Hamming code. Encoding of numerical information

In its functioning, any automated system faces the problem of adequate perception of data, the purity of the information received, the finding of errors, as well as their corrections. The more serious the tasks entrusted to the information processing object , the more complex and sensitive the system of determining the faulty elements of the software and the errors in the information flow it has to work.

One way to check the information flow for errors, and even to correct them, is the encoding of numerical information. There are many codes and methods used when working with different data. The so-called Hamming code is a classic pattern, which has become the starting point for creating more complex and sophisticated ways of finding and eliminating errors that occur during data transmission .

The history of the code begins in the mid-1940s. At this time, Richard Hamming mastered the Bell Model V account machine, working in the famous Bell Labs. Then it was an ultramodern mechanism using the electromechanical principle of action. The design of the machine used relay units. Their use did not give a significant gain in speed. A single turn took a few seconds. The data entry took place through the means of punched cards, and errors during their reading were not uncommon. On weekdays special codes were used to detect and correct the errors found. The machine informed the operator of the glow of the bulbs, which in turn corrected the error and restarted the calculation process. But on weekends, the process took place according to different rules. Having discovered the error, the machine automatically stopped the execution of the first program and proceeded to the execution of the other.

Since Hamming very often had to work on weekends, he was very annoyed by this behavior of the computer, because he had to restart the program on which he worked every time, and all the fault was the unreliability of punched cards. Several years he had to spend on building the most effective algorithms for correcting errors. As a result, by 1950 he was able to find and disclose the best way to solve this problem, now he is known throughout the world as the Hamming code.

The output, proposed by Richard Hemming, was immediately widespread. Methods of encoding information were replenished with several large blocks. For example, systematic codes are a large group, which consists of block, so-called separable codes (in other words those in which all symbols are divided into information and verification).

Systematic codes have a feature, the parity symbols are the result of linear operations on information symbols. At the same time, in any allowed code combination, it is possible to obtain a result from linear operations performed on a set of independent linear combination codes.

The Hamming code is a self-checking code. Such codes allow you to detect errors automatically during the transfer of data. To build them, you only need to assign one control (additional) binary digit to each word. The figure is chosen in such a way that in the total number of units when the image of the number is, by assumption, even.

If a single error occurs, it will change the parity in the total number of units.

Codes that lead to correcting errors in the automatic mode are called self-correcting. To build such a code, one control bit is not enough. The greatest interest is binary block codes that are corrective.

Summarizing, we can conclude that the Hamming code uses the principle of parity checking, where the number of single characters is examined.