Describe briefly syndrome decoding and incomplete decoding?
What will be an ideal response?
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.
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