a. Find the code rate, word error rate and number of word errors per year for the following codes (use 32 * 10^6 secs/year). Comment also on the need for retransmission.
b. How does the added length (30 vs. 14-15 in class) seem to have
affected performance?
a. Construct an IMLD table showing for each possible received vector the codeword to which it is decoded (if there is a unique closest codeword).
b. Find L(00000), the list of codewords decoded to 00000. Find L(11100), L(01110) and L(00111) also.
c. Make a table showing, for each codeword, and for each error
vector of weight 0, 1, or 2 whether the error is (C) corrected, (D)
detected, or (F) falsely corrected (miscorrected).
Which error vectors can be corrected by the code (independently of
which codeword is sent)?
d. Suppose that the codeword 00000 is sent over a reasonably good channel (q=1-p < 10^(-3)). The probabability of more than 2 errors occurring is then very small, so we can approximate the performance of the code using the data in the table from part c. Compute, as a function of p, for each of the codewords, the probability of (C) correction, (D) detection, and (F) false correction.
e. Suppose q=1-p = 10^(-4). Evaluate and tabulate the results in d.
f. Comment on the results in d. and e.
g. Suppose we use a less aggresive correction procedure, correcting only if the received vector is a distance 0 or 1 from a codeword. How would this change the performance? That is, what would be the probabilities for correction, detection, and false correction? Evaluate for arbitrary p as in d. above. Then for q = 1-p = 10^(-4) as in e.