Flexible LDPC Decoder Architectures

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td align="left">Code rate</td><td align="center"></td><td align="center"><span style="width: 23.450001px;"><svg height="14.85" id="M135" style="vertical-align:-2.22495pt" version="1.1" viewbox="0 0 23.450001 14.85" width="23.450001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,8.222,12.012)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.017,-0,0,-.017,15.225,12.012)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg></span></td><td align="center"><span style="width: 23.450001px;"><svg height="14.85" id="M136" style="vertical-align:-2.22495pt" version="1.1" viewbox="0 0 23.450001 14.85" width="23.450001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,8.222,12.012)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,15.225,12.012)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg></span></td><td align="center"><span style="width: 23.450001px;"><svg height="14.85" id="M137" style="vertical-align:-2.22495pt" version="1.1" viewbox="0 0 23.450001 14.85" width="23.450001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><use xlink:href="#x33"></use></g><g transform="matrix(.017,-0,0,-.017,8.222,12.012)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,15.225,12.012)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg></span></td><td align="center"><span style="width: 23.450001px;"><svg height="14.85" id="M138" style="vertical-align:-2.22495pt" version="1.1" viewbox="0 0 23.450001 14.85" width="23.450001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
l-26 -65h-233z" id="x35"></path></g><g transform="matrix(.017,-0,0,-.017,8.222,12.012)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,15.225,12.012)"><path d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5
t96 -62.5q53 0 78 45.5t25 105.5q0 68 -35 116t-99 48z" id="x36"></path></g>
</svg></span></td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td align="left" colspan="2"><svg height="15.875" id="M139" style="vertical-align:-3.41931pt" version="1.1" viewbox="0 0 41.125 15.875" width="41.125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M759 25v-25h-339v25q54 6 71.5 20.5t17.5 52.5v228h-241v-228q0 -40 17 -54q16 -13 72 -19v-25h-336v25q54 8 69 20q16 13 16 53v479q0 41 -16.5 55t-68.5 19v25h336v-25q-54 -4 -71.5 -18.5t-17.5 -55.5v-204h241v204q0 41 -17.5 55.5t-71.5 18.5v25h339v-25
q-51 -4 -69.5 -19t-18.5 -55v-479q0 -40 16 -53q15 -12 72 -20z" id="x1D407"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.288,15.637)"><path d="M372 352v-2q176 -27 176 -159q0 -99 -95 -151q-73 -40 -196 -40h-221v28q65 5 78.5 19t13.5 76v404q0 63 -12 77t-72 18v28h257q102 0 150 -34q26 -18 41 -48.5t15 -65.5q0 -111 -135 -150zM213 362h47q80 0 117.5 32t37.5 96q0 56 -33 92t-100 36q-41 0 -56 -10
q-13 -8 -13 -50v-196zM213 328v-203q0 -54 17 -72.5t66 -18.5q67 1 110.5 37t43.5 110q0 147 -192 147h-45z" id="x42"></path></g><g transform="matrix(.012,-0,0,-.012,19.998,15.637)"><path d="M673 0h-245v28q47 6 58 16t1 39l-55 154h-213q-31 -87 -36 -129q-16 -47 -5 -61t68 -19v-28h-226v28q50 7 68.5 23.5t43.5 80.5l214 524l24 9l193 -536q23 -63 41.5 -79.5t68.5 -21.5v-28zM418 280l-81 255h-2q-74 -197 -101 -255h184z" id="x41"></path></g><g transform="matrix(.012,-0,0,-.012,28.185,15.637)"><path d="M409 504l-29 -5q-16 60 -44.5 96t-86.5 36q-54 0 -82.5 -32t-28.5 -77q0 -51 30.5 -82.5t96.5 -65.5l35.5 -18t33 -19.5t33.5 -23.5l27 -25.5t24.5 -32t13.5 -36.5t6 -45q0 -80 -62 -134.5t-160 -54.5q-47 0 -98 15q-22 7 -50 21q-8 23 -27 155l30 7q7 -27 18 -52
t30 -51.5t49 -42.5t67 -16q56 0 88 32.5t32 87.5q0 51 -31.5 82t-98.5 67q-80 44 -110 73q-55 53 -55 124q0 75 56 126.5t150 51.5q53 0 126 -23z" id="x53"></path></g><g transform="matrix(.012,-0,0,-.012,33.682,15.637)"><path d="M517 162l29 -4q-18 -100 -35 -158h-482v28q68 5 83.5 20t15.5 77v398q0 66 -13 80t-73 19v28h446q0 -8 8 -144l-29 -4q-11 51 -32 85q-11 17 -35 23t-78 6h-76q-23 0 -28 -5t-5 -27v-228h94q67 0 83 12t25 63h29v-191h-29q-10 54 -26 65.5t-81 11.5h-95v-189
q0 -65 24 -81q19 -13 104 -13q57 0 83 7t43 27q28 33 50 94z" id="x45"></path></g>
</svg> matrix (WiMax/WiFi)</td><td align="center"><span style="width: 50.299999px;"><svg height="10.9125" id="M140" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 50.299999 10.9125" width="50.299999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,8.222,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,20.155,10.862)"><path d="M528 54l-36 -38l-198 201l-198 -201l-36 38l197 200l-197 201l36 38l198 -202l198 202l36 -38l-197 -201z" id="xD7"></path></g><g transform="matrix(.017,-0,0,-.017,33.907,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,42.066,10.862)"><use xlink:href="#x34"></use></g>
</svg></span></td><td align="center"><span style="width: 42.137501px;"><svg height="11.125" id="M141" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 42.137501 11.125" width="42.137501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M249 635q70 0 116 -43t46 -105q0 -46 -28 -80q-22 -25 -80 -64q62 -35 97 -75t35 -99q0 -81 -63 -131t-135 -50q-83 0 -137.5 45.5t-54.5 123.5q0 52 45 95q29 28 89 64q-109 62 -109 155q0 66 50.5 115t128.5 49zM238 603q-42 0 -67.5 -31t-25.5 -72q0 -50 32.5 -79.5
t98.5 -62.5q61 48 61 124q0 59 -29.5 90t-69.5 31zM248 20q46 0 76.5 33.5t30.5 89.5q0 50 -39 85.5t-110 71.5q-81 -54 -81 -137q0 -67 35.5 -105t87.5 -38z" id="x38"></path></g><g transform="matrix(.017,-0,0,-.017,11.996,10.862)"><use xlink:href="#xD7"></use></g><g transform="matrix(.017,-0,0,-.017,25.748,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,33.907,10.862)"><use xlink:href="#x34"></use></g>
</svg></span></td><td align="center"><span style="width: 42.137501px;"><svg height="11.225" id="M142" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 42.137501 11.225" width="42.137501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.963)"><use xlink:href="#x36"></use></g><g transform="matrix(.017,-0,0,-.017,11.996,10.963)"><use xlink:href="#xD7"></use></g><g transform="matrix(.017,-0,0,-.017,25.748,10.963)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,33.907,10.963)"><use xlink:href="#x34"></use></g>
</svg></span></td><td align="center"><span style="width: 42.137501px;"><svg height="10.9125" id="M143" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 42.137501 10.9125" width="42.137501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><use xlink:href="#x34"></use></g><g transform="matrix(.017,-0,0,-.017,11.996,10.862)"><use xlink:href="#xD7"></use></g><g transform="matrix(.017,-0,0,-.017,25.748,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,33.907,10.862)"><use xlink:href="#x34"></use></g>
</svg></span></td></tr><tr><td align="left"><svg height="15.4" id="M144" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 23.6875 15.4" width="23.6875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28
q45 4 67 18.5t35 45.5q16 38 74 233l52 173q24 79 11.5 98t-89.5 26l6 28h177l136 -508l337 508h172z" id="x1D440"></path></g>
<g transform="matrix(.012,-0,0,-.012,17.412,15.187)"><path d="M452 333q0 -82 -46 -164t-116 -128q-81 -53 -158 -53q-26 0 -51 13t-37 32q-26 41 -6 134l91 431q7 40 2.5 47t-34.5 7h-33l2 25q36 4 72.5 13t58.5 15.5t28 6.5q10 0 4 -29l-91 -391h2q65 77 130 116.5t105 39.5q36 0 56.5 -32t20.5 -83zM365 316q0 76 -35 76
q-31 0 -93.5 -49t-107.5 -110q-12 -37 -17 -70q-9 -65 12 -96.5t59 -31.5q31 0 56 14q53 29 89.5 105t36.5 162z" id="x1D44F"></path></g>
</svg> (WiMax/WiFi)</td><td align="center"></td><td align="center">
												12
											</td><td align="center">
												8
											</td><td align="center">
												6
											</td><td align="center">
												4
											</td></tr><tr><td align="left" rowspan="2"><svg height="15.4" id="M145" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 23.0375 15.4" width="23.0375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M1004 650l-6 -29q-54 -6 -71 -19.5t-51 -74.5l-271 -539h-33l-98 506h-3l-258 -506h-30l-78 532q-10 67 -21.5 80t-66.5 21l6 29h241l-8 -29l-26 -5q-34 -6 -41 -16t-3 -47l59 -425h4l251 510h31l102 -510h2q150 299 198 423q14 40 8.5 48.5t-47.5 16.5l-28 5l7 29h231z
" id="x1D44A"></path></g>
<g transform="matrix(.012,-0,0,-.012,17.338,15.187)"><path d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26
q13 -21 0 -43z" id="x1D45F"></path></g>
</svg>− <svg height="15.4" id="M146" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 26.8125 15.4" width="26.8125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D44A"></use></g>
<g transform="matrix(.012,-0,0,-.012,17.338,15.187)"><path d="M383 397q0 -32 -35 -49q-12 -6 -23 8q-37 45 -84 45t-90 -71q-40 -65 -40 -167q0 -57 22 -86t59 -29q38 0 81.5 24.5t69.5 51.5l16 -21q-44 -53 -104 -84t-109 -31q-56 0 -89.5 41t-33.5 117q0 61 30 124t79 105q33 28 81 50.5t86 22.5q34 0 59 -15.5t25 -35.5z" id="x1D450"></path></g>
</svg></td><td align="center">WiMax</td><td align="center"><span style="width: 45.3125px;"><svg height="11.225" id="M147" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 45.3125 11.225" width="45.3125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,10.963)"><path d="M447 623l8 -12l-283 -613l-74 -10l-7 11q174 283 297 551h-216q-48 0 -62.5 -12t-33.5 -63h-29q10 60 18 148h382z" id="x37"></path></g><g transform="matrix(.017,-0,0,-.017,17.658,10.963)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,-0,0,-.017,31.41,10.963)"><use xlink:href="#x36"></use></g>
</svg></span></td><td align="center"><span style="width: 53.462502px;"><svg height="11.225" id="M148" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 53.462502 11.225" width="53.462502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,10.963)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,13.884,10.963)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,25.818,10.963)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,39.57,10.963)"><use xlink:href="#x36"></use></g>
</svg></span></td><td align="center"><span style="width: 53.462502px;"><svg height="11.225" id="M149" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 53.462502 11.225" width="53.462502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,10.963)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,13.884,10.963)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,25.818,10.963)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,39.57,10.963)"><use xlink:href="#x36"></use></g>
</svg></span></td><td align="center"><span style="width: 47.799999px;"><svg height="11.125" id="M150" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 47.799999 11.125" width="47.799999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,13.884,10.862)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,25.818,10.862)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,39.57,10.862)"><use xlink:href="#x34"></use></g>
</svg></span></td></tr><tr><td align="center"> WiFi</td><td align="center"><span style="width: 53.462502px;"><svg height="11.125" id="M151" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 53.462502 11.125" width="53.462502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,10.862)"><use xlink:href="#x38"></use></g><g transform="matrix(.017,-0,0,-.017,17.658,10.862)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,31.41,10.862)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,39.57,10.862)"><use xlink:href="#x32"></use></g>
</svg></span></td><td align="center"><span style="width: 53.462502px;"><svg height="11.125" id="M152" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 53.462502 11.125" width="53.462502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,10.862)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,13.884,10.862)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,25.818,10.862)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,39.57,10.862)"><use xlink:href="#x38"></use></g>
</svg></span></td><td align="center"><span style="width: 53.462502px;"><svg height="11.225" id="M153" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 53.462502 11.225" width="53.462502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,10.963)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,13.884,10.963)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,25.818,10.963)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,39.57,10.963)"><use xlink:href="#x36"></use></g>
</svg></span></td><td align="center"><span style="width: 47.799999px;"><svg height="10.9125" id="M154" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 47.799999 10.9125" width="47.799999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,13.884,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,25.818,10.862)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,39.57,10.862)"><use xlink:href="#x34"></use></g>
</svg></span></td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<b>H </b><sub>
                BASE</sub> parameters for WiMaX and WiFi LDPC codes.

VLSI Design

Flexible LDPC Decoder Architectures

Table 3