Binary block codes ppt

Coding binary block codes ppt is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compressionbinary block codes ppterror-correctionand data transmission and storage.

Codes are studied by various scientific disciplines—such as information theoryelectrical engineeringmathematicslinguisticsand computer science —for the purpose of designing efficient and reliable data binary block codes ppt methods.

This typically involves the removal of redundancy binary block codes ppt the correction or detection of errors binary block codes ppt the transmitted data. There are four types of coding: Data compression attempts to remove redundancy from the data from a source in order to transmit it more efficiently.

For example, Zip data compression makes data files smaller, for purposes such as 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. This work focuses on the problem of how best to encode the information a sender wants to transmit.

In this fundamental work he used tools in probability theory, developed by Norbert Wienerwhich were in their nascent stages of being 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 It is an binary block codes ppt code capable of correcting up to three errors in each 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. Data can be seen as a random variable X: The concatenation of code words C x 1. Entropy of a source is the measure of information. Basically, source codes try to reduce the redundancy present in the source, and represent the source with fewer bits that carry more information. Data 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 binary block codes ppt 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 of this code mainly depend on the probability of errors happening during transmission. In a typical Binary block codes ppt, the impairment is mainly dust or scratches.

CDs use cross-interleaved Reed—Solomon coding to spread the data out over the disk. 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 we will examine the three repetitions bit by bit and take a majority vote. The twist on this is that we don't merely send the bits in order. The block of data bits is first divided into 4 smaller blocks. Then we cycle through the block and send one bit from the first, then the second, binary block codes ppt. 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 binary block codes ppt which are very effective at correcting the "burst" error of a scratch or a dust spot when this interleaving technique is used. Other codes are more appropriate 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 binary block codes ppt can cause binary block codes ppt 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. The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched.

Algebraic coding theory is basically divided into two major types of codes: It analyzes the following three properties of a code — mainly: Linear block codes have the property of linearityi. There are block codes that are not linear, but it is difficult to prove that a code is a good one without this property.

Linear block codes are summarized by their symbol alphabets e. Block codes are tied to the sphere packing problem, which has received some attention over the years. In two dimensions, it is easy to visualize. Take a bunch of pennies flat on the table and push them together. The result is a hexagon pattern like a bee's nest.

But block codes rely on more dimensions which cannot easily be visualized. The powerful 24,12 Golay code used in deep space communications uses 24 binary block codes ppt. If used as a binary code which it usually is the dimensions refer to the 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. The only nontrivial and useful perfect codes are the distance-3 Hamming codes with parameters satisfying 2 r — 1, 2 binary block codes ppt — 1 — r3and the [23,12,7] binary and [11,6,5] ternary Golay codes. Another code property is the number of neighbors that a single codeword may have.

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 binary block codes ppt very rapidly. The result is the 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 a single neighbor, but the number of neighbors can be large enough so the total error probability actually suffers. Properties of linear block codes are used in many applications. For example, the syndrome-coset uniqueness property of linear block codes is used in binary block codes ppt shaping, [6] one of the best known shaping codes.

This same property is used in sensor networks for distributed source coding. The idea behind a convolutional code is to make every codeword symbol be the weighted sum of the various input message symbols. This is like convolution used in LTI systems to find the binary block codes ppt 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 the 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 be 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 searching only the most likely paths. Although not optimum, they have generally been found to give good results in low noise environments.

Convolutional codes are used in voiceband modems V. Cryptography or cryptographic coding is the practice and study of techniques for secure communication in the presence of third parties called adversaries. Modern cryptography exists at the intersection of the disciplines of mathematicscomputer scienceand electrical engineering.

Applications of cryptography include ATM cardscomputer passwordsand 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 original information only binary block codes ppt intended binary block codes ppt, 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 binary block codes ppt hardness assumptionsmaking 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.