Error correction, ARQ, FEC

4.2.3

Error Correction

4.2.3 Error Correction

• Once Detected, an error must be corrected.• Two basic approaches to error correction are

available, which are:

– Automatic-repeat-request (ARQ):– Forward error correction (FEC):

4.2.3 Error Correction

• Automatic-repeat request (ARQ):– ARQ procedures require the transmitter to resend

the portions of the exchange in which error have been detected.

• Forward error correction (FEC):– FEC techniques employ special codes that allow

the receiver to detect and correct a limited number of errors without referring to the transmitter.

ARQ Techniques

• Generally, ARQ procedures include the following actions by the receiver or the sender:

ARQ Techniques

• Receiver:

– Discard those frames in which errors are detected.

– For frames in which no error was detected, the receiver returns a positive acknowledgment to the sender.

– For the frame in which errors have been detected, the receiver returns negative acknowledgement to the sender.

ARQ Techniques

• Sender:

– Retransmit the frames in which the receiver has identified errors.

– After a pre-established time, the sender retransmits a frame that has not been acknowledged.

ARQ Techniques

• Three Common ARQ Techniques are:

– Stop-and-Wait– Go-back-n– Selective-repeat

ARQ Techniques

• Stop-and-Wait– The sender sends a frame and waits for

acknowledgment from the receiver.– This technique is slow– Suited for half-duplex connection.

ARQ Techniques

• Stop-and-Wait

ARQ Techniques

• Go-back-n:– The sender sends frames in a sequence and

receives acknowledgements from the receiver.

– On detecting an error, the receiver discards the corrupted frame, and ignores any further frames.

– The receiver notifies the sender of the number of frame it expects to receive.

ARQ Techniques

• Go-back-n:– On receipt of information, the sender begins re-

sending the data sequence starting from that frame.

– This technique is faster than stop-and-wait technique.

ARQ Techniques

• Selective-repeat:– Used on duplex connections.– The sender only repeats those frames for which

negative acknowledgment are received from the receiver, or no acknowledgment is received.

– The appearance of a repeated frame out of sequence may provide the receiver with additional complications.

Forward Error Correction

– Possible for the receiver to detect and correct errors without reference to the sender.

– This convenience is bought at the expense of adding more bits.

Forward Error Correction

• For example– If we only have two massages to send.– we represent one (A) by the bits 10101010,– And the other (B) by the bits 01010101.– If the receiver knows that the message is A or B

and no other, and it is provided with the ability to determine the logical distance between each incoming massage and the two known messages, this strategy will allow the receiver to correct for up to three bits in error. The prove is as follows.

Forward Error Correction

• Proof:– Suppose A is in error by 1 bit, so that

A’ = 00101010– The logical distance between the received pattern

and A is 1– And logical distance between the received pattern

and B is 7; – Thus A’ is likely to be A.

Forward Error Correction

– Suppose A is in error by 2 bit, so that

A’ = 01101010– The logical distance between the received pattern

and A is 2– And logical distance between the received pattern

and B is 6; – Thus A’ is likely to be A.

Forward Error Correction

– Suppose A is in error by 3 bit, so that

A’ = 01001010– The logical distance between the received pattern

and A is 3– And logical distance between the received pattern

and B is 5; – Thus A’ is likely to be A.

Forward Error Correction

– Suppose A is in error by 4 bit, so that

A’ = 01011010– The logical distance between the received pattern

and A is 4– And logical distance between the received pattern

and B is 4; – Thus A’ is likely to be A or B.

Forward Error Correction

• Continuing the sequence to higher levels of error makes A’ more likely to be B than A.

• For this particular case, the limit of correction is 3-bits in error.

Forward Error Correction

• Codes used to provide FEC (Forward Error Correction) are more sophisticated than our example. They can be divided into two types.– Linear Block Codes– Convolutional Codes