Average error exponent in Gallager low-density parity-check codes

We present a theoretical method for a direct evaluation of the average error exponent in Gallager error-correcting codes using methods of statistical physics. Results for the binary symmetric channel(BSC)are presented for codes of both finite and infinite connectivity.

Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

Average and reliability error exponents in low-density parity-check codes

We present a theoretical method for a direct evaluation of the average and reliability error exponents in low-density parity-check error-correcting codes using methods of statistical physics. Results for the binary symmetric channel are presented for codes of both finite and infinite connectivity.

Analysis of common attacks in public-key cryptosystems based on low-density parity-check codes

The security and reliability of a class of public-key cryptosystems against attacks by unauthorized parties, who had acquired partial knowledge of one or more of the private key components and/or of the message, were discussed. The standard statistical mechanical methods of dealing with diluted spin systems with replica symmetric considerations were analyzed. The dynamical transition which defined decryption success in practical situation was studied. The phase diagrams which showed the dynamical threshold as a function of the partial acquired knowledge of the private key were also presented.

An assessment of the performance of high density polyethylene copolymers for natural gas distribution pipes

The total thermoplastics pipe market in west Europe is estimated at 900,000 metric tonnes for 1977 and is projected to grow to some 1.3 million tonnes of predominantly PVC and polyolefins pipe by 1985. By that time, polyethylene for gas distribution pipe and fittings will represent some 30% of the total polyethylene pipe market. The performance characteristics of a high density polyethylene are significantly influenced by both molecular weight and type of comonomer; the major influences being in the long-term hoop stress resistance and the environmental stress cracking resistance. Minor amounts of hexene-1 are more effective than comonomers lower in the homologous series, although there is some sacrifice of density related properties. A synergistic improvement is obtained by combining molecular weight increase with copolymerisation. The Long-term design strength of polyethylene copolymers can be determined from hoop stress measurement at elevated temperatures and by means of a separation factor of approximate value 22, extrapolation can be made to room temperature performance for a water environment. A polyethylene of black composition has a sufficiently improved performance over yellow pigmented pipe to cast doubts on the validity of internationally specifying yellow coded pipe for gas distribution service. The chemical environment (condensate formation) that can exist in natural gas distribution networks has a deleterious effect on the pipe performance the reduction amounting to at least two decades in log time. Desorption of such condensate is very slow and the influence of the more aggressive aromatic components is to lead to premature stress cracking. For natural gas distribution purposes, the design stress rating should be 39 Kg/cm2 for polyethylenes in the molecular weight range of 150 - 200,000 and 55 Kg/cm2 for higher molecular weight materials.

Finite-size effects in low-density parity-check codes applied to cryptography

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Typical performance of regular low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Relationship between the free energy in statistical-mechanics approach and the mutual information used in the information-theory literature is established within a general framework; Gallager and MacKay-Neal codes are studied as specific examples of LDPC codes. It is shown that basic properties of these codes known for particular channels, including their potential to saturate Shannon's bound, hold for general symmetric channels. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel models.

Critical noise levels for low-density parity check decoding

We determine the critical noise level for decoding low-density parity check error-correcting codes based on the magnetization enumerator (M), rather than on the weight enumerator (W) employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived using the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Top-down lipidomics of low density lipoprotein reveal altered lipid profiles in advanced chronic kidney disease

This study compared the molecular lipidomic profi le of LDL in patients with nondiabetic advanced renal disease and no evidence of CVD to that of age-matched controls, with the hypothesis that it would reveal proatherogenic lipid alterations. LDL was isolated from 10 normocholesterolemic patients with stage 4/5 renal disease and 10 controls, and lipids were analyzed by accurate mass LC/MS. Top-down lipidomics analysis and manual examination of the data identifi ed 352 lipid species, and automated comparative analysis demonstrated alterations in lipid profi le in disease. The total lipid and cholesterol content was unchanged, but levels of triacylglycerides and N -acyltaurines were signifi cantly increased, while phosphatidylcholines, plasmenyl ethanolamines, sulfatides, ceramides, and cholesterol sulfate were signifi cantly decreased in chronic kidney disease (CKD) patients. Chemometric analysis of individual lipid species showed very good discrimination of control and disease sample despite the small cohorts and identifi ed individual unsaturated phospholipids and triglycerides mainly responsible for the discrimination. These fi ndings illustrate the point that although the clinical biochemistry parameters may not appear abnormal, there may be important underlying lipidomic changes that contribute to disease pathology. The lipidomic profi le of CKD LDL offers potential for new biomarkers and novel insights into lipid metabolism and cardiovascular risk in this disease. -Reis, A., A. Rudnitskaya, P. Chariyavilaskul, N. Dhaun, V. Melville, J. Goddard, D. J. Webb, A. R. Pitt, and C. M. Spickett. Topdown lipidomics of low density lipoprotein reveal altered lipid profi les in advanced chronic kidney disease. J. Lipid Res. 2015.

Stabilisation and characterisation of peroxide-crosslinked high density polyethylene

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The antioxidant role of vitamin E in polyolefins

Polymers are subject to oxidation throughout their lifecycle. Antioxidants are generally incorporated in polymers to inhibit or minimise oxidative degradation. Hindered phenolic antioxidants are important stabilisers for polyolefins. However, hindered phenols undergo chemical transformations while performing their antioxidant function during processing and fabrication. In addition, antioxidants are subject to loss from polymers during processing, or subsequently in-service. Migration of antioxidants is a major concern in applications involving polymers in direct contact with food and human environment. This concern is compounded by the realisation that very little is known about the nature and the migration behaviour of antioxidant transformation products. In this work, the antioxidant role of the biological antioxidant -tocopherol (Vitamin E) , which is structurally similar to many synthetic hindered phenols, is investigated in low density polyethylene (LDPE) and polypropylene (PP). The melt stabilising effectiveness of -tocopherol (Toc) was found to be very high, higher than that of commercial hindered phenol antioxidants, such as Irganox 1076 (Irg 1076) and Irganox 1010 (Irg 1010), after multiple extrusions, especially at very low concentrations. The high antioxidant activity of Toc was shown to be due, at least in part, to the formation of transformation products during processing. The main products formed are stereoisomers of dimers and trimers, as well as aldehydes and a quinone - the relative concentration of each was shown to depend on the processing severity, the initial antioxidant concentration and oxygen availability. These transformation products are shown to impart better, similar or lower melt stability to the polymer than the parent antioxidant. The nature of the products formed from Toc during processing was compared with those formed during processing of Irg 1076 and Irg 1010 with LDPE and a mechanism for the melt stabilisation of Toc was proposed and compared with the stabilisation mechanisms of the synthetic antioxidants Irg 1076 and Irg 1010.

Migration of additives from thermoplastic polymers

A homologous series of ultra-violet stabilisers containing 2-hydroxybenzophenone (HBP) moiety as a uv absorbing chromophore with varying alkyl chain lengths and sizes were prepared by known chemical synthesis. The strong absorbance of the HBP chromophore was utilized to evaluate the concentration of these stabilisers in low density polyethylene films and concentration of these stabilisers in low density polyethylene films and in relevant solvents by ultra-violet/visible spectroscopy. Intrinsic diffusion coefficients, equilibrium solubilities, volatilities from LDPE films and volatility of pure stabilisers were studied over a temperature range of 5-100oC. The effects of structure, molecular weight and temperature on the above parameters were investigated and the results were analysed on the basis of theoretical models published in the literature. It has been found that an increase in alkyl chain lengths does not change the diffusion coefficients to a significant level, while attachment of polar or branched alkyl groups change their value considerably. An Arrhenius type of relationship for the temperature dependence of diffusion coefficients seems to be valid only for a narrow temperature range, and therefore extrapolation of data from one temperature to another leads to a considerable error. The evidence showed that increase in additive solubility in the polymer is favoured by lower heat of fusions and melting points of additives. This implies the validity of simple regular solution theory to provide an adequate basis for understanding the solubility of additives in polymers The volubility of stabilisers from low density polyethylene films showed that of an additive from a polymer can be expressed in terms of a first-order kinetic equation. In addition the rate of loss of stabilisers was discussed in relation to its diffusion, solubility and volatility and found that all these factors may contribute to the additive loss, although one may be a rate determining factor. Stabiliser migration from LDPE into various solvents and food simulants was studied at temperatures 5, 23, 40 and 70oC; from the plots of rate of migration versus square root time, characteristic diffusion coefficients were obtained by using the solution of Fick's diffusion equations. It was shown that the rate of migration depends primarily on partition coefficients between solvent and the polymer of the additive and also on the swelling action of the contracting media. Characteristic diffusion coefficients were found to approach to intrinsic values in non swelling solvents, whereas in the case of highly swollen polymer samples, the former may be orders of magnitude greater than the latter.

Melting of polymers

The project set out to investigate the relative effectiveness of thermal conductive heating (from external resistance heaters) and viscous heating in the heating (and melting) of low density polyethylene. A model system was used in order to simplify the mathematical analysis. A theory was developed to describe both processes in the model apparatus. The results showed large differences between the experimental and predicted results at low melt temperatures (the predicted results were much greater than the experimental) . Analysis of the results indicated that the apparatus was probably not producing the required shear rates in the sample. The theory appeared to be satisfactory, in that it did not over estimate the viscous heating to any significant extent. The theoretical results could therefore be considered to be a reasonable estimate of the viscous heating.

The mechanisms of melt stabilisation of polyolefins

The effects of melt stabilisers on the oxidative degradation of polyolefins (polypropylene, low density polyethylene) have been studied under a variety of processing conditions . The changes in the both chemical and physical properties of unstabilised polymers occurring during processing were found to be strongly dependent on the amount of oxygen present in the mixer. 2 ,6 ,3' ,5' -tetra-tert-butyl-4'-phenoxy-4-methylene-2, 5-cyclohexadiene-1- one (galvinoxyl), iodine, nitroxyl radicals and cupric stearate were found to be very efficient melt stabilisers particularly when processed in a restricted amount of air. The mechanisms of their melt stabilising action have been investigated and a common cyclical regenerative mechanism involving both chain-breaking electron acceptor (CB-A) and chain-breaking electron donor (CB-D) antioxidant activity was found to be involved in each case. 2,6,3',5'-tetra-tert-butyl-4'-hydroxy phenyl-4-rrethylene-2,5-cyclohexadiene- 1-one (hydrogalvinoxy1), 4-hydroxy, 2,2,6, 6-tetra methyl-N-hydroxy piperidine and hydrogen iodide were formed together with olefinic unsaturation in the substrates during the melt processing of the polymers containing galvinoxyl, 4-hydroxy, 2,2,6, 6-tetra methyl piperidine oxyl and iodine respectively. No bonding of the melt stabilisers to the polymers was found to occur. Cupric stearate was found to undergo a similar redox reaction during its action as a melt stabiliser with the formation of unsaturation in the polymer. Evidence for the above processes is presented. The behaviours of melt stabilisers in the subsequent thermal and photooxidation of polyolefins have also been studied. Galvinoxyl which is very effective under both mild and severe processing canditions has been found to be an effective antioxidant during thermal oxidation (oven ageing) and it is also moderately good. as a photo-stabiliser. Iodine and cupric stearate acted efficiently during melt stabilisation of polymers, however they were both ineffective as thermo-oxidative antioxidants and UV stabilisers. Although the melt stabilisation effectiveness of stable nitroxyl radicals (e.g. 4-hydroxy, 2,2,6,6-tetra methyl piperidineoxyl and Bis- (2,2,6 ,6-tetra methyl-4- piperidinyl-N-oxyl) sebacate) is not as high as that of galvinoxyl during processing particularly in excess of air, they have been found to be much more efficient as UV stabilisers for polyolefins. The reasons for this are discussed.

The behaviour of antioxidants in polyolefins under conditions of U.V. exposure

The effects of antioxidants and stabilizers on the oxidative degradation of polyolefins (low density polyethylene [LDPE] and polypropylene [PPJ have been studied after subjecting to prior high temperature processing treatments. The changes in the both chemical and physical properties of unstabilized polymers occurring during processing were found to be strongly dependent on the amount of oxygen present in the mixer. Subsequent thermal and photo-oxidation showed very similar characteristics and the chromophore primarily responsible for:both thermo and photooxidative degradation of unstabilized polymers was found to be hydroperoxide formed during processing. Removal of hydroperoxide by heat treatment in an inert atmosphere although increasing ketonic carbonyl concentration, markedly decreased the rate of photo-oxidation, introducing an induction period similar to that of an unprocessed sample. It was concluded that hydroperoxides are the most important initiators in normally processed polymers during the early stages of photo-oxidation. Antioxidants such as metal dithiocarbamates which act by destroying peroxides into non-radica1 products were found to be efficient melt stabilizers for polyolefins and effective UV stabilizers during the initial photo-oxidation stage, whilst a phenolic antioxidant, n-octadecyl-3-(3',5'-di-terbutyl 4'hydroxypheny1) propionate (Irganox 1076) retarded photo-oxidation rate in the later stages. A typical 'UV absorber' 2-hydroxy-4-octyloxy-benzophenone (HOBP) has a minor thermal antioxidant action but retarded photo-oxidation at all stages. A substituated piperidine derivative, Bis [2.2.6.6-tetramethylpiperidlnyl-4] sebacate (Tinuvin 770) behaved as an pro-oxidant during thermal oxidation of polyolefins but was an effective stabilizer against UV light. The UV absorber, HOBP synergised effectively with both peroxide decomposing antioxidants (metal dithiocarbamates) and a chain-breaking antioxidant (Irganox 1076) during photo-oxidation of the poymers studed whereas the combined effect was additive during thermal oxidation. By contrast, the peroxide decornposers and chain-breaking antioxidant (Irganox 1076) which were effective synergists during thermal oxidation of LDPE· were antagonistic during photo-oxidation. The mechanisms of these processes are discussed.