Describe briefly syndrome decoding and incomplete decoding?

Question

What will be an ideal response?

Answer 1

Syndrome decoding: In linear block encoding, n?k parity bits are added to the

original message vector m which is k bits long. Hence, the transmitted vector c

and the received vector x at the decoder are n bits sequences. Syndrome

decoding consists of calculating the 1 × (n ? k) vector s which would either

uniquely map the received vector x to a possible match in c or if it is not

possible to correctly decode the received vector x, a non-null vector value of s

would indicate errors in transmission. In a linear block coding transmission, the

syndrome vector s can be calculated by







and H is called the parity check matrix and is given by concatenating the

transpose of the parity matrix P (k by n ? k matrix) and the identity matrix In?k

(n ? k by n ? k matrix).



Incomplete decoding: Incomplete decoding is not an independent decoding

method. Actually, it is combined with existing decoding methods to improve

their error correction capability. For example, the target of the maximum

likelihood (ML) decoding is to find the likely codeword after a codeword is

received. However, it is possible to have more than one such codeword. If using

the existing ML decoding, the decoder will arbitrarily select one of them.

However, it will request a retransmission in the incomplete ML decoding. It can

improve the error correction capability since the probability of continuous

decoding failure is much smaller than probability of single decoding failure.



Furthermore, incomplete decoding can be used in the other probability decoding

method.