Generalized stability condition for generalized and doubly-generalized LDPC codes

被引：3
|
作者：
Paolini, Enrico [1 ]
Fossorier, Marc [2 ]
Chiani, Marco [1 ,3 ]
机构：
[1] Univ Bologna, DEIS, Cesena, FC, Italy
[2] Univ Hawaii, EE Dept, Honolulu, HI 96822 USA
[3] Univ Bologna, DEIS, Cesena, Italy
来源：
2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7 | 2007年
关键词：
D O I：
10.1109/ISIT.2007.4557440
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
In this paper, the stability condition for low-density parity-check (LDPC) codes on the binary erasure channel (BEC) is extended to generalized LDPC (GLDPC) codes and doubly-generalized LDPC (D-GLDPC) codes. It is proved that, in both cases, the stability condition only involves the component codes with minimum distance 2. The stability condition for GLDPC codes is always expressed as an upper bound to the decoding threshold. This is not possible for D-GLDPC codes, unless all the generalized variable nodes have minimum distance at least 3. Furthermore, a condition called derivative matching is defined in the paper. This condition is sufficient for a GLDPC or D-GLDPC code to achieve the stability condition with equality. If this condition is satisfied, the threshold of D-GLDPC codes (whose generalized variable nodes have all minimum distance at least 3) and GLDPC codes can be expressed in closed form.
引用
收藏
页码：1536 / +
页数：2
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