20 Syndrome calculation for (7,4) cyclic code.
Step 3: Select the most likely candidate or maximize the a posteriori probability that the received
code word is correct.
A block diagram presenting the operation is presented below for the (7,4) code example with 2
erasures. Let??™s review these steps using an example.
Step 1: Identify the bit positions with the lowest signal strength, here we assume they correspond to
the following bit locations within the code word.
Step 2: Apply the patterns to the code words (the number of pattern is 2 4)
240 CHAPTER FIVE
Step 3: Apply the exhaustive search to find the most likely code word transmitted ( j 0, 1, 2, 3, 4).
Our goal is to maximize the following equation:
(5.45)
Let??™s provide some insight into the above operations. Let be equal to the signal strength corresponding
to the bit in the ith position in the code word. We select the two smallest values (possibly
provided they are below some threshold) and declare them as erasure bits. We create four candidates,
which is essentially an exhaustive search of the possible transmitted bits. This in turn provides performance
close to that of the maximum likelihood (ML) decoding. Each candidate is decoded and
then re-encoded.
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