Subject: correction to sample solution
From: Rajmohan Rajaraman (rraj@ccs.neu.edu)
Date: Thu Oct 18 2001 - 21:55:12 EDT
This note is regarding the solution to Problem 4(e) of PS1 given in
today's handout. Problem 4 concerns a 2-bit parity code, in which we
have a parity bit for the even bits and a parity bit for the odd bits.
The problem asked whether it helps to add a third parity bit which is
the parity of all the data bits in the string.
The sample solution says yes. This is correct, but the explanation
that follows is not right. The main reason that the third parity bit
helps is that it is the parity of the *data* bits and hence does not
include the 2 parity bits. The extra bit helps only in certain cases
when there is an error in one of the 2 parity bits. Consider the case
when there are no errors in the bits in the odd position, 1 error in a
bit in the even position, and an error in the parity bit corresponding
to the even positions. This error is not detected by the 2-bit code,
but is detected by the 3-bit code.
Sorry about this error. (I need to add error-correction codes to my
sample solutions!)
Rajmohan.
P.S.: I have made the correction to the sample solution document that
is available from the homepage.
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