Convergence Analysis and Design of Multiple Concatenated Codes
Convergence Analysis and Design of Multiple Concatenated Codes
Convergence Analysis and Design of Multiple Concatenated Codes
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<strong>Convergence</strong> <strong>Analysis</strong> <strong>and</strong> <strong>Design</strong> <strong>of</strong> <strong>Multiple</strong> <strong>Concatenated</strong> <strong>Codes</strong><br />
x ✲ π 0<br />
✲ π 1<br />
✲ π 2<br />
✲ π 3<br />
x 0 y 0 ✲<br />
z<br />
U 0 ✲ 0<br />
x 1 y<br />
✲ 1<br />
C<br />
✲ 1 U 1<br />
x 2 y<br />
✲ 2<br />
C<br />
✲ 2 U 2<br />
x 3 y<br />
✲ 3<br />
C<br />
✲ 3 U 3<br />
❅<br />
z 1 ✲<br />
z 2 ✲<br />
z 3<br />
✲<br />
<br />
❅<br />
❅<br />
❅<br />
M<br />
<br />
<br />
<br />
w<br />
<br />
<br />
<br />
<br />
s✲<br />
✓✏ ❄<br />
r ✲<br />
✒✑ M −1<br />
❅<br />
❅<br />
❅<br />
❅<br />
E(z 0 ) U<br />
−1<br />
✲<br />
0<br />
E(z 1 )<br />
✲ U<br />
−1<br />
1<br />
E(z 2 )<br />
✲ U<br />
−1<br />
2<br />
E(z 3 )<br />
✲ U<br />
−1<br />
3<br />
A(y 0 )<br />
A(y 1 )<br />
✲<br />
A(y 2 )<br />
✲<br />
A(y 3 )<br />
✲<br />
• <strong>Convergence</strong> analysis using projected EXIT charts, [1].<br />
• Optimal puncturing ratios for all 1/4 ≤ R ≤ 1, [2].<br />
C −1<br />
1<br />
C −1<br />
2<br />
C −1<br />
3<br />
E(x 0 ) π<br />
−1<br />
✲<br />
0<br />
E 0 (x)<br />
✲<br />
E(x 1 )<br />
✲ π<br />
−1<br />
E 1 (x)<br />
✲<br />
A(x<br />
1<br />
✛<br />
1) A π1 ✛<br />
1(x)<br />
E(x 2 )<br />
✲ π<br />
−1<br />
E 2 (x)<br />
✲<br />
A(x<br />
2<br />
✛<br />
2) A π2 ✛<br />
2(x)<br />
E(x 3 )<br />
✲ π<br />
−1<br />
E 3 (x)<br />
✲<br />
A(x<br />
3<br />
✛<br />
3) A π3 ✛<br />
3(x)<br />
• Optimal puncturing <strong>and</strong> energy distribution for all 1/4 ≤ R ≤ 1, [3].<br />
[1] F. Brännström, L. K. Rasmussen, <strong>and</strong> A. J. Grant, “<strong>Convergence</strong> analysis <strong>and</strong> optimal scheduling for multiple concatenated codes,”<br />
to appear in IEEE Trans. Inform. Theory, 2005.<br />
[2] F. Brännström, L. K. Rasmussen, <strong>and</strong> A. Grant, “Optimal puncturing for multiple parallel concatenated codes,” in Proc. IEEE<br />
Int. Symp. Inform. Theory (ISIT’04), Chicago, IL, June/July 2004, p. 154.<br />
[3] F. Brännström, <strong>and</strong> L. K. Rasmussen, “<strong>Multiple</strong> parallel concatenated codes with optimal puncturing <strong>and</strong> energy distribution,” to<br />
appear at IEEE Int. Conf. Commun. (ICC’05), Seoul, Korea, May 2005.<br />
<strong>Convergence</strong> <strong>Analysis</strong> <strong>and</strong> <strong>Design</strong> <strong>of</strong> <strong>Multiple</strong> <strong>Concatenated</strong> <strong>Codes</strong>, Fredrik Brännström 2005 7
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