A method for improving the code rate and error correction capability of a cyclic code

Currently, there has been an increasing demand for operational and trustworthy digital data transmission and storage systems. This demand has been augmented by the appearance of large-scale, high-speed data networks for the exchange, processing and storage of digital information in the different spheres. In this paper, we explore a way to achieve this goal. For given positive integers n,r, we establish that corresponding to a binary cyclic code C0[n,n-r], there is a binary cyclic code C[(n+1)3k-1,(n+1)3k-1-3kr], where k is a nonnegative integer, which plays a role in enhancing code rate and error correction capability. In the given scheme, the new code C is in fact responsible to carry data transmitted by C0. Consequently, a codeword of the code C0 can be encoded by the generator matrix of C and therefore this arrangement for transferring data offers a safe and swift mode. © 2013 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

A decoding procedure which improves code rate and error corrections

Corresponding to $C_{0}[n,n-r]$, a binary cyclic code generated by a primitive irreducible polynomial $p(X)\in \mathbb{F}_{2}[X]$ of degree $r=2b$, where $b\in \mathbb{Z}^{+}$, we can constitute a binary cyclic code $C[(n+1)^{3^{k}}-1,(n+1)^{3^{k}}-1-3^{k}r]$, which is generated by primitive irreducible generalized polynomial $p(X^{\frac{1}{3^{k}}})\in \mathbb{F}_{2}[X;\frac{1}{3^{k}}\mathbb{Z}_{0}]$ with degree $3^{k}r$, where $k\in \mathbb{Z}^{+}$. This new code $C$ improves the code rate and has error corrections capability higher than $C_{0}$. The purpose of this study is to establish a decoding procedure for $C_{0}$ by using $C$ in such a way that one can obtain an improved code rate and error-correcting capabilities for $C_{0}$.

A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code

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

A BCH code and a sequence of cyclic codes

This study establishes that for a given binary BCH code C0 n of length n generated by a polynomial g(x) ∈ F2[x] of degree r there exists a family of binary cyclic codes {Cm 2m−1(n+1)n}m≥1 such that for each m ≥ 1, the binary cyclic code Cm 2m−1(n+1)n has length 2m−1(n + 1)n and is generated by a generalized polynomial g(x 1 2m ) ∈ F2[x, 1 2m Z≥0] of degree 2mr. Furthermore, C0 n is embedded in Cm 2m−1(n+1)n and Cm 2m−1(n+1)n is embedded in Cm+1 2m(n+1)n for each m ≥ 1. By a newly proposed algorithm, codewords of the binary BCH code C0 n can be transmitted with high code rate and decoded by the decoder of any member of the family {Cm 2m−1(n+1)n}m≥1 of binary cyclic codes, having the same code rate.

Construction and decoding of BCH codes over chain of commutative rings

In this paper, we present a new construction and decoding of BCH codes over certain rings. Thus, for a nonnegative integer t, let A0 ⊂ A1 ⊂···⊂ At−1 ⊂ At be a chain of unitary commutative rings, where each Ai is constructed by the direct product of appropriate Galois rings, and its projection to the fields is K0 ⊂ K1 ⊂···⊂ Kt−1 ⊂ Kt (another chain of unitary commutative rings), where each Ki is made by the direct product of corresponding residue fields of given Galois rings. Also, A∗ i and K∗ i are the groups of units of Ai and Ki, respectively. This correspondence presents a construction technique of generator polynomials of the sequence of Bose, Chaudhuri, and Hocquenghem (BCH) codes possessing entries from A∗ i and K∗ i for each i, where 0 ≤ i ≤ t. By the construction of BCH codes, we are confined to get the best code rate and error correction capability; however, the proposed contribution offers a choice to opt a worthy BCH code concerning code rate and error correction capability. In the second phase, we extend the modified Berlekamp-Massey algorithm for the above chains of unitary commutative local rings in such a way that the error will be corrected of the sequences of codewords from the sequences of BCH codes at once. This process is not much different than the original one, but it deals a sequence of codewords from the sequence of codes over the chain of Galois rings.

Linear codes over finite local rings in a chain

For a positive integer $t$, let \begin{equation*} \begin{array}{ccccccccc} (\mathcal{A}_{0},\mathcal{M}_{0}) & \subseteq & (\mathcal{A}_{1},\mathcal{M}_{1}) & \subseteq & & \subseteq & (\mathcal{A}_{t-1},\mathcal{M}_{t-1}) & \subseteq & (\mathcal{A},\mathcal{M}) \\ \cap & & \cap & & & & \cap & & \cap \\ (\mathcal{R}_{0},\mathcal{M}_{0}^{2}) & & (\mathcal{R}_{1},\mathcal{M}_{1}^{2}) & & & & (\mathcal{R}_{t-1},\mathcal{M}_{t-1}^{2}) & & (\mathcal{R},\mathcal{M}^{2}) \end{array} \end{equation*} be a chain of unitary local commutative rings $(\mathcal{A}_{i},\mathcal{M}_{i})$ with their corresponding Galois ring extensions $(\mathcal{R}_{i},\mathcal{M}_{i}^{2})$, for $i=0,1,\cdots,t$. In this paper, we have given a construction technique of the cyclic, BCH, alternant, Goppa and Srivastava codes over these rings. Though, initially in \cite{AP} it is for local ring $(\mathcal{A},\mathcal{M})$, in this paper, this new approach have given a choice in selection of most suitable code in error corrections and code rate perspectives.

Statistical mechanics of error-correcting codes

We investigate the performance of error-correcting codes, 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 is obtained for finite K and C. We examine the finite-temperature case to assess the use of simulated annealing for decoding and extend the analysis to accommodate other types of noisy channels.

Finite connectivity systems as error-correcting codes

We investigate the performance of parity check codes using the mapping onto spin glasses proposed by Sourlas. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C parity checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for K?8 when the code rate K/C is finite. We then examine the finite temperature case to asses the use of simulated annealing methods for decoding, study the performance of the finite K case and extend the analysis to accommodate different types of noisy channels. The analogy between statistical physics methods and decoding by belief propagation is also discussed.

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.

Client QoE-oriented segment selection for DASH

A segment selection method controlled by Quality of Experience (QoE) factors for Dynamic Adaptive Streaming over HTTP (DASH) is presented in this paper. Current rate adaption algorithms aim to eliminate buffer underrun events by significantly reducing the code rate when experiencing pauses in replay. In reality, however, viewers may choose to accept a level of buffer underrun in order to achieve an improved level of picture fidelity or to accept the degradation in picture fidelity in order to maintain the service continuity. The proposed rate adaption scheme in our work can maximize the user QoE in terms of both continuity and fidelity (picture quality) in DASH applications. It is shown that using this scheme a high level of quality for streaming services, especially at low packet loss rates, can be achieved. Our scheme can also maintain a best trade-off between continuity-based quality and fidelity-based quality, by determining proper threshold values for the level of quality intended by clients with different quality requirements. In addition, the integration of the rate adaptation mechanism with the scheduling process is investigated in the context of a mobile communication network and related performances are analyzed.

Variabilidade da frequência cardíaca após treinamento concorrente : comparação entre homens e mulheres de meia-idade = Heart rate variability after concurrent training : comparison between middle-aged men and women

Universidade Estadual de Campinas . Faculdade de Educação Física

Efeito das sessões de familiarização sobre o pico de torque e taxa de desenvolvimento de torque : comparações entre jovens, meia idade e idosos = Effect of familiarization sessions on peak torque and rate of torque development : comparisons among young, middle age and elderly

Universidade Estadual de Campinas, Faculdade de Educação Física

Respostas agudas da variabilidade da frequência cardíaca após sesão de exercício de força com restrição de fluxo sanguíneo = : Acute responses of heart rate variabiblity afer blood flow restriction resistance exercise

Universidade Estadual de Campinas . Faculdade de Educação Física

Development of a quality use of medicines coding system to rate clinical pharmacists' medication review recommendations

Objective: To develop a 'quality use of medicines' coding system for the assessment of pharmacists' medication reviews and to apply it to an appropriate cohort. Method: A 'quality use of medicines' coding system was developed based on findings in the literature. These codes were then applied to 216 (111 intervention, 105 control) veterans' medication profiles by an independent clinical pharmacist who was supported by a clinical pharmacologist with the aim to assess the appropriateness of pharmacy interventions. The profiles were provided for veterans participating in a randomised, controlled trial in private hospitals evaluating the effect of medication review and discharge counselling. The reliability of the coding was tested by two independent clinical pharmacists in a random sample of 23 veterans from the study population. Main outcome measure: Interrater reliability was assessed by applying Cohen's kappa score on aggregated codes. Results: The coding system based on the literature consisted of 19 codes. The results from the three clinical pharmacists suggested that the original coding system had two major problems: (a) a lack of discrimination for certain recommendations e. g. adverse drug reactions, toxicity and mortality may be seen as variations in degree of a single effect and (b) certain codes e. g. essential therapy were in low prevalence. The interrater reliability for an aggregation of all codes into positive, negative and clinically non-significant codes ranged from 0.49-0.58 (good to fair). The interrater reliability increased to 0.72-0.79 (excellent) when all negative codes were excluded. Analysis of the sample of 216 profiles showed that the most prevalent recommendations from the clinical pharmacists were a positive impact in reducing adverse responses (31.9%), an improvement in good clinical pharmacy practice (25.5%) and a positive impact in reducing drug toxicity (11.1%). Most medications were assigned the clinically non-significant code (96.6%). In fact, the interventions led to a statistically significant difference in pharmacist recommendations in the categories; adverse response, toxicity and good clinical pharmacy practice measured by the quality use of medicine coding system. Conclusion: It was possible to use the quality use of medicine coding system to rate the quality and potential health impact of pharmacists' medication reviews, and the system did pick up differences between intervention and control patients. The interrater reliability for the summarised coding system was fair, but a larger sample of medication regimens is needed to assess the non-summarised quality use of medicines coding system.