We present a method to construct low-density paritycheck (LDPC) codes with low error floors on the binary symmetric channel. Codes are constructed so that their Tanner graphs are free of certain small trapping sets. These trapping sets are selected from the trapping set ontology for the Gallager A/B decoder. They are selected based on their relative harmfulness for a given decoding algorithm. We evaluate the relative harmfulness of different trapping sets for the sum-product algorithm by using the topological relations among them and by analyzing the decoding failures on one trapping set in the presence or absence of other trapping sets. We apply this method to construct structured LDPC codes. To facilitate the discussion, we give a new description of structured LDPC codes whose parity-check matrices are arrays of permutation matrices. This description uses Latin squares to define a set of permutation matrices that have disjoint support and to derive a simple necessary and sufficient condition for the Tanner graph of a code to be free of four cycles.

The failures of iterative decoders for low-density parity-check (LDPC) codes on the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC) can be understood in terms of combinatorial objects known as trapping sets. In this paper, we derive a systematic method to identify the most relevant trapping sets for decoding over the BSC in the error floor region. We elaborate on the notion of the critical number of a trapping set and derive a classification of trapping sets. We then develop the trapping set ontology, a database of trapping sets that summarizes the topological relations among trapping sets. We elucidate the usefulness of the trapping set ontology in predicting the error floor as well as in designing better codes.

No abstract

This paper introduces a class of structured lowdensity parity-check (LDPC) codes whose parity check matrices are arrays of permutation matrices. The permutation matrices are obtained from Latin squares and form a finite field under some matrix operations. They are chosen so that the Tanner graphs do not contain subgraphs harmful to iterative decoding algorithms. The construction of column-weight-three codes is presented. Although the codes are optimized for the Gallager A/B algorithm over the binary symmetric channel (BSC), their error performance is very good on the additive white Gaussian noise channel (AWGNC) as well.

The halophilic aquatic bacterium, Vibrio parahaemolyticus, is an important aquatic pathogen, also capable of causing acute hepatopancreatic necrosis disease (AHPND) in shrimp resulting in significant economic losses. Therefore, there is an urgent need to develop anti-infective strategies to control AHPND. The gnotobiotic Artemia model is used to establish whether a phenolic compound phloroglucinol is effective against the AHPND strain V. parahaemolyticus MO904. We found that pretreatment with phloroglucinol, at an optimum concentration (30 µM), protects axenic brine shrimp larvae against V. parahaemolyticus infection and induced heat shock protein 70 (Hsp70) production (twofolds or more) as compared with the control. We further demonstrated that the Vibrio-protective effect of phloroglucinol was caused by its prooxidant effect and is linked to the induction of Hsp70. In addition, RNA interference confirms that phloroglucinol-induced Hsp70 mediates the survival of brine shrimp larvae against V. parahaemolyticus infection. The study was validated in xenic Artemia model and in a Macrobrachium rosenbergii system. Pretreatment of xenic brine shrimp larvae (30 µM) and Macrobrachium larvae (5 µM) with phloroglucinol increases the survival of xenic brine shrimp and Macrobrachium larvae against subsequent V. parahaemolyticus challenge. Taken together, our study provides substantial evidence that the prooxidant activity of phloroglucinol induces Hsp70 production protecting brine shrimp, A. franciscana, and freshwater shrimp, M. rosenbergii, against the AHPND V. parahaemolyticus strain MO904. Probably, phloroglucinol treatment might become part of a holistic strategy to control AHPND in shrimp.