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From: killsnoopers on 9 Nov 2009 08:56
>dvsarwate(a)yahoo.com <dvsarwate(a)gmail.com> wrote:
>
>>On Jul 31, 1:44�am, spop...(a)speedymail.org (Steve Pope) wrote:
>
>
>>> Actually, it takes only k clock cycles to compute this remainder.
>
>>If the bits are entering the decoder serially, it takes n clock cycles
>>to get them all into the decoder. So I am not sure how one can get
>>the remainder of "v(x) divided by Mi(x)" or "v(x) divided by G(x)"
>>in just k clock cycles. Perhaps Steve Pope will elucidate further.
>
>Sure. After those first k received bits, you will have computed a value
>which, when added (xor'ed) with the remaining received bits
>(which are the check locations) will be the remainder R(x). Since
>this addition is a trivial operation, you can start evaluating R(x)
>by Horner's method as these final check bits start
>coming in, and you will have the resulting syndrome by the same point
>in time that you would have, had you evaluated v(x) directly.
>
>So -- at least typically -- there is no difference in latency
>between the two methods; the one method has more polynomial
>shift register operations over GF(2) while the other has more
>time spent in Horner's method in GF(2^m).
>
>I have however often done it the way you suggest. The two methods
>are competitive. The important thing (for latency) is to have
>all the syndromes available immediately after receiving the last
>symbol from the channel.
>
>Steve
>
>

Actually division by g(x) to get the remainder and treat that as error
polynomial won't work. It will give another codeword but not the desired
codeword. You can verify this. But a simple way to see this is incorrect is
that the remainder has degree less that of g(x) which means it can only
change bits of the received codeword upto it, so if errors occured
elsewhere it cannot correct them.

Has anyone written a c or matlab program to find the hamming distance of a
block code ? I know its possible to write on, but if one already available,
might as well simply use it.




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