Typical performance of gallager-type error-correcting codes

The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this method, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity is saturated for many of the codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding.

Statistical mechanics of typical set decoding

The performance of "typical set (pairs) decoding" for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding method, errors occur, either when the information transmission is corrupted by atypical noise, or when multiple typical sequences satisfy the parity check equation as provided by the received corrupted codeword. We show that the average error rate for the second type of error over a given code ensemble can be accurately evaluated using the replica method, including the sensitivity to message length. Our approach generally improves the existing analysis known in the information theory community, which was recently reintroduced in IEEE Trans. Inf. Theory 45, 399 (1999), and is believed to be the most accurate to date. © 2002 The American Physical Society.

Typical performance of 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. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.

Typical behavior of relays in communication channels

The typical behavior of the relay-without-delay channel under low-density parity-check coding and its multiple-unit generalization, termed the relay array, is studied using methods of statistical mechanics. A demodulate-and- forward strategy is analytically solved using the replica symmetric ansatz which is exact in the system studied at Nishimori's temperature. In particular, the typical level of improvement in communication performance by relaying messages is shown in the case of a small and a large number of relay units. © 2007 The American Physical Society.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Typical performance of generalised vector channels

We introduce a general matrix formulation for multiuser channels and analyse the special cases of Multiple-Input Multiple-Output channels, channels with interference and relay arrays under LDPC coding using methods developed for the statistical mechanics of disordered systems. We use the replica method to provide results for the typical overlaps of the original and recovered messages and discuss their implications. The results obtained are consistent with belief propagation and density evolution results but also complement them giving additional insights into the information dynamics of these channels with unexpected effects in some cases.

Gender and autistic personality traits predict perspective-taking ability in typical adults

Adopting another’s visual perspective is exceedingly common and may underlie successful social interaction and empathizing with others. The individual differences responsible for success in perspective-taking, however, remain relatively undiscovered. We assessed whether gender and autistic personality traits in normal college student adults predict the ability to adopt another’s visual perspective. In a task differentially recruiting VPT-1 which involves following another’s line of sight, and VPT-2 which involves determining how another may perceive an object differently given their unique perspective (VPT-2), we found effects of both gender and autistic personality traits. Specifically, we demonstrate slowed VPT-2 but not VPT-1 performance in males and females with relatively high ASD-characteristic personality traits; this effect, however was markedly stronger in males than females. Results contribute to knowledge regarding ASD-related personality traits in the general population and the individual differences modulating perspective-taking abilities.

Structural and chemical modifications of typical South African biomasses during torrefaction

Torrefaction experiments were carried out for three typical South African biomass samples (softwood chips, hardwood chips and sweet sorghum bagasse) to a weight loss of 30wt.%. During torrefaction, moisture, non-structural carbohydrates and hemicelluloses were reduced, resulting in a structurally modified torrefaction product. There was a reduction in the average crystalline diameter (La) (XRD), an increase in the aromatic fraction and a reduction in aliphatics (substituted and unsubstituted) (CPMAS 13C NMR). The decrease in the aliphatic components of the lignocellulosic material under the torrefaction conditions also resulted in a slight ordering of the carbon lattice. The degradation of hemicelluloses and non-structural carbohydrates increased the inclusive surface area of sweet sorghum bagasse, while it did not change significantly for the woody biomasses.

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.

Combustion and emission characteristics of a typical biodiesel engine operated on waste cooking oil derived biodiesel

Waste cooking oils can be converted into fuels to provide economical and environmental benefits. One option is to use such fuels in stationary engines for electricity generation, co-generation or tri-generation application. In this study, biodiesel derived from waste cooking oil was tested in an indirect injection type 3-cylinder Lister Petter biodiesel engine. We compared the combustion and emission characteristics with that of fossil diesel operation. The physical and chemical properties of pure biodiesel (B100) and its blends (20% and 60% vol.) were measured and compared with those of diesel. With pure biodiesel fuel, full engine power was achieved and the cylinder gas pressure diagram showed stable operation. At full load, peak cylinder pressure of B100 operation was almost similar to diesel and peak burn rate of combustion was about 13% higher than diesel. For biodiesel operation, occurrences of peak burn rates were delayed compared to diesel. Fuel line injection pressure was increased by 8.5-14.5% at all loads. In comparison to diesel, the start of combustion was delayed and 90% combustion occurred earlier. At full load, the total combustion duration of B100 operation was almost 16% lower than diesel. Biodiesel exhaust gas emissions contained 3% higher CO2 and 4% lower NOx, as compared to diesel. CO emissions were similar at low load condition, but were decreased by 15 times at full load. Oxygen emission decreased by around 1.5%. Exhaust gas temperatures were almost similar for both biodiesel and diesel operation. At full engine load, the brake specific fuel consumption (on a volume basis) and brake thermal efficiency were respectively about 2.5% and 5% higher compared to diesel. Full engine power was achieved with both blends, and little difference in engine performance and emission results were observed between 20% and 60% blends. The study concludes that biodiesel derived from waste cooking oil gave better efficiency and lower NOx emissions than standard diesel. Copyright © 2012 SAE International.