2D Parity Check Part 1, Document Files PDF

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2D Parity Check Code Arpit BTECH/10369/18 DCCN ASSIGNMENT

A multidimensional parity-check code (MDPC) is a simple type of error correcting code that operates by arranging the message into a multidimensional grid, and calculating a parity digit for each row and column. In general, an n-dimensional parity scheme can correct n/2 errors. The two-dimensional parity-check code, usually called the optimal rectangular code, is the most popular form of multidimensional parity-check code. Assume that the goal is to transmit the four-digit message "1234", using a two-dimensional parity scheme. First the digits of the message are arranged in a rectangular pattern: 12 34 Parity digits are then calculated by summing each column and row separately: 123 347 46 The eight-digit sequence "12334746" is the message that is actually transmitted. If any single error occurs during transmission then this error can not only be detected but can also be corrected as well. Let us

suppose that the received message contained an error in the first digit. The receiver rearranges the message into the grid:

923 347 46 The receiver can see that the first row and also the first column add up incorrectly. Using this knowledge and the assumption that only one error occurred, the receiver can correct the error. In order to handle two errors, a 4-dimensional scheme would be required, at the cost of more parity digits. TWO DIMENSIONAL PARITY: WORKING We will make a Two Dimensional array from the message bit. After that, according to the even or odd parity, We will fill the last column and last row of the matrix.

Total Parity Bits – i + j + 1 (Row+Column+1) Here Parity Bit = 3 + 5 +1 = 9 One point is to remember that the Value of (i, j ) should be of message array i.e. in spite of having the value of i = 4, j = 6 (which is of array with parity bits). we will take the value of the message array i.e i=3, j=5.

Row and column parity bits are known as Redundant Bits i.e i+j+1. The code that is to be transmitted will be the whole message included Redundant Bits. For ex :

Now, this code is transmitted and reaches the receiver side, where the receiver will again form a similar Two Dimensional array.

CASES OCCURS IN TWO DIMENSIONAL PARITY CASE 1 : Suppose a bit is in error. Then it can be easily detected and the code is corrected. As shown in fig.

CASE 2 : When two erroneous bits are detected and corrected. The undesired part is that two other bits were also detected as an incorrect bit.

CASE 3 : When odd no. of error takes place in a particular row or particular column.

CASE 4 : When even no. of error takes place in a particular row.

CASE 5 : Where the error is not detected so not corrected.

DRAWBACKS ●

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In some cases, an only odd number of bit errors can be detected and corrected but even number of errors can only be detected but not corrected. In some cases, this method is not able to detect even no bit error....