A formalized optimum code search for q-ary trellis codes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Erasure error correcting codes applied to DTN communications.

The space environment has always been one of the most challenging for communications, both at physical and network layer. Concerning the latter, the most common challenges are the lack of continuous network connectivity, very long delays and relatively frequent losses. Because of these problems, the normal TCP/IP suite protocols are hardly applicable. Moreover, in space scenarios reliability is fundamental. In fact, it is usually not tolerable to lose important information or to receive it with a very large delay because of a challenging transmission channel. In terrestrial protocols, such as TCP, reliability is obtained by means of an ARQ (Automatic Retransmission reQuest) method, which, however, has not good performance when there are long delays on the transmission channel. At physical layer, Forward Error Correction Codes (FECs), based on the insertion of redundant information, are an alternative way to assure reliability. On binary channels, when single bits are flipped because of channel noise, redundancy bits can be exploited to recover the original information. In the presence of binary erasure channels, where bits are not flipped but lost, redundancy can still be used to recover the original information. FECs codes, designed for this purpose, are usually called Erasure Codes (ECs). It is worth noting that ECs, primarily studied for binary channels, can also be used at upper layers, i.e. applied on packets instead of bits, offering a very interesting alternative to the usual ARQ methods, especially in the presence of long delays. A protocol created to add reliability to DTN networks is the Licklider Transmission Protocol (LTP), created to obtain better performance on long delay links. The aim of this thesis is the application of ECs to LTP.

Learning Spike-Based Population Codes by Reward and Population Feedback

We investigate a recently proposed model for decision learning in a population of spiking neurons where synaptic plasticity is modulated by a population signal in addition to reward feedback. For the basic model, binary population decision making based on spike/no-spike coding, a detailed computational analysis is given about how learning performance depends on population size and task complexity. Next, we extend the basic model to n-ary decision making and show that it can also be used in conjunction with other population codes such as rate or even latency coding.

Compressed sensing based cyclic feature spectrum sensing for cognitive radios

Spectrum sensing is currently one of the most challenging design problems in cognitive radio. A robust spectrum sensing technique is important in allowing implementation of a practical dynamic spectrum access in noisy and interference uncertain environments. In addition, it is desired to minimize the sensing time, while meeting the stringent cognitive radio application requirements. To cope with this challenge, cyclic spectrum sensing techniques have been proposed. However, such techniques require very high sampling rates in the wideband regime and thus are costly in hardware implementation and power consumption. In this thesis the concept of compressed sensing is applied to circumvent this problem by utilizing the sparsity of the two-dimensional cyclic spectrum. Compressive sampling is used to reduce the sampling rate and a recovery method is developed for re- constructing the sparse cyclic spectrum from the compressed samples. The reconstruction solution used, exploits the sparsity structure in the two-dimensional cyclic spectrum do-main which is different from conventional compressed sensing techniques for vector-form sparse signals. The entire wideband cyclic spectrum is reconstructed from sub-Nyquist-rate samples for simultaneous detection of multiple signal sources. After the cyclic spectrum recovery two methods are proposed to make spectral occupancy decisions from the recovered cyclic spectrum: a band-by-band multi-cycle detector which works for all modulation schemes, and a fast and simple thresholding method that works for Binary Phase Shift Keying (BPSK) signals only. In addition a method for recovering the power spectrum of stationary signals is developed as a special case. Simulation results demonstrate that the proposed spectrum sensing algorithms can significantly reduce sampling rate without sacrifcing performance. The robustness of the algorithms to the noise uncertainty of the wireless channel is also shown.

Error detection and correction in binary parallel digital computers /

"Retyped October, 1964"

Simple Gallager codes for BSC

We investigate the performance of Gallager type error- correcting codes for Binary Symmetric Channels, where the code word comprises products of K bits selected from the original message and decoding is carried out utilizing a connectivity tensor with C connections per index. Shannon's bound for the channel capacity is recovered for large K and zero temperature when the code rate K/C is finite. Close to optimal error-correcting capability, with improved decoding properties is obtained for finite K and C.

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.

Low density parity check codes: a statistical physics perspective

The modem digital communication systems are made transmission reliable by employing error correction technique for the redundancies. Codes in the low-density parity-check work along the principles of Hamming code, and the parity-check matrix is very sparse, and multiple errors can be corrected. The sparseness of the matrix allows for the decoding process to be carried out by probability propagation methods similar to those employed in Turbo codes. The relation between spin systems in statistical physics and digital error correcting codes is based on the existence of a simple isomorphism between the additive Boolean group and the multiplicative binary group. Shannon proved general results on the natural limits of compression and error-correction by setting up the framework known as information theory. Error-correction codes are based on mapping the original space of words onto a higher dimensional space in such a way that the typical distance between encoded words increases.

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.

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.

Studies of the cationic polymerisation of vinylic and energetic cyclic ether monomers

The cationic polymerisation of various monomers, including cyclic ethers bearing energetic nitrate ester (-ON02) groups, substituted styrenes and isobutylene has been investigated. The main reaction studied has been the ring-opening polymerisation of 3- (nitratomethyl)-3-methyl oxetane (NIMMO) using the alcohol/BF3.0Et2 binary initiator system. A series of di-, tri- and tetrafunctional telechelic polymers has been synthesised. In order to optimise the system, achieve controlled molecular weight polymers and understand the mechanism of polymerisation the effects of certain parameters on the molecular weight distribution, as determined by Size Exclusion Chromatography, have been examined. This shows the molecular weight achieved depends on a combination of factors including -OH concentration, addition rate of monomer and, most importantly, temperature. A lower temperature and OH concentration tends to produce higher molecular weight, whereas, slower addition rates of monomer, either have no significant effect or produce a lower molecular weight polymer. These factors were used to increase the formation of a cyclic oligomer, by a side reaction, and suggest, that the polymerisation of NIMMO is complicated with endbiting and back biting reactions, along with other transfer/termination processes. These observations appear to fit the model of an active-chain end mechanism. Another cyclic monomer, glycidyl nitrate (GLYN), has been polymerised by the activated monomer mechanism. Various other monomers have been used to end-cap the polymer chains to produce hydroxy ends which are expected to form more stable urethane links, than the glycidyl nitrate ends, when cured with isocyanates. A novel monomer, butadiene oxide dinitrate (BODN), has been prepared and its homopolymerisation and copolymerisation with GL YN studied. In concurrent work the carbocationic polymerisations of isobutylene or substituted styrenes have been studied. Materials with narrow molecular weight distributions have been prepared using the diphenyl phosphate/BCl3 initiator. These systems and monomers are expected to be used in the synthesis of thermoplastic elastomers.

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.