On the Growth Rate of the Weight Distribution of Irregular Doubly-Generalized LDPC Codes

In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC) codes is derived. The expression is compact and generalizes existing results for LDPC and generalized LDPC (GLDPC) codes. Assuming that there exist check and variable nodes with minimum distance 2, it is shown that the growth rate depends only on these nodes. An important connection between this new result and the stability condition of D-GLDPC codes over the BEC is highlighted. Such a connection, previously observed for LDPC and GLDPC codes, is now extended to the case of D-GLDPC codes.Comment: 10 pages, 1 figure, presented at the 46th Annual Allerton Conference on Communication, Control and Computing (this version includes additional appendix

Spectral Shape of Check-Hybrid GLDPC Codes

This paper analyzes the asymptotic exponent of both the weight spectrum and the stopping set size spectrum for a class of generalized low-density parity-check (GLDPC) codes. Specifically, all variable nodes (VNs) are assumed to have the same degree (regular VN set), while the check node (CN) set is assumed to be composed of a mixture of different linear block codes (hybrid CN set). A simple expression for the exponent (which is also referred to as the growth rate or the spectral shape) is developed. This expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. Furthermore, it is shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function.Comment: 6 pages, 3 figures. Presented at the IEEE ICC 2010, Cape Town, South Africa. A minor typo in equation (9) has been correcte

Growth Rate of the Weight Distribution of Doubly-Generalized LDPC Codes: General Case and Efficient Evaluation

The growth rate of the weight distribution of irregular doubly-generalized LDPC (D-GLDPC) codes is developed and in the process, a new efficient numerical technique for its evaluation is presented. The solution involves simultaneous solution of a 4 x 4 system of polynomial equations. This represents the first efficient numerical technique for exact evaluation of the growth rate, even for LDPC codes. The technique is applied to two example D-GLDPC code ensembles.Comment: 6 pages, 1 figure. Proc. IEEE Globecom 2009, Hawaii, USA, November 30 - December 4, 200

Stability of Iterative Decoding of Multi-Edge Type Doubly-Generalized LDPC Codes Over the BEC

Using the EXIT chart approach, a necessary and sufficient condition is developed for the local stability of iterative decoding of multi-edge type (MET) doubly-generalized low-density parity-check (D-GLDPC) code ensembles. In such code ensembles, the use of arbitrary linear block codes as component codes is combined with the further design of local Tanner graph connectivity through the use of multiple edge types. The stability condition for these code ensembles is shown to be succinctly described in terms of the value of the spectral radius of an appropriately defined polynomial matrix.Comment: 6 pages, 3 figures. Presented at Globecom 2011, Houston, T

Spectral Shape of Doubly-Generalized LDPC Codes: Efficient and Exact Evaluation

This paper analyzes the asymptotic exponent of the weight spectrum for irregular doubly-generalized LDPC (D-GLDPC) codes. In the process, an efficient numerical technique for its evaluation is presented, involving the solution of a 4 x 4 system of polynomial equations. The expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. The spectral shape is shown to admit a particularly simple form in the special case where all variable nodes are repetition codes of the same degree, a case which includes Tanner codes; for this case it is also shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function. Finally, using these new results, weight and stopping set size spectral shapes are evaluated for some example generalized and doubly-generalized LDPC code ensembles.Comment: 17 pages, 6 figures. To appear in IEEE Transactions on Information Theor

On a Class of Doubly-Generalized LDPC Codes with Single Parity-Check Variable Nodes

A class of doubly-generalized low-density parity-check (D-GLDPC) codes, where single parity-check (SPC) codes are used as variable nodes (VNs), is investigated. An expression for the growth rate of the weight distribution of any D-GLDPC ensemble with a uniform check node (CN) set is presented at first, together with an analytical technique for its efficient evaluation. These tools are then used for detailed analysis of a case study, namely, a rate-1/2 D-GLDPC ensemble where all the CNs are (7,4) Hamming codes and all the VNs are length-7 SPC codes. It is illustrated how the VN representations can heavily affect the code properties and how different VN representations can be combined within the same graph to enhance some of the code parameters. The analysis is conducted over the binary erasure channel. Interesting features of the new codes include the capability of achieving a good compromise between waterfall and error floor performance while preserving graphical regularity, and values of threshold outperforming LDPC counterparts.Comment: 2009 IEEE Int. Symp. on Information Theory. 5 pages, 3 figure

Presence of Leptospira spp. in Caiman latirostris (Crocodylia, Alligatoridae) populations in Santa Fe, Argentina

Leptospirosis is a disease caused by pathogenic spirochetes of the genus Leptospira, transmitted by wild and domestic animals. Rodents play a fundamental role in the transmission cycle of this zoonosis but the function of reptiles is unknown. For example, crocodilians could play an important role in the transmission of this disease by living in ideal environments (bodies of shallow water and high temperatures) for the colonization of this bacterium. However, few studies have documented the presence of zoonotic diseases in caiman populations. Our objective was to assess the prevalence of antibodies to leptospira and the presence of Leptospira spp. in wild and captive Caiman latirostris. Blood samples were taken from 45 individuals (20 wild and 25 captive). Before extraction, we cleaned each caiman's neck in order to prevent contamination of samples. We determined the presence of antibodies in serum by microscopic agglutination test (MAT) and polymerase chain reaction (PCR) to detect DNA of the bacteria. We excluded 9 of the 45 samples analyzed by MAT because 5 had lipemic serum and 4 were contaminated (colonized by other organisms). Of the 36 caimans studied by microscopic agglutination test (MAT), 56% (20/36) were considered reactive (titers ≥50). In 74% (14/19) of captive samples and 35% (6/17) of wild samples, antibodies to leptospira were detected by MAT. The serogroup with highest occurrence was Pyrogenes (85%, n = 17/20), presenting coagglutinations with Icterohaemorrhagiae (25%, n = 5/20). One sample from a captive animal was positive for PCR, and we could not isolate leptospires because of agar contamination. Of the 45 blood agar media, 17.8% were contaminated and the rest were negative. This work determined the presence of Leptospira spp. in one caiman and a high prevalence of antibodies in captive caiman relative to wild individuals.Fil: Bauso, Jazmín. Provincia de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Universidad Autónoma de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción; Argentina. Universidad Nacional del Litoral. Facultad de Bioquímica y Ciencias Biológicas; Argentina. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias. Departamento de Ciencias Naturales. Laboratorio de Zoología Aplicada: Anexo Vertebrados (FHUC-UNL/MASPyMA); ArgentinaFil: Simoncini, Melina Soledad. Provincia de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Universidad Autónoma de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción; Argentina. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias. Departamento de Ciencias Naturales. Laboratorio de Zoología Aplicada: Anexo Vertebrados (FHUC-UNL/MASPyMA); ArgentinaFil: Chiani, Yosena. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorios e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Respiratorias; ArgentinaFil: Schmeling, María F.. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorios e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Respiratorias; ArgentinaFil: Larriera, Alejandro. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias. Departamento de Ciencias Naturales. Laboratorio de Zoología Aplicada: Anexo Vertebrados (FHUC-UNL/MASPyMA); Argentina. Universidad Nacional del Litoral. Facultad de Bioquímica y Ciencias Biológicas; ArgentinaFil: Vanasco, Norma Bibiana. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorios e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Respiratorias; Argentina. Universidad Nacional del Litoral. Facultad de Bioquímica y Ciencias Biológicas; ArgentinaFil: Piña, Carlos Ignacio. Provincia de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Universidad Autónoma de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción; Argentina. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias. Departamento de Ciencias Naturales. Laboratorio de Zoología Aplicada: Anexo Vertebrados (FHUC-UNL/MASPyMA); Argentin