Longitudinal Redundancy Check (LRC)/2-D Parity Check

Longitudinal Redundancy Check (LRC) is also known as 2-D parity check. In this method, data which the user want to send is organised into tables of rows and columns. A block of bit is divided into table or matrix of rows and columns. In order to detect an error, a redundant bit is added to the whole block and this block is transmitted to receiver. The receiver uses this redundant row to detect error. After checking the data for errors, receiver accepts the data and discards the redundant row of bits.

Example :
If a block of 32 bits is to be transmitted, it is divided into matrix of four rows and eight columns which as shown in the following figure :

Figure: LRC

In this matrix of bits, a parity bit (odd or even) is calculated for each column. It means 32 bits data plus 8 redundant bits are transmitted to receiver. Whenever data reaches at the destination, receiver uses LRC to detect error in data.

Advantage :
LRC is used to detect burst errors.

Example : Suppose 32 bit data plus LRC that was being transmitted is hit by a burst error of length 5 and some bits are corrupted as shown in the following figure :

Figure : Burst error & LRC

The LRC received by the destination does not match with newly corrupted LRC. The destination comes to know that the data is erroneous, so it discards the data.

Disadvantage :
The main problem with LRC is that, it is not able to detect error if two bits in a data unit are damaged and two bits in exactly the same position in other data unit are also damaged.

Example : If data 110011 010101 is changed to 010010110100.

Figure : Two bits at same bit position damaged in 2 data units

In this example 1st and 6th bit in one data unit is changed . Also the 1st and 6th bit in second unit is changed.