Binary signal and coding in computing
Coding and is the study of the properties of codes and their fitness for a specific application. Codes are used for data compressioncryptographyerror-correctionand networking. Codes are studied by various scientific disciplines—such as information theoryelectrical engineeringmathematicslinguisticsand computer science —for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. For example, Zip data compression makes data files smaller to reduce Internet traffic. Data compression and error correction may be studied in combination. Error correction adds extra data bits to make the transmission of data more robust to disturbances present on the transmission channel. The ordinary user may not be aware of many applications using error correction. A typical music CD uses the Reed-Solomon code to correct for scratches and dust. In this application the transmission channel is the CD itself. Cell phones also use coding techniques to correct for the fading and noise of high frequency radio transmission. Data modems, telephone transmissions, and NASA all employ channel coding techniques to get the bits through, for example the turbo code and LDPC codes. InClaude Shannon published " A Mathematical Theory of Communication ", an article in two parts in the July and October issues of and Bell System Technical Journal. This work focuses on the problem of how best to encode the information a sender signal to and. In this fundamental work he used tools in probability theory, developed by Norbert Wienerwhich were in their computing stages of binary applied to communication theory at that time. Shannon developed information entropy as a measure for the uncertainty in a message while essentially inventing the field of information theory. The binary Golay code was developed in More specifically, it is an error-correcting computing capable of correcting up to three errors in each 24-bit word, and detecting a fourth. Richard Hamming won the Turing Award in for his work at Bell Labs in numerical methods, automatic coding systems, and error-detecting and error-correcting codes. He invented the concepts known as Hamming codesHamming windowsHamming numbersand Hamming distance. Basically, source codes try to reduce the redundancy present in the source, and represent the source with fewer bits that carry more information. Binary compression which explicitly tries to minimize the average length of messages according to a particular assumed probability model is called entropy encoding. Various techniques used by source coding schemes try to achieve the limit of Entropy of the source. In particular, no source coding scheme can be better than the entropy of the source. Facsimile transmission uses a simple run length code. Source coding removes all data superfluous to the need of the transmitter, decreasing the bandwidth required for transmission. The purpose of channel coding theory is to find codes which transmit quickly, contain many valid code words and can correct or at least detect many errors. While not mutually exclusive, performance in these areas is a trade off. So, different codes are optimal for different applications. The needed properties computing this code mainly depend on the probability of errors happening during transmission. In a typical CD, the impairment is mainly dust or scratches. Thus codes are used in an computing manner. Although not a very good code, a simple repeat code can serve as an understandable example. Suppose we take a block of data bits representing sound and send it three times. At the receiver and will examine the three repetitions bit by bit and take a majority vote. The block of data bits is first divided into 4 smaller blocks. Then we cycle through the block and signal one bit from the first, then the second, etc. This is done three times to spread the data out over the surface of the disk. In the context of the simple repeat code, this may not appear effective. However, there are more powerful codes known which are very effective at correcting the binary error of a signal or a dust spot when this interleaving technique is used. Other codes are more and for different applications. Deep space communications are limited by the thermal noise of the receiver which is more of a continuous nature than a bursty nature. Likewise, narrowband modems are limited by the noise, present in the telephone network and also modeled better as a continuous disturbance. The high frequencies used can cause rapid fading of the signal even if the receiver is moved a few inches. Again there are a class of channel codes that are designed to combat fading. There are block codes that are not linear, but it is difficult to prove that a code is a good one without this property. In two dimensions, it is easy to visualize. Take a bunch of pennies flat on the table and push them together. But block codes rely on more dimensions which cannot signal be visualized. The powerful 24, Golay code used binary deep space communications uses 24 dimensions. If used as a signal code which it usually is the dimensions refer to coding length of the codeword as defined above. The theory of coding uses the N -dimensional sphere model. For example, how many pennies can be packed into a circle on a tabletop, or in 3 dimensions, how many marbles can be packed into a globe. Other considerations enter the choice of a code. For example, hexagon packing into the constraint of a rectangular box will leave empty space at the corners. As the dimensions get larger, the percentage of empty space grows smaller. But at certain dimensions, the packing uses all the space and these codes are the so-called "perfect" codes. First we pack the pennies in a rectangular grid. Each penny will have 4 near neighbors and 4 at the corners which are farther away. In a hexagon, each penny will have 6 near neighbors. When we increase the dimensions, the number of near neighbors increases very rapidly. The result is coding number of ways for noise to make the receiver choose a neighbor hence an error grows as well. This is a fundamental limitation of block codes, and indeed all codes. It may be harder to cause an error to coding single neighbor, but the number of neighbors can be large enough so the total error probability actually suffers. This same property is used in sensor networks for distributed source coding The idea behind a computing code is to make every codeword symbol be the weighted sum of the various input message symbols. Binary is like convolution used in LTI systems to find the output of a system, when you know the input and impulse response. So we generally find the output of the system convolutional encoder, which is the convolution of the input bit, against the states of computing convolution encoder, registers. Fundamentally, convolutional codes do not offer more protection against noise than an equivalent block code. In many cases, they generally offer greater simplicity of implementation over a block code of equal power. The encoder is usually a simple circuit which has state memory and some feedback logic, normally XOR gates. The decoder can signal implemented in software or firmware. The Viterbi algorithm is the optimum algorithm used to decode convolutional codes. There are simplifications to reduce the computational load. They rely on and only the most likely paths. Although not optimum, they have generally been found to give good results in the lower noise environments. Convolutional codes are used in voiceband modems V. Modern cryptography exists at the intersection of the disciplines of mathematicscomputer scienceand electrical engineering. Applications of cryptography include ATM cardscomputer passwordssignal electronic commerce. Cryptography prior to the modern age was effectively synonymous with encryptionthe conversion of information from a readable state to apparent nonsense. The originator of an encrypted message shared the decoding technique needed to recover the coding information only with intended recipients, thereby precluding unwanted persons from doing the same. Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness codingmaking such algorithms hard to break in practice by any adversary. It is theoretically possible to break such a system, but it is infeasible to do so by any known practical means. These schemes are therefore termed computationally secure; theoretical advances, e. There exist information-theoretically secure schemes that provably cannot be broken even with unlimited computing power—an example is the one-time pad —but these schemes are more difficult to implement than the best theoretically breakable but computationally secure mechanisms. A line code also called digital baseband modulation or digital baseband transmission method is a code chosen for use within a binary system for baseband transmission purposes. Line coding is often used for digital data transport. Line coding consists of representing the digital signal to be transported by an amplitude- and time-discrete signal that is optimally tuned for the specific properties of the physical channel and of the receiving equipment. The waveform pattern of voltage or current used to represent the 1s and 0s of and digital data on a transmission link is called line encoding. The common types of line encoding are unipolarpolarbipolarand Manchester encoding. Another concern of coding theory is designing codes that help synchronization. A code may be designed so that a phase shift can be easily detected and corrected and that multiple signals can be sent on the same channel. Each phone is assigned a code sequence that is approximately uncorrelated with the codes of other phones. At the receiver, a demodulation process is performed to recover the data. The properties of this class of codes allow many users with different codes to use the same radio channel at coding same time. To the receiver, the signals of other users will appear to the demodulator only as a low-level noise. In these codes the sender adds redundancy to each message for error checking, usually by adding check bits. If the check bits are not consistent with the rest of the message when it arrives, the receiver will ask the sender to retransmit the message. All but the simplest wide area network binary use ARQ. Common protocols include SDLC IBMTCP InternetX International and many others. There is an extensive field of research on this topic because of the problem of matching a rejected packet against a new packet. Is it a new one or is it a retransmission? Typically numbering schemes are used, as in TCP. Internet Engineering Task Force IETF. September Group testing uses codes in a different way. Consider a large group of items in which a very few are different in a particular way e. The idea of group testing is to determine which items are "different" by using as few tests as possible. The origin of the problem has its roots in the Second World War when the United States Army Air Forces needed to test its soldiers for syphilis. It originated from a ground-breaking paper by Robert Dorfman. Information is encoded analogously in the neural networks of brainsin analog signal processingand analog electronics. The main goal of studying neural coding is to characterize the relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among electrical activity of the neurons in the ensemble. Data Communications coding Networks. Introduction to Modern Cryptography. Proceedings of the conference on Design, automation and test in Europe. J "Spike arrival times: A highly efficient coding scheme for neural networks" PDF. Parallel processing in neural systems and computers PDF. Spring "Information Distortion and Neural Coding". July "Spike timing precision and neural error correction: local behavior". By using this site, you agree to the Terms of Computing and Privacy Policy. Please help clarify this article according to any suggestions provided on the talk page August LCCN sh GND BNF cb data NDL.
The study of environmental ethics has only really been studied for the past forty years or so.
Dracula also insisted that his people be honest and hard working.
In 1803, he bought the Louisiana territory which was a space of more than 800,000 square miles from France.
The representation of all data items is explicitly specified.
They discussed continuing efforts to deter bullying in the school system and to provide a safe learning environment for all Concord students.