Iterative Receiver Design

8.5: Low-Density Parity-Check Codes

8.5 Low-Density Parity-Check Codes

8.5.1 Description

Low-density parity-check (LDPC) codes are a class of codes whose parity-check matrices are sparse in the sense that they contain very few ones per column. They are generally created starting from a sparse parity-check matrix H, from which we then derive a systematic generator matrix G [46, 87]. In this section we will cover how LDPC codes are created, what their factor graphs look like, and how they are decoded using the SPA. As with RA codes, we will work with a running example. We start from a parity-check matrix H given by


Algorithm 8.1: Decoding RA codes: forward backward phase
1: take care of special cases:   <span class="inlinemediaobject"><a NAME="IMG_1164"> href="portalcontent.asp?bkid=23174&image_src=https://images.books24x7.com/bookimages/id_23174/fig175%5F01%5F0%2Ejpg&image_id=1164&previd=IMG_1164"> target="_parent"><img alt="Image from book"> border="0"> height="18"> id="IMG_1164"> src="https://images.books24x7.com/bookimages/id_23174/fig175_01.jpg"> title="Click To expand"> width="166"></a></span>   <span class="inlinemediaobject"><a NAME="IMG_1165"> href="portalcontent.asp?bkid=23174&image_src=https://images.books24x7.com/bookimages/id_23174/fig175%5F02%5F0%2Ejpg&image_id=1165&previd=IMG_1165"> target="_parent"><img alt="Image from book"> border="0"> height="21"> id="IMG_1165"> src="https://images.books24x7.com/bookimages/id_23174/fig175_02.jpg"> title="Click To expand"> width="183"></a></span>   <span class="inlinemediaobject"><img alt="Image from book"> border="0"> height="18"> id="IMG_1166"> src="https://images.books24x7.com/bookimages/id_23174/fig175_03.jpg"> title=""> width="116"></span>   <span class="inlinemediaobject"><a NAME="IMG_1167"> href="portalcontent.asp?bkid=23174&image_src=https://images.books24x7.com/bookimages/id_23174/fig175%5F04%5F0%2Ejpg&image_id=1167&previd=IMG_1167"> target="_parent"><img alt="Image from book"> border="0"> height="22"> id="IMG_1167"> src="https://images.books24x7.com/bookimages/id_23174/fig175_04.jpg"> title="Click To expand"> width="212"></a></span>2: <b class="bold">for</b> <i class="emphasis">k</i> = 2 to <i class="emphasis">N</i><sub<i class="emphasis">c</i></sub> <span class="unicode">?</span> 1 <b class="bold">do</b>3:   compute forward messages:     <span class="inlinemediaobject"><a NAME="IMG_1168"> href="portalcontent.asp?bkid=23174&image_src=https://images.books24x7.com/bookimages/id_23174/fig175%5F05%5F0%2Ejpg&image_id=1168&previd=IMG_1168"> target="_parent"><img alt="Image from book"> border="0"> height="18"> id="IMG_1168"> src="https://images.books24x7.com/bookimages/id_23174/fig175_05.jpg"> title="Click To expand"> width="165"></a></span>     <span class="inlinemediaobject"><a NAME="IMG_1169"> href="portalcontent.asp?bkid=23174&image_src=https://images.books24x7.com/bookimages/id_23174/fig175%5F06%5F0%2Ejpg&image_id=1169&previd=IMG_1169"> target="_parent"><img alt="Image...

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