Minimum Distance Distribution of Irregular Generalized LDPC Code Ensembles

In this paper, the minimum distance distribution of irregular generalized LDPC (GLDPC) code ensembles is investigated. Two classes of GLDPC code ensembles are analyzed; in one case, the Tanner graph is regular from the variable node perspective, and in the other case the Tanner graph is completely unstructured and irregular. In particular, for the former ensemble class we determine exactly which ensembles have minimum distance growing linearly with the block length with probability approaching unity with increasing block length. This work extends previous results concerning LDPC and regular GLDPC codes to the case where a hybrid mixture of check node types is used.Comment: 5 pages, 1 figure. Submitted to the IEEE International Symposium on Information Theory (ISIT) 201

Effects of the repeated distribution of sainfoin hay on the resistance and the resilience of goats naturally infected with gastrointestinal nematodes

Due to the high prevalence of anthelmintic resistance in goats, the need to explore novel approaches to control nematodes and to reduce the exclusive reliance on chemotherapy is strongly demanded in this host species. In sheep, several studies have shown that the consumption of tannin-rich legume forages was associated with positive effects on host resilience and resistance to parasite infection. In goats, studies on such interactions between tanniferous plants and nematode infections remain few. The objectives of the current study were to examine under natural conditions the effects of consumption of sainfoin hay by goats on the parasite populations and on host resilience. Eighteen adult cull goats naturally infected with Haemonchus contortus, Teladorsagia circumcincta and Trichostrongylus colubriformis were used in the study. At the start of the assay, the goats were allocated into two groups, balanced according to weight and the levels of egg excretion. The two groups grazed separate pastures for 3 months with similar stocking rates. Goats from group S received each month indoors, for 7 days, sainfoin hay and control goats (group C) received hay of ryegrass. The diets in both groups were made isoenergetic and isoproteic and the refusals measured. Individual parasitological and pathophysiological measurements were performed fortnightly in order to compare host resistance and resilience. At the end of the study, five goats per group were necropsied. The distribution of sainfoin was associated with: (1) a higher consumption of hay; (2) significant, lower levels of nematode egg excretion which was associated with a decrease in worm fertility but no change in worm population; however, the number of intestinal worms was reduced by 50% in group S; (3) a better host resilience. In particular, after 2 months of grazing, two control goats died and half of the remaining animals needed to be treated whereas this was not the case in group S. These differences were related to significant changes in pepsinogen and phosphate values (PCV) but not in pepsinogen and phosphate concentrations. These results demonstrate that a repeated distribution of sainfoin hay to grazing goats might be beneficial in regard of pasture contamination and host resilience. They suggest that administration of sainfoin hay might represent a valuable alternative and adjunct to reduce nematode infections in dairy goat flock. # 2004 Elsevier B.V. All rights reserved

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

Effects of condensed tannins on goats experimentally infected with Haemonchus contortus.

Although the use of tanniferous plants or condensed tannins as an alternative to anthelmintics to control gastrointestinal nematodes has been largely documented in sheep, studies remain scarce in goats. The objective of this study was therefore to assess the possible impact of condensed tannins in goats infected with adult Haemonchus contortus. Two groups of cull goats were experimentally infected with 10.000 L3 of H. contortus. After 4 weeks, quebracho extracts, representing 5% of the diet DM, were administered for 8 days to one of the two groups. Goats of the second group remained as controls. One week after the end of quebracho administration, the goats were euthanised. Individual egg excretion and pathophysiological parameters were measured weekly during the study. At the end of the study, worm counts were assessed and histological samples from the abomasa were taken to count the numbers of mucosal mast cells, globule leukocytes and eosinophils. The administration of tannins was associated with a significant decrease in egg excretion, which persisted until the end of experiment. This reduction was not associated with any difference in worm number but with a significant decrease in female fecundity. No significant changes in the mucosal density of the three inflammatory cell types were detected between the two groups. These results indicate that the major consequence of tannin consumption in goats is a reduction in worm fecundity and egg output, which does not seem related to significant changes in the local mucosal response

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