Two-Dimensional Iterative Processing for DAB Receivers Based on Trellis-Decomposition

<table>Trellis representation of the states <svg height="11.2125" id="M90" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 84.387497 11.2125" width="84.387497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.2125)">
<g transform="translate(72,-63.03)">
<text transform="matrix(1,0,0,-1,-71.95,66.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑧</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.71,63.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.84,66.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">𝑧</tspan>
</text>
<text transform="matrix(1,0,0,-1,-49.39,63.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-44.51,66.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">…</tspan>
<tspan style="font-size: 12.50px; " x="19.79225" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="24.993498" y="0">𝑧</tspan>
</text>
<text transform="matrix(1,0,0,-1,-13.27,63.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑁</tspan>
</text>
</g>
</g>
</svg> and the differentially encoded symbols <svg height="10.925" id="M91" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 84.537498 10.925" width="84.537498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑎</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.67,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.8,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">𝑎</tspan>
</text>
<text transform="matrix(1,0,0,-1,-49.31,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-44.44,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">…</tspan>
<tspan style="font-size: 12.50px; " x="19.79225" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="25.006001" y="0">𝑎</tspan>
</text>
<text transform="matrix(1,0,0,-1,-13.16,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑁</tspan>
</text>
</g>
</g>
</svg> in the incoherent case. An edge between two subsequent states indicates that a transition between these states is possible. Note that the trellis can be decomposed into eight unconnected subtrellises.</table>

Journal of Electrical and Computer Engineering

fig4

Figure 4

Figure 4: Two-Dimensional Iterative Processing for DAB Receivers Based on Trellis-Decomposition 