#include?“rs.h“



void?encode_rs（int?recd[nn]?int?data[kk]?int??bb[nn-kk]）
/*?take?the?string?of?symbols?in?data[i]?i=0..（k-1）?and?encode?systematically
to?produce?2*tt?parity?symbols?in?bb[0]..bb[2*tt-1]
data[]?is?input?and?bb[]?is?output?in?polynomial?form.
Encoding?is?done?by?using?a?feedback?shift?register?with?appropriate
connections?specified?by?the?elements?of?gg[]?which?was?generated?above.
Codeword?is?c（X）?=?data（X）*X**（nn-kk）+?b（X）?*/
{
	int?ij?;
	int?feedback?;
	for?（i=0;?i		bb[i]?=?0?;
	for?（i=kk-1;?i>=0;?i--）
	{
		feedback?=?index_of[data[i]^bb[nn-kk-1]]?;
		if?（feedback?!=?-1）
		{?
			for?（j=nn-kk-1;?j>0;?j--）
				if?（gg[j]?!=?-1）
					bb[j]?=?bb[j-1]^alpha_to[（gg[j]+feedback）%nn]?;
				else
					bb[j]?=?bb[j-1]?;
			bb[0]?=?alpha_to[（gg[0]+feedback）%nn]?;
		}
		else
		{
			for?（j=nn-kk-1;?j>0;?j--）
				bb[j]?=?bb[j-1]?;
			bb[0]?=?0?;
		}?;
}?;

	for?（i=0;?i		recd[i]?=?bb[i]?;
	for?（i=0;?i		recd[i+nn-kk]?=?data[i]?;
}?



void?decode_rs（int?recd[nn]?int?dataout[kk]）
/*?assume?we?have?received?bits?grouped?into?mm-bit?symbols?in?recd[i]
i=0..（nn-1）?and?recd[i]?is?index?form?（ie?as?powers?of?alpha）.
We?first?compute?the?2*tt?syndromes?by?substituting?alpha**i?into?rec（X）?and
evaluating?storing?the?syndromes?in?s[i]?i=1..2tt?（leave?s[0]?zero）?.
Then?we?use?the?Berlekamp?iteration?to?find?the?error?location?polynomial
elp[i].?If?the?degree?of?the?elp?is?>tt?we?cannot?correct?all?the?errors
and?hence?just?put?out?the?information?symbols?uncorrected.?If?the?degree?of
elp?is?<=tt?we?substitute?alpha**i??i=1..n?into?the?elp?to?get?the?roots
hence?the?inverse?roots?the?error?location?numbers.?If?the?number?of?errors
located?does?not?equal?the?degree?of?the?elp?we?have?more?than?tt?errors
and?cannot?correct?them.?Otherwise?we?then?solve?for?the?error?value?at
the?error?location?and?correct?the?error.?The?procedure?is?that?found?in
Lin?and?Costello.?For?the?cases?where?the?number?of?errors?is?known?to?be?too
large?to?correct?the?information?symbols?as?received?are?output?（the
advantage?of?systematic?encoding?is?that?hopefully?some?of?the?information
symbols?will?be?okay?and?that?if?we?are?in?luck?the?errors?are?in?the
parity?part?of?the?transmitted?codeword）.?Of?course?these?insoluble?cases
can?be?returned?as?error?flags?to?the?calling?routine?if?desired.?*/
{
	int?ijuq?;
	int?elp[nn-kk+2][nn-kk]?d[nn-kk+2]?l[nn-kk+2]?u_lu[nn-kk+2]?s[nn-kk+1]?;
	int?count=0?syn_error=0?root[tt]?loc[tt]?z[tt+1]?err[nn]?reg[tt+1]?;
	/*?first?form?the?syndromes?*/
	for?（i=1;?i<=nn-kk;?i++）
	{?
		s[i]?=?0?;
		for?（j=0;?j			if?（recd[j]!=-1）
			s[i]?^=?alpha_to[（recd[j]+i*j）%nn]?;?/*?recd[j]?in?index?form?*/
/*?convert?syndrome?from?polynomial?form?to?index?form?*/
		if?（s[i]!=0）?syn_error=1?;?/*?set?flag?if?non-zero?syndrome?=>?error?*/
			s[i]?=?index_of[s[i]]?;
	}?;
	if?（syn_error）?/*?if?errors?try?and?co

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????9507??2014-06-18?08:55??rs（6.17）\rs.cpp
?????文件?????????876??2014-06-18?08:54??rs（6.17）\rs.h
?????文件?????????611??2014-06-18?08:54??rs（6.17）\test_rs.cpp
?????目錄???????????0??2014-06-18?09:00??rs（6.17）\