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

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

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

Reliable Quantum Communications Based on Asymmetry in Distillation and Coding

The reliable provision of entangled qubits is an essential precondition in a variety of schemes for distributed quantum computing. This is challenged by multiple nuisances, such as errors during the transmission over quantum links, but also due to degradation of the entanglement over time due to decoherence. The latter can be seen as a constraint on the latency of the quantum protocol, which brings the problem of quantum protocol design into the context of latency-reliability constraints. We address the problem through hybrid schemes that combine: indirect transmission based on teleportation and distillation, and direct transmission, based on quantum error correction (QEC). The intuition is that, at present, the quantum hardware offers low fidelity, which demands distillation; on the other hand, low latency can be obtained by QEC techniques. It is shown that, in the proposed framework, the distillation protocol gives rise to asymmetries that can be exploited by asymmetric quantum error correcting code, which sets the basis for unique hybrid distillation and coding design. Our results show that ad hoc asymmetric codes give, compared with conventional QEC, a performance boost and codeword size reduction both in a single-link and in a quantum network scenario

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

Contention-Based mMTC/URLLC Coexistence Through Coded Random Access and Massive MIMO

Radio access network slicing is considered a key feature in next-generation multiple access. In this paper, we investigate the coexistence between massive machine-type communication (mMTC) and ultra-reliable low-latency communication (URLLC) services. To meet their heterogeneous requirements, we propose a novel grant-free scheme that leverages coded random access, massive multiple-input multiple-output (MIMO) processing, and both the preamble and the power domain to enable non-orthogonal access on shared frequency and time resources. To illustrate the concept, mMTC users transmit packet replicas having different preambles in various time slots, capitalizing on the temporal domain. Meanwhile, the URLLC users apply a more aggressive strategy that leverages pilot mixture and power diversity to meet the stringent latency and reliability requirements. Contention resolution is achieved through a signal processing algorithm based on successive interference cancellation (SIC). We show that the co-design of signal processing and access protocol is crucial to meet both service requirements, and we derive fundamental limits where possible. In instances where direct derivation proves impractical, we conduct symbol-level simulations of the whole system to gain comprehensive insights. The simulations reveal that the proposed scheme can satisfy mMTC/URLLC coverage density, reliability, and latency requirements, while outperforming orthogonal allocation schemes

Whole genome characterization of Shiga toxin-producing Escherichia coli in Free-ranging Red Deer from Italian Central Alps

Free-ranging red deer (Cervus elaphus) in Stelvio National Park (Italian Alps) have been suggested as potential carriers for LEE-negative, subAB positive Shiga toxin-producing Escherichia coli (STEC), which have been reported in human diseases. This work describes the genomic characterization of such isolates in order to define the zoonotic potential of wildlife-associated STEC. Whole genome analysis of 9 STEC isolates collected in the Stelvio National Park during the winter season 2016-2017 from feces of culled free-ranging red deer was performed. One STEC isolate harbored stx1 and stx2 genes, whereas 5 and 3 possessed stx2 and stx1 only, respectively. Subtype stx1a was carried by three strains and stx1c was observed in one isolate. Only subytpe stx2b was observed in the six stx2 positive strains. No STEC isolate possessed the eaeA gene. The serogroups identified included O146, O91, O113 and O174. Seven isolates of serogroups O146, O91 or O113 possessed the subAB locus. The core genome MLST analysis of the four O146:H28 showed that the strains’ genomes fell within the 37-95 alleles differences. Our results strengthen the hypothesis that red deer may represent carriers for LEE-negative, subAB positive STEC strains. Such strains display features similar to those causing illness to humans. The similarity in the genome of O146 STEC strains suggests that a population of these STEC isolates is circulating in the area. Our findings underline the zoonotic potential of STEC strains isolated from wild ruminants, including free-ranging deer

Free-ranging red deer (Cervus elaphus) as carriers of potentially zoonotic Shiga toxin-producing Escherichia coli

Shiga toxin-producing E. coli (STEC) are zoonotic foodborne pathogens of outmost importance and interest has been raised in recent years to define the potential zoonotic role of wildlife in STEC infection. This study aimed to estimate prevalence of STEC in free-ranging red deer (Cervus elaphus) living in areas with different anthropisation levels and describe the characteristics of strains in order to evaluate the potential risk posed to humans. Two-hundred one deer faecal samples collected in 2016–2018 from animals of Central Italian Alps were examined by bacteriological analysis and PCR screening of E. coli colonies for stx1, stx2 and eae genes. STEC strains were detected in 40 (19.9%) deer, with significantly higher prevalence in offspring than in yearlings. Whole genome analysis was performed to characterise a subset of 31 STEC strains. The most frequently detected serotype was O146:H28 (n = 10, 32.3%). Virulotyping showed different stx subtypes combinations, with stx2b-only (n = 15, 48.4%) being the most prevalent. All STEC lacked the eae gene but harbored additional virulence genes, particularly adhesins, toxins and/or other colonisation factors also described in STEC isolated from disease in humans. The most frequently detected genes were astA (n = 22, 71%), subAB (n = 21, 68%), iha (n = 26, 83.9%) and lpfA (n = 24, 77%). Four hybrid STEC/Enterotoxigenic E. coli strains were also identified. According to the most recent paradigm for pathogenicity assessment of STEC issued by the European Food Safety Authority, our results suggest that red deer are carriers of STEC strains that may have zoonotic potential, regardless of the anthropisation levels. Particular attention should be drawn to these findings while handling and preparing game meat. Furthermore, deer may release STEC in the environment, possibly leading to the contamination of soil and water sources