Construction of Near-Optimum Burst Erasure Correcting Low-Density Parity-Check Codes

In this paper, a simple, general-purpose and effective tool for the design of low-density parity-check (LDPC) codes for iterative correction of bursts of erasures is presented. The design method consists in starting from the parity-check matrix of an LDPC code and developing an optimized parity-check matrix, with the same performance on the memory-less erasure channel, and suitable also for the iterative correction of single bursts of erasures. The parity-check matrix optimization is performed by an algorithm called pivot searching and swapping (PSS) algorithm, which executes permutations of carefully chosen columns of the parity-check matrix, after a local analysis of particular variable nodes called stopping set pivots. This algorithm can be in principle applied to any LDPC code. If the input parity-check matrix is designed for achieving good performance on the memory-less erasure channel, then the code obtained after the application of the PSS algorithm provides good joint correction of independent erasures and single erasure bursts. Numerical results are provided in order to show the effectiveness of the PSS algorithm when applied to different categories of LDPC codes.Comment: 15 pages, 4 figures. IEEE Trans. on Communications, accepted (submitted in Feb. 2007

Generalized Stability Condition for Generalized and Doubly-Generalized LDPC Codes

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 doublygeneralized 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 DGLDPC 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.Comment: 5 pages, 2 figures, to appear in Proc. of IEEE ISIT 200

High density balsamic vinegar: application of stable isotope ratio analysis to determine watering down

Aceto balsamico di Modena IGP (ABM) is an Italian worldwide appreciated PGI (Protected Geographical Indication) vinegar, obtained from cooked and/or concentrated grape must (at least 20% of the volume), with the addition of at least 10% of wine vinegar and a maximum 2% of caramel for color stability (EU Reg. 583/ 2009). The geographical origin of ABM ingredients is never specified. Since 2013, the European Committee for Standardization (CEN) has issued a method for determining the water fraudulently added to the vinegar and the balsamic vinegar product (EN16466-3 18O-IRMS). The method is based on the stable isotope ratios analysis of the bulk AMB sample (expressed as δ18O in ‰ with respect to the international standard V-SMOW2). Balsamic vinegars with very high density (higher than 1.37 g / mL of sugar) are available on the market. They are obtained by adding a high amount of concentrated must or by a long aging of the product in the barrel, which leads to an intense evaporation and concentration. Products with such high density cannot be analyzed by using the official method as reported in the EN16466-3 18O-IRMS. Indeed, in this conditions, the equilibration between CO2 and the water in the sample, being the base principle of the process, does not occur. In this work, the official method has been modified and validated, calculating repeatability (r) and reproducibility (R), by proceeding with a prior dilution of the sample and by applying a correction to the data in order to eliminate the diluent isotopic contribution. Considering the limit value of δ18O for a non-watered product reported in the literature for vinegar and for rectified concentrated must [1-2], the threshold limit of δ18O below which the ABM product can be considered as adulterated was identified. References [1] J. Agric. Food Chem. 2014, 62, 32, 8197–8203 [2] Food Control 2013, 29(1), 107–11

Identification-detection group testing protocols for COVID-19 at high prevalence

Group testing allows saving chemical reagents, analysis time, and costs, by testing pools of samples instead of individual samples. We introduce a class of group testing protocols with small dilution, suited to operate even at high prevalence (5–10%), and maximizing the fraction of samples classified positive/negative within the first round of tests. Precisely, if the tested group has exactly one positive sample then the protocols identify it without further individual tests. The protocols also detect the presence of two or more positives in the group, in which case a second round could be applied to identify the positive individuals. With a prevalence of 5 % and maximum dilution 6, with 100 tests we classify 242 individuals, 92 % of them in one round and 8 % requiring a second individual test. In comparison, the Dorfman’s scheme can test 229 individuals with 100 tests, with a second round for 18.5 % of the individuals

Massive Grant-Free Access with Massive MIMO and Spatially Coupled Replicas

Massive multiple access schemes, capable of serving a large number of uncoordinated devices while fulfilling reliability and latency constraints, are proposed. The schemes belong to the class of grant-free coded random access protocols and are tailored to massive multiple input multiple output (MIMO) base station processing. High reliability is obtained owing to an intra-frame spatial coupling effect, triggered by a simple device access protocol combined with acknowledgements (ACKs) from the base station. To provide system design guidelines, analytical bounds on error floor and latency are also derived. The proposed schemes are particularly interesting to address the challenges of massive machine-type communications in the framework of next generation massive multiple access systems