[Commit-gnuradio] [gnuradio] 09/39: fec: LDPC: Adding scripts to generate matrices for encoder.

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commit 27871a568e51ca6e196ccb7b8415f892b6c8a843
Author: tracierenea <address@hidden>
Date:   Sat Jul 12 13:46:17 2014 -0500

    fec: LDPC: Adding scripts to generate matrices for encoder.
    
    Adding python scripts which generate parity check matrices for use
    with the LDPC Richardson Urbanke encoder. A significant amount of
    matrix manipulation is required, so this process should be done before
    using the encoder at run time. For large matrices, it will take quite
    a while.
---
 gr-fec/python/fec/LDPC/Generate_LDPC_matrix.py     |  79 +++
 .../fec/LDPC/Generate_LDPC_matrix_functions.py     | 619 +++++++++++++++++++++
 2 files changed, 698 insertions(+)

diff --git a/gr-fec/python/fec/LDPC/Generate_LDPC_matrix.py 
b/gr-fec/python/fec/LDPC/Generate_LDPC_matrix.py
new file mode 100644
index 0000000..c815682
--- /dev/null
+++ b/gr-fec/python/fec/LDPC/Generate_LDPC_matrix.py
@@ -0,0 +1,79 @@
+#!/usr/bin/env python
+#
+# Copyright 2014 Free Software Foundation, Inc.
+#
+# This file is part of GNU Radio
+#
+# GNU Radio is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3, or (at your option)
+# any later version.
+#
+# GNU Radio is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with GNU Radio; see the file COPYING.  If not, write to
+# the Free Software Foundation, Inc., 51 Franklin Street,
+# Boston, MA 02110-1301, USA.
+#
+
+from Generate_LDPC_matrix_functions import *
+
+# This is an example of how to generate a parity check matrix for
+# use with the LDPC Richardson Urbanke encoder. A significant amount
+# of matrix manipulation is required, so this process should be done
+# before using the encoder at run-time. This process can take quite
+# a while, with more time required for larger matrices. 
+
+# Not all attempts to create a parity check matrix will be
+# successful. The script will terminate and output error messages
+# when the process fails. To increase verbosity, edit the verbose
+# variable at the top of Generate_LDPC_matrix_functions.py.
+
+# Because random number generation and
+# shuffling methods are used, it is not possible to predict what
+# starting conditions will result in success. It requires a bit of 
+# trial and error. 
+
+# ----------------------------------------------------------------- #
+
+# First, generate a regular LDPC parity check matrix. Specify
+# the properties desired. For example:
+n = 200   # number of columns, corresponds to codeword length
+p = 3     # column weight
+q = 5     # row weight
+
+parity_check_matrix = LDPC_matrix(n_p_q = [n,p,q])
+
+# Richardson and Urbanke's preprocessing method requires a full rank
+# matrix to start. The matrices generated by the 
+# regular_LDPC_code_contructor function will never be full rank. So,
+# use the get_full_rank_H_matrix function. 
+newH = get_full_rank_H_matrix(parity_check_matrix.H)
+
+# At this point, the matrix is no longer regular. (The row/column
+# weights are not the same for all rows/columns.)
+
+# Next, some preprocessing steps need to be performed as described
+# Richardson and Urbanke in Modern Coding Theory, Appendix A. This
+# can take a while...
+[bestH,g] = get_best_matrix(newH,100)
+
+# Print out some of the resulting properties. 
+n = bestH.shape[1]
+k = n - bestH.shape[0]
+print "Parity check matrix properties:"
+print "\tSize :", bestH.shape
+print "\tRank :", linalg.matrix_rank(bestH)
+print "\tRate : %.3f" % ((k*1.0)/n)
+print "\tn    :", n, " (codeword length)"
+print "\tk    :", k, " (info word length)"
+print "\tgap  : %i" % g
+
+# Save the matrix to an alist file for future use: 
+alist_filename = "n_%04i_k_%04i_gap_%02i.alist" % (n,k,g)
+parity_check_matrix.write_alist_file(alist_filename,bestH)
+print '\nMatrix saved to alist file:', alist_filename, "\n"
\ No newline at end of file
diff --git a/gr-fec/python/fec/LDPC/Generate_LDPC_matrix_functions.py 
b/gr-fec/python/fec/LDPC/Generate_LDPC_matrix_functions.py
new file mode 100644
index 0000000..85f8ce9
--- /dev/null
+++ b/gr-fec/python/fec/LDPC/Generate_LDPC_matrix_functions.py
@@ -0,0 +1,619 @@
+#!/usr/bin/env python
+#
+# Copyright 2014 Free Software Foundation, Inc.
+#
+# This file is part of GNU Radio
+#
+# GNU Radio is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3, or (at your option)
+# any later version.
+#
+# GNU Radio is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with GNU Radio; see the file COPYING.  If not, write to
+# the Free Software Foundation, Inc., 51 Franklin Street,
+# Boston, MA 02110-1301, USA.
+#
+
+import string
+from numpy import *
+from numpy.random import shuffle, randint
+from numpy.linalg import inv, det
+
+# 0 gives no debug output, 1 gives a little, 2 gives a lot
+verbose = 0
+
+class LDPC_matrix:
+  """ Class for a LDPC parity check matrix """
+  def __init__(self, alist_filename = None, 
+             n_p_q = None, 
+             H_matrix = None):
+    if (alist_filename != None):
+      self.H = self.read_alist_file(alist_filename)
+    elif (n_p_q != None):
+      self.H = self.regular_LDPC_code_contructor(n_p_q)
+    elif (H_matrix != None):
+      self.H = H_matrix
+    else:
+      print 'Error: provide either an alist filename,', 
+      print 'parameters for constructing regular LDPC parity',
+      print 'check matrix, or a numpy array.'
+
+    self.rank = linalg.matrix_rank(self.H)
+    self.numRows = self.H.shape[0]
+    self.n = self.H.shape[1]
+    self.k = self.n -self.numRows
+
+  def read_alist_file(self,filename):
+    """
+    This function reads in an alist file and creates the
+    corresponding parity check matrix H. The format of alist
+    files is described at:
+    http://www.inference.phy.cam.ac.uk/mackay/codes/alist.html
+    """
+
+    myfile    = open(filename,'r')
+    data      = myfile.readlines()
+    size      = string.split(data[0])
+    numCols   = int(size[0])
+    numRows   = int(size[1])
+    H = zeros((numRows,numCols))
+    for lineNumber in arange(4,4+numCols):
+      indices = string.split(data[lineNumber])
+      for index in indices:
+        H[int(index)-1,lineNumber-4] = 1
+    # The subsequent lines in the file list the indices for where
+    # the 1s are in the rows, but this is redundant 
+    # information.
+
+    return H
+
+  def write_alist_file(self,filename,H,verbose=0):
+    """
+    This function writes an alist file for the parity check
+    matrix. The format of alist files is desribed at: 
+    http://www.inference.phy.cam.ac.uk/mackay/codes/alist.html
+    """
+
+    myfile = open(filename,'w')
+
+    numRows = H.shape[0]
+    numCols = H.shape[1]
+
+    tempstring = `numCols` + ' ' + `numRows` + '\n'
+    myfile.write(tempstring)
+
+    tempstring1 = ''
+    tempstring2 = ''
+    maxRowWeight = 0
+    for rowNum in arange(numRows):
+      nonzeros = array(H[rowNum,:].nonzero())
+      rowWeight = nonzeros.shape[1]
+      if rowWeight > maxRowWeight:
+        maxRowWeight = rowWeight
+      tempstring1 = tempstring1 + `rowWeight` + ' '
+      for tempArray in nonzeros:
+        for index in tempArray:
+          tempstring2 = tempstring2 + `index+1` + ' '
+        tempstring2 = tempstring2 + '\n'
+    tempstring1 = tempstring1 + '\n'
+
+    tempstring3 = ''
+    tempstring4 = ''
+    maxColWeight = 0
+    for colNum in arange(numCols):
+      nonzeros = array(H[:,colNum].nonzero())
+      colWeight = nonzeros.shape[1]
+      if colWeight > maxColWeight:
+        maxColWeight = colWeight
+      tempstring3 = tempstring3 + `colWeight` + ' '
+      for tempArray in nonzeros:
+        for index in tempArray:
+          tempstring4 = tempstring4 + `index+1` + ' '
+        tempstring4 = tempstring4 + '\n'
+    tempstring3 = tempstring3 + '\n'
+
+    tempstring = `maxColWeight` + ' ' + `maxRowWeight` + '\n'
+    # write out max column and row weights
+    myfile.write(tempstring)
+    # write out all of the column weights
+    myfile.write(tempstring3) 
+    # write out all of the row weights
+    myfile.write(tempstring1) 
+    # write out the nonzero indices for each column
+    myfile.write(tempstring4) 
+    # write out the nonzero indices for each row
+    myfile.write(tempstring2) 
+    # close the file
+    myfile.close()
+
+  def regular_LDPC_code_contructor(self,n_p_q):
+    """
+    This function constructs a LDPC parity check matrix
+    H. The algorithm follows Gallager's approach where we create 
+    p submatrices and stack them together. Reference: Turbo 
+    Coding for Satellite and Wireless Communications, section
+    9,3.
+
+    Note: the matrices computed from this algorithm will never
+    have full rank. (Reference Gallager's Dissertation.) They 
+    will have rank = (number of rows - p + 1). To convert it
+    to full rank, use the function get_full_rank_H_matrix
+    """
+
+    n = n_p_q[0]  # codeword length
+    p = n_p_q[1]  # column weight
+    q = n_p_q[2]  # row weight
+    # TODO: There should probably be other guidelines for n/p/q,
+    # but I have not found any specifics in the literature....
+
+    # For this algorithm, n/p must be an integer, because the
+    # number of rows in each submatrix must be a whole number.
+    ratioTest = (n*1.0)/q
+    if ratioTest%1 != 0:
+      print '\nError in regular_LDPC_code_contructor: The'
+      print 'ratio of inputs n/q must be a whole number.\n'
+      return
+
+    # First submatrix first: 
+    m = (n*p)/q  # number of rows in H matrix
+    submatrix1 = zeros((m/p,n))  
+    for row in arange(m/p):
+      range1 = row*q
+      range2 = (row+1)*q 
+      submatrix1[row,range1:range2] = 1
+    H = submatrix1
+
+    # Create the other submatrices and vertically stack them on.
+    submatrixNum = 2
+    newColumnOrder = arange(n)
+    while submatrixNum <= p:
+      submatrix = zeros((m/p,n))
+      shuffle(newColumnOrder)
+
+      for columnNum in arange(n):
+        submatrix[:,columnNum] = \
+                      submatrix1[:,newColumnOrder[columnNum]]
+
+      H = vstack((H,submatrix))
+      submatrixNum = submatrixNum + 1 
+
+    # Double check the row weight and column weights.
+    size = H.shape
+    rows = size[0]
+    cols = size[1]
+
+    # Check the row weights.
+    for rowNum in arange(rows):
+      nonzeros = array(H[rowNum,:].nonzero())
+      if nonzeros.shape[1] != q:
+        print 'Row', rowNum, 'has incorrect weight!'
+        return
+
+    # Check the column weights
+    for columnNum in arange(cols):
+      nonzeros = array(H[:,columnNum].nonzero())
+      if nonzeros.shape[1] != p:
+        print 'Row', columnNum, 'has incorrect weight!'
+        return
+
+    return H
+
+def greedy_upper_triangulation(H):
+  """
+  This function performs row/column permutations to bring
+  H into approximate upper triangular form via greedy 
+  upper triangulation method outlined in Modern Coding 
+  Theory Appendix 1, Section A.2
+  """
+  H_t  = H.copy()
+
+  # Per email from Dr. Urbanke, author of this textbook, this
+  # algorithm requires H to be full rank
+  if linalg.matrix_rank(H_t) != H_t.shape[0]:
+      print 'Rank of H:',linalg.matrix_rank(tempArray)
+      print 'H has', H_t.shape[0], 'rows'
+      print 'Error: H must be full rank.'
+      return
+
+  size = H_t.shape
+  n = size[1]
+  k = n - size[0]
+  g = t = 0
+
+  while t != (n-k-g):
+    H_residual = H_t[t:n-k-g,t:n]
+    size       = H_residual.shape
+    numRows    = size[0]
+    numCols    = size[1]
+
+    minResidualDegrees = zeros((1,numCols))
+
+    for colNum in arange(numCols):
+      nonZeroElements = array(H_residual[:,colNum].nonzero())
+      minResidualDegrees[0,colNum] = nonZeroElements.shape[1]
+
+    # Find the minimum nonzero residual degree
+    nonZeroElementIndices = minResidualDegrees.nonzero()
+    nonZeroElements=minResidualDegrees[nonZeroElementIndices[0],\
+                                       nonZeroElementIndices[1]]
+    minimumResidualDegree = nonZeroElements.min()
+
+    # Get indices of all of the columns in H_t that have degree
+    # equal to the min positive residual degree, then pick a
+    # random column c.
+    indices = (minResidualDegrees == minimumResidualDegree)\
+                                     .nonzero()[1]
+    indices = indices + t
+    if indices.shape[0] == 1:
+      columnC = indices[0]
+    else:
+      randomIndex = randint(0,indices.shape[0],(1,1))[0][0]
+      columnC = indices[randomIndex]
+
+    Htemp = H_t.copy()
+
+    if minimumResidualDegree == 1:
+      # This is the 'extend' case
+      rowThatContainsNonZero = H_residual[:,columnC-t]\
+                                         .nonzero()[0][0]
+      
+      # Swap column c with column t. (Book says t+1 but we 
+      # index from 0, not 1.)
+      Htemp[:,columnC] = H_t[:,t]
+      Htemp[:,t] = H_t[:,columnC]
+      H_t = Htemp.copy()
+      Htemp = H_t.copy()
+      # Swap row r with row t. (Book says t+1 but we index from 
+      # 0, not 1.)
+      Htemp[rowThatContainsNonZero + t,:] = H_t[t,:]
+      Htemp[t,:] = H_t[rowThatContainsNonZero + t,:]
+      H_t = Htemp.copy()
+      Htemp = H_t.copy()
+    else:
+      # This is the 'choose' case.
+      rowsThatContainNonZeros = H_residual[:,columnC-t]\
+                                          .nonzero()[0]
+      
+      # Swap column c with column t. (Book says t+1 but we 
+      # index from 0, not 1.)
+      Htemp[:,columnC] = H_t[:,t]
+      Htemp[:,t] = H_t[:,columnC]
+      H_t = Htemp.copy()
+      Htemp = H_t.copy()
+
+      # Swap row r1 with row t
+      r1 = rowsThatContainNonZeros[0]
+      Htemp[r1+t,:] = H_t[t,:]
+      Htemp[t,:] = H_t[r1+t,:]
+      numRowsLeft = rowsThatContainNonZeros.shape[0]-1
+      H_t = Htemp.copy()
+      Htemp = H_t.copy()
+
+      # Move the other rows that contain nonZero entries to the
+      # bottom of the matrix. We can't just swap them, 
+      # otherwise we will be pulling up rows that we pushed 
+      # down before. So, use a rotation method.
+      for index in arange (1,numRowsLeft+1):
+        rowInH_residual = rowsThatContainNonZeros[index]
+        rowInH_t = rowInH_residual + t - index +1
+        m = n-k
+        # Move the row with the nonzero element to the 
+        # bottom; don't update H_t.
+        Htemp[m-1,:] = H_t[rowInH_t,:] 
+        # Now rotate the bottom rows up.
+        sub_index = 1
+        while sub_index < (m - rowInH_t):
+          Htemp[m-sub_index-1,:] = H_t[m-sub_index,:]
+          sub_index = sub_index+1
+        H_t = Htemp.copy()
+        Htemp = H_t.copy()
+
+      # Save temp H as new H_t.
+      H_t = Htemp.copy()
+      Htemp = H_t.copy()
+      g = g + (minimumResidualDegree - 1)
+
+    t = t + 1
+
+  if g == 0:
+    if verbose: print 'Error: gap is 0.'
+    return
+
+  # We need to ensure phi is nonsingular.
+  T = H_t[0:t, 0:t]
+  E = H_t[t:t+g,0:t]
+  A = H_t[0:t,t:t+g]
+  C = H_t[t:t+g,t:t+g]
+  D = H_t[t:t+g,t+g:n] 
+
+  invTmod2array = inv_mod2(T)
+  temp1  = dot(E,invTmod2array) % 2
+  temp2  = dot(temp1,A) % 2
+  phi    = (C - temp2) % 2
+  if phi.any():
+    try:
+      # Try to take the inverse of phi.
+      invPhi = inv_mod2(phi)
+    except linalg.linalg.LinAlgError:
+      # Phi is singular
+      if verbose > 1: print 'Initial phi is singular'
+    else:
+      # Phi is nonsingular, so we need to use this version of H.
+      if verbose > 1: print 'Initial phi is nonsingular'
+      return [H_t, g, t]
+  else:
+    if verbose: print 'Initial phi is all zeros:\n', phi
+
+  # If the C and D submatrices are all zeros, there is no point in
+  # shuffling them around in an attempt to find a good phi.
+  if not (C.any() or D.any()):
+    if verbose: 
+      print 'C and D are all zeros. There is no hope in',
+      print 'finding a nonsingular phi matrix. '
+    return
+
+  # We can't look at every row/column permutation possibility
+  # because there would be (n-t)! column shuffles and g! row
+  # shuffles. g has gotten up to 12 in tests, so 12! would still
+  # take quite some time. Instead, we will just pick an arbitrary 
+  # number of max iterations to perform, then break.
+  maxIterations = 300
+  iterationCount = 0
+  columnsToShuffle = arange(t,n) 
+  rowsToShuffle = arange(t,t+g)
+
+  while iterationCount < maxIterations:
+    if verbose > 1: print 'iterationCount:', iterationCount
+    tempH = H_t.copy()
+
+    shuffle(columnsToShuffle)
+    shuffle(rowsToShuffle)
+    index = 0
+    for newDestinationColumnNumber in arange(t,n):
+      oldColumnNumber = columnsToShuffle[index]
+      tempH[:,newDestinationColumnNumber] = \
+                                         H_t[:,oldColumnNumber]
+      index +=1
+
+    tempH2 = tempH.copy()
+    index = 0
+    for newDesinationRowNumber in arange(t,t+g):
+      oldRowNumber = rowsToShuffle[index]
+      tempH[newDesinationRowNumber,:] = tempH2[oldRowNumber,:]
+      index +=1
+    
+    # Now test this new H matrix.
+    H_t = tempH.copy()
+    T = H_t[0:t, 0:t]
+    E = H_t[t:t+g,0:t]
+    A = H_t[0:t,t:t+g]
+    C = H_t[t:t+g,t:t+g]
+    invTmod2array = inv_mod2(T)
+    temp1  = dot(E,invTmod2array) % 2
+    temp2  = dot(temp1,A) % 2
+    phi    = (C - temp2) % 2
+    if phi.any():
+      try:
+        # Try to take the inverse of phi.
+        invPhi = inv_mod2(phi)
+      except linalg.linalg.LinAlgError:
+        # Phi is singular
+        if verbose > 1: print 'Phi is still singular'
+      else:
+        # Phi is nonsingular, so we're done.
+        if verbose: 
+          print 'Found a nonsingular phi on',
+          print 'iterationCount = ', iterationCount
+        return [H_t, g, t]
+    else:
+      if verbose > 1: print 'phi is all zeros'
+
+    iterationCount +=1
+
+  # If we've reached this point, then we haven't found a
+  # version of H that has a nonsingular phi.
+  if verbose: print '--- Error: nonsingular phi matrix not found.'
+
+
+def inv_mod2(squareMatrix):
+  """
+  Calculates the mod 2 inverse of a matrix.
+  """
+  A = squareMatrix.copy()
+  t = A.shape[0]
+
+  # Special case for one element array [1]
+  if A.size == 1 and A[0] == 1:
+    return array([1])
+
+  Ainverse = inv(A)
+  B = det(A)*Ainverse
+  C = B % 2
+
+  # Encountered lots of rounding errors with this function.
+  # Previously tried floor, C.astype(int), and casting with (int)
+  # and none of that works correctly, so doing it the tedious way.
+
+  test = dot(A,C) % 2
+  tempTest = zeros_like(test)
+  for colNum in arange(test.shape[1]):
+    for rowNum in arange(test.shape[0]):
+      value = test[rowNum,colNum]
+      if (abs(1-value)) < 0.01:
+        # this is a 1
+        tempTest[rowNum,colNum] = 1
+      elif (abs(2-value)) < 0.01:
+        # there shouldn't be any 2s after B % 2, but I'm 
+        # seeing them!
+        tempTest[rowNum,colNum] = 0
+      elif (abs(0-value)) < 0.01:
+        # this is a 0
+        tempTest[rowNum,colNum] = 0
+      else: 
+        if verbose > 1: 
+          print 'In inv_mod2. Rounding error on this',
+          print 'value? Mod 2 has already been done.',
+          print 'value:', value
+
+  test = tempTest.copy()
+
+  if (test - eye(t,t) % 2).any():
+    if verbose:
+      print 'Error in inv_mod2: did not find inverse.'
+    # TODO is this the most appropriate error to raise?
+    raise linalg.linalg.LinAlgError
+  else:
+    return C
+
+def swap_columns(a,b,arrayIn):
+  """
+  Swaps two columns in a matrix.
+  """
+  arrayOut = arrayIn.copy()
+  arrayOut[:,a] = arrayIn[:,b]
+  arrayOut[:,b] = arrayIn[:,a]
+  return arrayOut
+
+def move_row_to_bottom(i,arrayIn):
+  """"
+  Moves a specified row (just one) to the bottom of the matrix,
+  then rotates the rows at the bottom up.
+  
+  For example, if we had a matrix with 5 rows, and we wanted to
+  push row 2 to the bottom, then the resulting row order would be: 
+  1,3,4,5,2
+  """
+  arrayOut = arrayIn.copy()
+  numRows = arrayOut.shape[0]
+  # Push the specified row to the bottom.
+  arrayOut[numRows-1] = arrayIn[i,:]
+  # Now rotate the bottom rows up.
+  index = 2
+  while (numRows-index) >= i:
+    arrayOut[numRows-index,:] = arrayIn[numRows-index+1]
+    index = index + 1
+  return arrayOut
+
+def get_full_rank_H_matrix(H):
+  """
+  This function accepts a parity check matrix H and, if it is not
+  already full rank, will determine which rows are dependent and 
+  remove them. The updated matrix will be returned.
+  """
+  tempArray = H.copy()
+  if linalg.matrix_rank(tempArray) == tempArray.shape[0]:
+    if verbose > 1: print 'Returning H; it is already full rank.'
+    return tempArray
+  
+  numRows = tempArray.shape[0]
+  numColumns = tempArray.shape[1] 
+  limit = numRows
+  rank = 0
+  i = 0
+
+  # Create an array to save the column permutations.
+  columnOrder = arange(numColumns).reshape(1,numColumns)
+
+  # Create an array to save the row permutations. We just need
+  # this to know which dependent rows to delete.
+  rowOrder = arange(numRows).reshape(numRows,1)
+
+  while i < limit: 
+    if verbose > 1: print 'In get_full_rank_H_matrix; i:', i
+    # Flag indicating that the row contains a non-zero entry
+    found  = False
+    for j in arange(i, numColumns):
+      if tempArray[i, j] == 1: 
+        # Encountered a non-zero entry at (i, j)
+        found =  True 
+        # Increment rank by 1
+        rank = rank + 1    
+        # Make the entry at (i,i) be 1   
+        tempArray = swap_columns(j,i,tempArray)  
+        # Keep track of the column swapping
+        columnOrder = swap_columns(j,i,columnOrder)
+        break
+    if found == True:
+      for k in arange(0,numRows): 
+        if k == i: continue
+        # Checking for 1's 
+        if tempArray[k, i] == 1:
+          # Add row i to row k
+          tempArray[k,:] = tempArray[k,:] + tempArray[i,:]
+          # Addition is mod2
+          tempArray = tempArray.copy() % 2 
+          # All the entries above & below (i, i) are now 0 
+      i = i + 1
+    if found == False:
+      # Push the row of 0s to the bottom, and move the bottom
+      # rows up (sort of a rotation thing).
+      tempArray = move_row_to_bottom(i,tempArray)
+      # Decrease limit since we just found a row of 0s
+      limit -= 1 
+      # Keep track of row swapping
+      rowOrder = move_row_to_bottom(i,rowOrder)
+
+  # Don't need the dependent rows
+  finalRowOrder = rowOrder[0:i]
+
+  # Reorder H, per the permutations taken above .
+  # First, put rows in order, omitting the dependent rows.
+  newNumberOfRowsForH = finalRowOrder.shape[0]
+  newH = zeros((newNumberOfRowsForH, numColumns))
+  for index in arange(newNumberOfRowsForH):
+    newH[index,:] = H[finalRowOrder[index],:]
+
+  # Next, put the columns in order.
+  tempHarray = newH.copy()
+  for index in arange(numColumns):
+    newH[:,index] = tempHarray[:,columnOrder[0,index]]
+
+  if verbose:
+    print 'original H.shape:', H.shape
+    print 'newH.shape:', newH.shape
+
+  return newH
+
+def get_best_matrix(H,numIterations=100):
+  """
+  This function will run the Greedy Upper Triangulation algorithm
+  for numIterations times, looking for the lowest possible gap. 
+  The submatrices returned are those needed for real-time encoding.
+  """
+
+  hadFirstJoy = 0
+  index = 1
+  while index <= numIterations:
+    if verbose: 
+      print '--- In get_best_matrix, index:', index
+    try:
+      [betterH, gap, t]  = greedy_upper_triangulation(H)
+    except:
+      if verbose > 1: 
+        print 'greedy_upper_triangulation must have had error'
+    else:
+      if not hadFirstJoy: 
+        hadFirstJoy = 1 
+        bestGap = gap
+        bestH = betterH.copy()
+        bestT = t
+      elif gap < bestGap:
+        bestGap = gap
+        bestH = betterH.copy()
+        bestT = t
+
+    index += 1
+
+  if hadFirstJoy:
+    return [bestH,bestGap]
+  else:
+    if verbose: 
+      print 'Error: Could not find appropriate H form',
+      print 'for encoding.'
+    return