Statistical mechanics of low-density parity check error-correcting codes over Galois fields

A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Statistical physics of low density parity check error correcting codes

We study the performance of Low Density Parity Check (LDPC) error-correcting codes using the methods of statistical physics. LDPC codes are based on the generation of codewords using Boolean sums of the original message bits by employing two randomly-constructed sparse matrices. These codes can be mapped onto Ising spin models and studied using common methods of statistical physics. We examine various regular constructions and obtain insight into their theoretical and practical limitations. We also briefly report on results obtained for irregular code constructions, for codes with non-binary alphabet, and on how a finite system size effects the error probability.

Representation and parameterisation issues in genetic algorithms

A multi-chromosome GA (Multi-GA) was developed, based upon concepts from the natural world, allowing improved flexibility in a number of areas including representation, genetic operators, their parameter rates and real world multi-dimensional applications. A series of experiments were conducted, comparing the performance of the Multi-GA to a traditional GA on a number of recognised and increasingly complex test optimisation surfaces, with promising results. Further experiments demonstrated the Multi-GA's flexibility through the use of non-binary chromosome representations and its applicability to dynamic parameterisation. A number of alternative and new methods of dynamic parameterisation were investigated, in addition to a new non-binary 'Quotient crossover' mechanism. Finally, the Multi-GA was applied to two real world problems, demonstrating its ability to handle mixed type chromosomes within an individual, the limited use of a chromosome level fitness function, the introduction of new genetic operators for structural self-adaptation and its viability as a serious real world analysis tool. The first problem involved optimum placement of computers within a building, allowing the Multi-GA to use multiple chromosomes with different type representations and different operators in a single individual. The second problem, commonly associated with Geographical Information Systems (GIS), required a spatial analysis location of the optimum number and distribution of retail sites over two different population grids. In applying the Multi-GA, two new genetic operators (addition and deletion) were developed and explored, resulting in the definition of a mechanism for self-modification of genetic material within the Multi-GA structure and a study of this behaviour.

A non-linear encoder using a binary counterfor pulse-code modulation

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Systematic screening of compressed ODT excipients:cellulosic versus non-cellulosic

The successful development of compressed ODTs utilises low compression forces to create a porous structure whereby excipients are added to enhance wicking/swelling action or provide strength to the fragile tablet framework. In this work, a systematic investigation comparing materials from two different categories was employed to understand their functionality in binary mixture tablets of the most commonly used diluent mannitol. Cellulose based excipients such as HPC (SSL-SFP), L-HPC (NBD-022) and MCC (Avicel PH-102) were compared with non-cellulosic materials such as PEO (POLYOX WSR N-10) and Crospovidone (XL-10). Pure excipient properties were studied using Heckel Plot, compressibility profile, SEM and XRPD, whereas the prepared binary mixture compacts were studied for hardness, disintegration time and friability. Results from our investigation provide insight into differences encountered in product performance of ODT upon inclusion of additional materials. For example, non-cellulosic excipients Polyox and Crospovidone showed higher plasticity (Py values 588 and 450MPa) in pure form but not in binary mixtures of mannitol. Cellulosic excipients, nonetheless, offer faster disintegration (<30 sec) specifically L-HPC and MCC tablets. Disintegration time for tablets with fully substituted-HPC was prolonged (200-500 sec) upon increasing concentration between 1-10% due to gelation/matrix formation. It can be concluded that despite the reasonably good plasticity of both cellulosic and non-cellulosic excipients in pure form, the mechanical strength in binary mixtures is negatively impacted by the fragmentation/fracture effect of mannitol. © 2014 Bentham Science Publishers.

Systematic screening of compressed ODT excipients : cellulosic versus non-cellulosic

The successful development of c ompressed ODTs utilises low compression force s to create a porous structure whereby excipients are added to enhance wicking/swelling action or p rovide strength to the fragile tablet framework. In this work, a systematic investigation comparing materials from two different categories was employed to understand their functionality in binary mixture tablets of the most commonly used diluent mannitol. Cellulose based excipients such as HPC (SSL-SFP), L-HPC (NBD -022) and MCC (Avicel PH -102 ) were compared with non -cellulosic materials such as PEO (POLYOX WSR N -10) and Crospovidone (XL -10). P ure excipient properties were studied using Heckel Plot, compre ssibility profile, SEM and XR PD, w hereas the prepared binary mixture compacts were studied for hardness, disintegration time and friability. Results from our investigation provide insight into differences encountered in product performance of ODT upon inclusion of additional materials. For example, non -cellulosic excipients Polyox and Crospovidone showed higher plasticity (Py values 588 and 450 MPa) in pure form but not in binary mixtures of mannitol . Cellulosic excipients, nonetheless, offer faster disintegration (