Automated synthesis of delay-reduced Reed-Muller universal logic module networks

This paper presents a new approach to implement Reed-Muller Universal Logic Module (RM-ULM) networks with reduced delay and hardware for synthesizing logic functions given in Reed-Muller (RM) form. Replication of single control line RM-ULM is used as the only design unit for defining any logic function. An algorithm is proposed that does exhaustive branching to reduce the number of levels and modules required to implement any logic function in RM form. This approach attains a reduction in delay, and power over other implementations of functions having large number of variables.

Divisible Codes - A Survey

This paper surveys parts of the study of divisibility properties of codes. The survey begins with the motivating background involving polynomials over finite fields. Then it presents recent results on bounds and applications to optimal codes.

Minimal Codewords in Linear Codes

2000 Mathematics Subject Classification: 94B05, 94B15.

A Geometric Approach for Turbo Decoding of Reed-Solomon Codes in QAM Modulation Schemes

This work studies the turbo decoding of Reed-Solomon codes in QAM modulation schemes for additive white Gaussian noise channels (AWGN) by using a geometric approach. Considering the relations between the Galois field elements of the Reed-Solomon code and the symbols combined with their geometric dispositions in the QAM constellation, a turbo decoding algorithm, based on the work of Chase and Pyndiah, is developed. Simulation results show that the performance achieved is similar to the one obtained with the pragmatic approach with binary decomposition and analysis.

Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

Hamming and Reed-Solomon codes over certain rings

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Inter-Packet Symbol Approach To Reed-Solomon FEC Codes For RTP-Multimedia Stream Protection

This paper presents an alternative Forward Error Correction scheme, based on Reed-Solomon codes, with the aim of protecting the transmission of RTP-multimedia streams: the inter-packet symbol approach. This scheme is based on an alternative bit structure that allocates each symbol of the Reed-Solomon code in several RTP-media packets. This characteristic permits to exploit better the recovery capability of Reed-Solomon codes against bursty packet losses. The performance of our approach has been studied in terms of encoding/decoding time versus recovery capability, and compared with other proposed schemes in the literature. The theoretical analysis has shown that our approach allows the use of a lower size of the Galois Fields compared to other solutions. This lower size results in a decrease of the required encoding/decoding time while keeping a comparable recovery capability. Finally, experimental results have been carried out to assess the performance of our approach compared to other schemes in a simulated environment, where models for wireless and wireline channels have been considered.

Efficient Transmitter/Receiver Architectures for High Performance Wireless Applications

The thesis focuses on efficient design methods and reconfiguration architectures suitable for higher performance wireless communication .The work presented in this thesis describes the development of compact,inexpensive and low power communication devices that are robust,testable and capable of handling multiple communication standards.A new multistandard Decimation Filter Design Toolbox is developed in MATLAB GUIDE environment.RNS based dual-mode decimation filters reconfigurable for WCDMA/WiMAX and WCDMA/WLANa standards are designed and implemented.It offers high speed operation with lesser area requirement and lower dynamic power dissipation.A novel sigma-delta based direct analog-to-residue converter that reduces the complexity of RNS conversion circuitry is presented.The performance of an OFDM communication system with a new RRNS-convolutional concatenated coding is analysed and improved BER performance is obtained under different channel conditions. Easily testable MAC units for filters are presented using Reed-Muller logic for realization.

Implementation of Reed-Solomon RS (255,239) Code

In this paper the construction of Reed-Solomon RS(255,239) codeword is described and the process of coding and decoding a message is simulated and verified. RS(255,239), or its shortened version RS(224,208) is used as a coding technique in Low-Power Single Carrier (LPSC) physical layer, as described in IEEE 802.11ad standard. The encoder takes 239 8-bit information symbols, adds 16 parity symbols and constructs 255-byte codeword to be transmitted through wireless communication channel. RS(255,239) codeword is defined over Galois Field GF and is used for correcting upto 8 symbol errors. RS(255,239) code construction is fully implemented and Simulink test project is constructed for testing and analyzing purposes.

Mutational meltdown in primary endosymbionts: selection limits Muller's ratchet

Background Primary bacterial endosymbionts of insects (p-endosymbionts) are thought to be undergoing the process of Muller's ratchet where they accrue slightly deleterious mutations due to genetic drift in small populations with negligible recombination rates. If this process were to go unchecked over time, theory predicts mutational meltdown and eventual extinction. Although genome degradation is common among p-endosymbionts, we do not observe widespread p-endosymbiont extinction, suggesting that Muller's ratchet may be slowed or even stopped over time. For example, selection may act to slow the effects of Muller's ratchet by removing slightly deleterious mutations before they go to fixation thereby causing a decrease in nucleotide substitutions rates in older p-endosymbiont lineages. Methodology/Principal Findings To determine whether selection is slowing the effects of Muller's ratchet, we determined the age of the Candidatus Riesia/sucking louse assemblage and analyzed the nucleotide substitution rates of several p-endosymbiont lineages that differ in the length of time that they have been associated with their insect hosts. We find that Riesia is the youngest p-endosymbiont known to date, and has been associated with its louse hosts for only 13–25 My. Further, it is the fastest evolving p-endosymbiont with substitution rates of 19–34% per 50 My. When comparing Riesia to other insect p-endosymbionts, we find that nucleotide substitution rates decrease dramatically as the age of endosymbiosis increases. Conclusions/Significance A decrease in nucleotide substitution rates over time suggests that selection may be limiting the effects of Muller's ratchet by removing individuals with the highest mutational loads and decreasing the rate at which new mutations become fixed. This countering effect of selection could slow the overall rate of endosymbiont extinction.

Bodhidharma Crossing the Yangzi River on a Reed

Li Yaofu; 2 ft. 9 47/64 in.x 1 ft. 1 5/16 in.; hanging scroll, ink on paper

A fuzzy reed-frost model for epidemic spreading

In this paper, we present a fuzzy approach to the Reed-Frost model for epidemic spreading taking into account uncertainties in the diagnostic of the infection. The heterogeneities in the infected group is based on the clinical signals of the individuals (symptoms, laboratorial exams, medical findings, etc.), which are incorporated into the dynamic of the epidemic. The infectivity level is time-varying and the classification of the individuals is performed through fuzzy relations. Simulations considering a real problem with data of the viral epidemic in a children daycare are performed and the results are compared with a stochastic Reed-Frost generalization

Analytical results on Muller's ratchet effect in growing populations

Fontanari introduced [Phys. Rev. Lett. 91, 218101 (2003)] a model for studying Muller's ratchet phenomenon in growing asexual populations. They studied two situations, either including a death probability for each newborn or not, but were able to find analytical (recursive) expressions only in the no-decay case. In this Brief Report a branching process formalism is used to find recurrence equations that generalize the analytical results of the original paper besides confirming the interesting effects their simulations revealed.

Reliability-based evaluation of design code provisions for circular concrete-filled steel columns

This paper presents an investigation of design code provisions for steel-concrete composite columns. The study covers the national building codes of United States, Canada and Brazil, and the transnational EUROCODE. The study is based on experimental results of 93 axially loaded concrete-filled tubular steel columns. This includes 36 unpublished, full scale experimental results by the authors and 57 results from the literature. The error of resistance models is determined by comparing experimental results for ultimate loads with code-predicted column resistances. Regression analysis is used to describe the variation of model error with column slenderness and to describe model uncertainty. The paper shows that Canadian and European codes are able to predict mean column resistance, since resistance models of these codes present detailed formulations for concrete confinement by a steel tube. ANSI/AISC and Brazilian codes have limited allowance for concrete confinement, and become very conservative for short columns. Reliability analysis is used to evaluate the safety level of code provisions. Reliability analysis includes model error and other random problem parameters like steel and concrete strengths, and dead and live loads. Design code provisions are evaluated in terms of sufficient and uniform reliability criteria. Results show that the four design codes studied provide uniform reliability, with the Canadian code being best in achieving this goal. This is a result of a well balanced code, both in terms of load combinations and resistance model. The European code is less successful in providing uniform reliability, a consequence of the partial factors used in load combinations. The paper also shows that reliability indexes of columns designed according to European code can be as low as 2.2, which is quite below target reliability levels of EUROCODE. (C) 2009 Elsevier Ltd. All rights reserved.