CSC 310, SPRING 2004, ASSIGNMENT 4, OUTPUT AND DISCUSSION.

When run on the 50 received vectors provided, using the command

   a4-sol a4-H <a4-r

the program produced the following output:

 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1
 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1
 0 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0
 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 1
 2 0 0 1 1 2 1 0 1 0 1 1 1 0 1 2 2 2 0 1 0 0 2 0 0 1 1 0 0 1 1 1 1 1 0  Not fully decoded
 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0
 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0
 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0
 0 0 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0
 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0
 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1
 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 1
 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0
 1 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1
 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1
 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1
 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0
 0 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 0
 1 0 1 1 1 1 1 0 0 0 1 2 0 0 0 0 1 2 0 2 0 1 1 1 2 2 2 0 0 2 2 2 0 2 2  Not fully decoded
 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1
 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1
 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1
 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1
 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1
 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1
 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1
 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0
 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1
 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1
 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1
 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1
 1 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0
 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1
 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 2 0 0 0 2 1 0 0 1 1 2 0 1 1 2 1 1 1 0 1  Not fully decoded
 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0
 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1
 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0
 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0
 1 1 0 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 1
 0 1 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 1
 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0
 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1
 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1
 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1
 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0
 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0
 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0
 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1
 2 1 0 2 0 0 0 0 2 1 0 0 2 0 0 0 0 1 1 0 0 2 1 2 1 1 2 0 2 1 1 1 2 0 0  Not fully decoded
 0 1 1 2 0 2 0 0 2 1 0 1 0 1 0 0 0 0 1 2 0 2 0 2 1 1 0 0 0 2 0 1 0 0 1  Not fully decoded

As can be seen, 5 out of the 50 received vectors were not fully
decoded using the decoding algorithm.  To see whether an optimal
decoding algorithm would have been able to decode these received
vectors correctly, I changed the first remaining erasure in each of
these 5 messages to both 0 and 1, producing the following 10 vectors:

 0 0 0 1 1 2 1 0 1 0 1 1 1 0 1 2 2 2 0 1 0 0 2 0 0 1 1 0 0 1 1 1 1 1 0
 1 0 0 1 1 2 1 0 1 0 1 1 1 0 1 2 2 2 0 1 0 0 2 0 0 1 1 0 0 1 1 1 1 1 0
 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 2 0 2 0 1 1 1 2 2 2 0 0 2 2 2 0 2 2
 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 2 0 2 0 1 1 1 2 2 2 0 0 2 2 2 0 2 2
 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 2 1 0 0 1 1 2 0 1 1 2 1 1 1 0 1
 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 2 1 0 0 1 1 2 0 1 1 2 1 1 1 0 1
 0 1 0 2 0 0 0 0 2 1 0 0 2 0 0 0 0 1 1 0 0 2 1 2 1 1 2 0 2 1 1 1 2 0 0
 1 1 0 2 0 0 0 0 2 1 0 0 2 0 0 0 0 1 1 0 0 2 1 2 1 1 2 0 2 1 1 1 2 0 0
 0 1 1 0 0 2 0 0 2 1 0 1 0 1 0 0 0 0 1 2 0 2 0 2 1 1 0 0 0 2 0 1 0 0 1
 0 1 1 1 0 2 0 0 2 1 0 1 0 1 0 0 0 0 1 2 0 2 0 2 1 1 0 0 0 2 0 1 0 0 1

Running the program on these vectors produced the following output:

 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0  Not a codeword (fails check 7)
 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0
 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 0
 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1  Not a codeword (fails check 1)
 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1
 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1
 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0
 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0  Not a codeword (fails check 8)
 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1
 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1

From this, we can conclude that the first, second, and fourth of the
received vectors that were not fully decoded would have been fully
decoded by an optimal decoding algorithm, since only one codeword is
compatible with these received vectors.  However, no decoding
algorithm would be able to decode (with certainty) the other two
received vectors that were not fully decoded, since there are two
codewords compatible with each of these received vectors.