title: How to determine LDPC generator matrix form parity check matrix (802.16e)
body: <p>I have parity check table <code>H</code> for 802.16e standard with <code>1/2</code> rate and expansion factor <code>96</code>:</p>
  <pre><code>Hb = 
  -1 94 73 -1 -1 -1 -1 -1 55 83 -1 -1 7 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
  -1 27 -1 -1 -1 22 79 9 -1 -1 -1 12 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1
  -1 -1 -1 24 22 81 -1 33 -1 -1 -1 0 -1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1
  61 -1 47 -1 -1 -1 -1 -1 65 25 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 -1 -1 -1
  -1 -1 39 -1 -1 -1 84 -1 -1 41 72 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 -1 -1
  -1 -1 -1 -1 46 40 -1 82 -1 -1 -1 79 0 -1 -1 -1 -1 0 0 -1 -1 -1 -1 -1
  -1 -1 95 53 -1 -1 -1 -1 -1 14 18 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1
  -1 11 73 -1 -1 -1 2 -1 -1 47 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1
  12 -1 -1 -1 83 24 -1 43 -1 -1 -1 51 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1
  -1 -1 -1 -1 -1 94 -1 59 -1 -1 70 72 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1
  -1 -1 7 65 -1 -1 -1 -1 39 49 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0
  43 -1 -1 -1 -1 66 -1 41 -1 -1 -1 26 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0
  </code></pre>
  <p>Then I get <code>H</code> in binary form with sizes <code>1152x2304</code>: <a href="https://i.stack.imgur.com/nq8pr.png" rel="nofollow noreferrer">spy(H) img</a></p>
  <p>I want to get a matrix generator <code>G</code> from <code>H</code>, how can I do it? I need to encode words by multiplying words by a generator matrix (<code>cw = m*G</code>, where <code>m</code> - input word, <code>cw</code> - code word).</p>
  <p>I try different ways, but at the end i cant reach <code>nnz(mod(G*H', 2))</code> equal <code>0</code>.</p>