Single Error Correction Implementation

Single Error Correction Implementation

When we transmit data, at receiver the received data must be identical to transmitted .this happened if there is no any distortion in the transmission path  i.e. the channel is idle, but as that known in practical  fields there is no idealist can be achieved . So there are some distortion offered data that transmitted.

Hence the duty of the receiver is to detect whether the transmitted data in error or not .and if there error then can correct it or not.

We divide the work in receiver into two ways

Detecting the error

                     This done by the circuit called the syndrome circuit.

Correction of error

                     If there error is detected then the receiver try to correct it.

In this part we will studies the correction part for cyclic code

Theoretically

    The relation says that

“The received vector = transmitted vector + error”

    Then

The transmitted vector = received vector +error

     Note

The sign (+) means exclusive or summing

Number of bits that can be detected

For linear block code we find that the theory states that:-

“A linear block code with minimum distance d_min  Can correct up to [(d_min -1)/2] errors. And detect up to [d_min -1] errors in each code word.

Example

If d_min=3     hence we can

·        Detect up to [d_min-1] =2 bit in errors. but we will able to correct [(d_min-1)/2]=1 bit only

Example

If d_min= 4 hence we can:

·        detect up to 3 bits in errors  ,and correct only 2 bits

Single Error Correction

·        In single error correction d_min=3

·        Hence we can detect up to 2 bits in errors .but we able to correct only one bit.

The circuit shown is used to correct only on bit

Block Diagram

  

 

The operation of correction circuit is divided into three parts as shown  in block diagram

Getting The Data

The received vector is inserted to circuit as it coming from encoder (in serial form) then at output it obtained in parallel form.

Getting The Error Vector

To get the error vector we use 3-to-8 line decoder which it’s input is the syndrome. Ands as the structure of this line decoder gives only one state to each syndrome word .then we get only one state at output of line decoder for each syndrome word. Which correspond to error vector.

Getting Correct Code Vector

Once we obtained the received vector in parallel form. it added to the line decoder output by using XOR GATES the output of this gates represent the correct code vector.