27. Noiseproof codes design techniques: code with parity check, code with threefold repetition, Hamming's code.

In order to detect and fix the problem, apply the so-called "error control codes," that is encoded message so that the receiving party knew there was an error or not, and often can correct errors when they occur. This coding is that the transmitted message includes additional characters. They do not have the information directly related to the transmitted message, but can provide information on the occurrence of transmission errors. In other words, their purpose - to control the accuracy of the transmission of the main messages. For this reason, input additional characters are called - control (or check). The most obvious way to detect and correct errors is that each data bit 0 repeats a block of n zeros, and each bit is 1 - a block of n units. If we assume that the noise in the communication channel distort less than half of the bits in each transmitted block, the decoding n-bit block containing perhaps erroneous simvoly.Esli block length n is chosen sufficiently large, we almost avoid the possibility of errors but messaging will go a snail's pace. For this reason, the specified code (called a "code with the repetition of" 3) does not have much practical value. Another method of encoding a message, which is called "code with the overall parity-check" can therefore detect any odd number of errors, but the "missing" distortion if the number of errors chetno.Kod with repetition, as described in the beginning, and with a common code parity check - to some extent antipodes. The possibility of the first correct errors theoretically unlimited, but it is very "slow." The second is very fast (just one extra bit), but often "frivolous." In actual communication channels usually have to consider the possibility of errors in more than one bit, so in pure form with a common code parity check is rarely used. More often use multiple codes parity of bits (and, consequently, multiple parity checks). They can not only detect but also correct errors, and not just single but multiple, and, moreover, to do so more efficiently than the code we've mentioned repeatedly.Hamming code is a set of error-correction code s that can be used to detect and correct bit errors that can occur when computer data is moved or stored. Hamming code is named for R. W. Hamming of Bell Labs.Like other error-correction code, Hamming code makes use of the concept of parity and parity bit s, which are bits that are added to data so that the validity of the data can be checked when it is read or after it has been received in a data transmission. Using more than one parity bit, an error-correction code can not only identify a single bit error in the data unit, but also its location in the data unit.

28. Communication channels various models: discrete, continuous.

A channel connection is meant a collection of devices, and physical media, providing transfer of messages from one location to another (or from one instant to another). If the channel is used to transmit digital messages, it is called a discrete channel. Is called continuous channel for transmission of continuous messages. Channels used for the transmission of continuous signals, called continuous. These channels still find wide application, for example, telephone equipment, broadcasting. Real continuous channels are complex non-linear inertial objects, the characteristics of which vary randomly over time. For the analysis of such channels are developed mathematical models of various levels of difficulty and the adequacy of the real channels. Models that have received the most widespread - a kind of a Gaussian channel. The data transfer speed in a continuous channel - this is the amount of information that is transmitted by an average taken continuous signals υ (t), relative to the transmitted u (t) per unit time. Discrete channel - the channel for the transmission of digital signals. A discrete channel is: - From the physical transmission signals in both directions, and - A pair of channel service units. Digital channels are characterized by: - Transmission rate (bits per second), and - Value of noise.