Error Detection Codes

Error Detection Codes
Odd parity check code
Cat with a simple construction
Correction codes

Verification code
This is the simplest redundancy code. It is formed by adding a group of information bits 1 redundant check digit when generating a word code to the check digit is written down 0 If the sum of the units is encrypted and 1 If the sum is odd
In the future, when you transfer a record of reading and storage, the word is transmitted with a check digit.
If the control device detects an odd number of units in the receiving word, an error indication is formed
With parity checking, it has a small redundancy and does not require much equipment for implementing control.

Identify single errors and group error reports from an odd number

Codes with a simple construction of its basis is the repetition of input information.
1 part of the code informational 2 part of the error check if there is a mismatch, the error detects both single and group errors are implemented on the elements of addition modulo 2 and in the formation of an error modulo or

When using, additional characters are introduced for each digit of control bits.

2k is greater than M + N + 1

The minimum number of control bits 3
the number of test bits
m number of information bits
N total number of digits

The number of information bits

The number of control bits
When monitoring and correcting 4 bit information words, the transmitted message will be as follows:

The value of the digits of the control bits is as follows

check digit k1 must provide parity of 1
In bits, the number in the binary representation contains 1 in the first digit

K2 and K3 similarly

When finding K1 K2 K3 the value of the control bits is not taken into account, it is equal to the sum modulo two information bits

Answer

If an error is found, it is summed modulo 2 2 control information bits

If an error is detected and the result in an erroneous discharge is passed through the inverter, we build a circuit for the formation of test bits

Distorted in the seventh wire So you need to connect through the inverter

The number of the distorted digit is determined by converting the binary to decimal combination