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
相关论文
共 50 条
  • [21] On the minimum distance of generalized LDPC codes
    Otmani, Ayoub
    Tillich, Jean-Pierre
    Andriyanova, Iryna
    2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7, 2007, : 751 - +
  • [22] Ensemble Weight Enumerators for Protograph-Based Doubly Generalized LDPC Codes
    Wang, Yige
    Wang, Chung-Li
    Fossorier, Marc
    2008 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-6, 2008, : 1168 - +
  • [23] From Product Codes to Structured Generalized LDPC Codes
    Lentmaier, Michael
    Liva, Gianluigi
    Paolini, Enrico
    Fettweis, Gerhard
    2010 5TH INTERNATIONAL ICST CONFERENCE ON COMMUNICATIONS AND NETWORKING IN CHINA (CHINACOM), 2010,
  • [24] Generalized LDPC Codes with Convolutional Code Constraints
    Farooq, Muhammad Umar
    Moloudi, Saeedeh
    Lentmaier, Michael
    2020 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2020, : 479 - 484
  • [25] Generalized quad, hex, and octagon LDPC codes
    Liu, ZY
    Pados, DA
    GLOBECOM '05: IEEE Global Telecommunications Conference, Vols 1-6: DISCOVERY PAST AND FUTURE, 2005, : 1137 - 1141
  • [26] GENERALIZED SERIAL SCHEDULES FOR ITERATIVE DECODING OF LDPC CODES
    Presman, Noam
    Sharon, Eran
    Litsyn, Simon
    2008 IEEE 25TH CONVENTION OF ELECTRICAL AND ELECTRONICS ENGINEERS IN ISRAEL, VOLS 1 AND 2, 2008, : 105 - 109
  • [27] Spatially Coupled Generalized LDPC Codes: Introduction and Overview
    Costello, Daniel J., Jr.
    Mitchell, David G. M.
    Olmos, Pablo M.
    Lentmaier, Michael
    PROCEEDINGS OF 2018 IEEE 10TH INTERNATIONAL SYMPOSIUM ON TURBO CODES & ITERATIVE INFORMATION PROCESSING (ISTC), 2018,
  • [28] On the Thresholds of Generalized LDPC Convolutional Codes Based on Protographs
    Lentmaier, Michael
    Fettweis, Gerhard P.
    2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 2010, : 709 - 713
  • [29] Enumerators for Protograph-Based Ensembles of LDPC and Generalized LDPC Codes
    Abu-Surra, Shadi
    Divsalar, Dariush
    Ryan, William E.
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (02) : 858 - 886
  • [30] Irregular Generalized LDPC codes in Practical Communication Scenarios
    Bocharova, Irina E.
    Kudryashov, Boris D.
    Mikelsaar, Sander
    2022 IEEE INFORMATION THEORY WORKSHOP (ITW), 2022, : 517 - 522
12345