of decoder synchronism that often leads to error propagation. Recent advances in the development of VLC that limit the effect of error propagation, such as reversible VLC and self-synchronising VLC, contribute further to their popularity. However, it is still important to model the performance of various VLC code sets so that comparisons can be made between different coding schemes and for different applications. Communicating sequential processes (CSP) is a well-established formal description technique that allows one to analyse the behaviour of concurrently evolving processes. It has been successfully applied to industrial-scale problems. The paper describes how CSP can be applied to the modelling of the resync process of VLC. This approach offers three main advantages. First, a complete model comprises processes and events as basic building blocks, making this approach highly scalable. Second, different semantic models provide different level of abstraction. Third, tools are available for automatic generation of sync sequences, which also provide a measure of sync performance. This facilitates comparisons of different VLC schemes in addition to code sets obtained using a given coding scheme.

The investigation of the multipath QoS-routing dynamic tensor model with quality of service guarantees over the multiple metrics is presented. The expression for modeling state of the network router interface is used for representing the average packet delay as time-varying function. The conditions of ensuring QoS for the set of metrics as the packet rate and average delay are expressed. The novelty of the model is that the network metric is a function of time, and it takes into account that the average queue length and average packet delay take their limit values after convergence time. The results of the research demonstrated that the use of the dynamic tensor model allows ensuring QoS requirements more precisely.

There are numerous scenarios in source coding where not only the code length but the importance of each value should also be taken into account. Different from the traditional coding theorems, by adding the importance weights for the length of the codes, we define the average cost of the weighted codeword length as an importance-aware measure of the codes. This novel information theoretical measure generalizes the average codeword length by assigning importance weights for each symbol according to users' concerns through focusing on user's selections. With such definitions, coding theorems of the bounds are derived and the outcomes are shown to be extensions of traditional coding theorems.

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In this study, the authors consider the class of anti-uniform Huffman (AUH) codes. The authors derived tight lower and upper bounds on the average codeword length, entropy and redundancy of finite and infinite AUH codes in terms of the alphabet size of the source. These bounds are tighter than similar bounds. Also a tight upper bound on the entropy of AUH codes is presented in terms of the average cost of the code. The Fibonacci distribution is introduced, which plays a fundamental role in AUH codes. It is shown that such distributions maximise the average length and the entropy of the code for a given alphabet size. The authors also show that the minimum average cost of a code is achieved by an AUH codes in a highly unbalanced cost regime.

Prefix codes such as Huffman codes are commonly used for loseless data compression. The class of synchronizing codes is often chosen to improve error resilience or to enable parallel decoding of data. Such codes have a special sequence whose occurrence realigns decoding process leading to recovery from errors in a data stream. In the present paper we identify a class of codes whose synchronizability depends only on the lengths of codewords. Namely, we show that every maximal finite prefix code with only two codeword lengths is synchronizing if and only if these lengths are coprime.