This preview shows page 1. Sign up to view the full content.
Unformatted text preview: arbitrary decision. (We have
tacitly assumed that the a priori probability of the sender sending a message 0 is the same 4 LECTURE 6. COPING WITH BIT ERRORS Figure 6-1: Probability of a decoding error with the replication code that replaces each bit b with c copies
of b. The code rate is 1/c. as a 1.)
We can write the probability of decoding error for the replication code as, being a bit
careful with the limits of the summation:
if c odd
i= 2 i p (1 − p)
P (decoding error) =
c−i + 1 c pc/2 (1 − p)c/2 if c even
i= c i p (1 − p)
2 When c is even, we add a term at the end to account for the fact that the decoder has a
ﬁfty-ﬁfty chance of guessing correctly when it receives a codeword with an equal number
of 0’s and 1’s.
Figure 6-1 shows the probability of decoding error from Eq.(6.2) as a function of the
code rate for the replication code. The y -axis is on a log scale, and the probability of error
is more or less a straight line with negative slope (if you ignore the...
View Full Document
- Fall '13