subroutine osd174(llr,apmask,norder,decoded,cw,nhardmin,dmin)
!
! An ordered-statistics decoder for the (174,87) code.
! 
include "ldpc_174_87_params.f90"

integer*1 apmask(N),apmaskr(N)
integer*1 gen(K,N)
integer*1 genmrb(K,N),g2(N,K)
integer*1 temp(K),m0(K),me(K),mi(K),misub(K),e2sub(N-K),e2(N-K)
integer indices(N),nxor(N)
integer*1 cw(N),ce(N),c0(N),hdec(N)
integer*1 decoded(K)
integer indx(N)
real llr(N),rx(N),absrx(N)
logical first
data first/.true./
save first,gen

if( first ) then ! fill the generator matrix
  gen=0
  do i=1,M
    do j=1,22
      read(g(i)(j:j),"(Z1)") istr
        do jj=1, 4 
          irow=(j-1)*4+jj
          if( btest(istr,4-jj) ) gen(irow,i)=1
        enddo
    enddo
  enddo
  do irow=1,K
    gen(irow,M+irow)=1
  enddo
first=.false.
endif

! Re-order received vector to place systematic msg bits at the end.
rx=llr(colorder+1) 
apmaskr=apmask(colorder+1)


! Hard decisions on the received word.
hdec=0            
where(rx .ge. 0) hdec=1

! Use magnitude of received symbols as a measure of reliability.
absrx=abs(rx) 
call indexx(absrx,N,indx)  

! Re-order the columns of the generator matrix in order of decreasing reliability.
do i=1,N
  genmrb(1:K,i)=gen(1:K,indx(N+1-i))
  indices(i)=indx(N+1-i)
enddo

! Do gaussian elimination to create a generator matrix with the most reliable
! received bits in positions 1:K in order of decreasing reliability (more or less). 
do id=1,K ! diagonal element indices 
  do icol=id,K+20  ! The 20 is ad hoc - beware
    iflag=0
    if( genmrb(id,icol) .eq. 1 ) then
      iflag=1
      if( icol .ne. id ) then ! reorder column
        temp(1:K)=genmrb(1:K,id)
        genmrb(1:K,id)=genmrb(1:K,icol)
        genmrb(1:K,icol)=temp(1:K) 
        itmp=indices(id)
        indices(id)=indices(icol)
        indices(icol)=itmp
      endif
      do ii=1,K
        if( ii .ne. id .and. genmrb(ii,id) .eq. 1 ) then
          genmrb(ii,1:N)=ieor(genmrb(ii,1:N),genmrb(id,1:N))
        endif
      enddo
      exit
    endif
  enddo
enddo

g2=transpose(genmrb)

! The hard decisions for the K MRB bits define the order 0 message, m0. 
! Encode m0 using the modified generator matrix to find the "order 0" codeword. 
! Flip various combinations of bits in m0 and re-encode to generate a list of
! codewords. A pre-processing step selects a subset of these codewords. 
! Return the member of the subset with the smallest Euclidean distance to the
! the received word.

hdec=hdec(indices)   ! hard decisions from received symbols
m0=hdec(1:K)         ! zero'th order message
absrx=absrx(indices) 
rx=rx(indices)       
apmaskr=apmaskr(indices)

call mrbencode(m0,c0,g2,N,K)
nxor=ieor(c0,hdec)
nhardmin=sum(nxor)
dmin=sum(nxor*absrx)

cw=c0
ntotal=0
nrejected=0
nt=40          ! Count the errors in the nt best bits in the redundancy part of the cw 
ntheta=12      ! Reject the codeword without computing distance if # errors exceeds ntheta 

! norder should be 1, 2, or 3.
! if norder = 1, do one loop, no pre-processing
! if norder = 2, do norder=1, then norder=2 using first W&H pre-processing rule
! if norder = 3, do norder=2, then norder=3 using first W&H pre-processing rule

if(norder.lt.1) goto 998  ! norder=0
if(norder.gt.3) norder=3

if( norder.eq. 1) then
   nord=1
   npre=0
elseif(norder.eq.2) then
   nord=1
   npre=1
elseif(norder.eq.3) then
   nord=2
   npre=1
endif

do iorder=1,nord
   if( iorder.eq. 1 ) then
      misub(1:K-1)=0
      misub(K)=1
      iflag=K
   elseif( iorder.eq. 2 ) then
      misub(1:K-2)=0
      misub(K-1:K)=1 
      iflag=K-1
   endif
   do while(iflag .ge.0)
      if(iorder.eq.nord .and. npre.eq.0) then
         iend=iflag
      else
         iend=1
      endif
      do n1=iflag,iend,-1
         mi=misub
         mi(n1)=1
         if(any(iand(apmaskr(1:K),mi).eq.1)) cycle
         ntotal=ntotal+1
         me=ieor(m0,mi)
         if(n1.eq.iflag) then
            call mrbencode(me,ce,g2,N,K)
            e2sub=ieor(ce(K+1:N),hdec(K+1:N))
            e2=e2sub
            nd1Kpt=sum(e2sub(1:nt))+1
            d1=sum(ieor(me(1:K),hdec(1:K))*absrx(1:K))
         else
            e2=ieor(e2sub,g2(K+1:N,n1))
            nd1Kpt=sum(e2(1:nt))+2
         endif
         if(nd1Kpt .le. ntheta) then
            call mrbencode(me,ce,g2,N,K)
            nxor=ieor(ce,hdec)
            if(n1.eq.iflag) then
               dd=d1+sum(e2sub*absrx(K+1:N))
            else
               dd=d1+ieor(ce(n1),hdec(n1))*absrx(n1)+sum(e2*absrx(K+1:N))
            endif
            if( dd .lt. dmin ) then
               dmin=dd
               cw=ce
               nhardmin=sum(nxor)
               nd1Kptbest=nd1Kpt
            endif
         else 
            nrejected=nrejected+1
         endif
      enddo
! Get the next test error pattern, iflag will go negative
! when the last pattern with weight iorder has been generated.
      call nextpat(misub,k,iorder,iflag)
   enddo
enddo

!write(*,*) 'rejected, total, nd1Kptbest: ',nrejected, ntotal, nd1Kptbest

998 continue
! Re-order the codeword to place message bits at the end.
cw(indices)=cw
hdec(indices)=hdec
decoded=cw(K+1:N) 
cw(colorder+1)=cw ! put the codeword back into received-word order
return
end subroutine osd174

subroutine mrbencode(me,codeword,g2,N,K)
integer*1 me(K),codeword(N),g2(N,K)
! fast encoding for low-weight test patterns
  codeword=0
  do i=1,K
    if( me(i) .eq. 1 ) then
      codeword=ieor(codeword,g2(1:N,i))
    endif
  enddo
return
end subroutine mrbencode

subroutine nextpat(mi,k,iorder,iflag)
  integer*1 mi(k),ms(k)
! generate the next test error pattern
  ind=-1
  do i=1,k-1
     if( mi(i).eq.0 .and. mi(i+1).eq.1) ind=i 
  enddo
  if( ind .lt. 0 ) then ! no more patterns of this order
    iflag=ind
    return
  endif
  ms=0
  ms(1:ind-1)=mi(1:ind-1)
  ms(ind)=1
  ms(ind+1)=0
  if( ind+1 .lt. k ) then
     nz=iorder-sum(ms)
     ms(k-nz+1:k)=1
  endif
  mi=ms
  do i=1,k  ! iflag will point to the lowest-index 1 in mi
    if(mi(i).eq.1) then
      iflag=i 
      exit
    endif
  enddo
  return
end subroutine nextpat