New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes

This paper presents several new construction techniques for low-density parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on specific classes of combinatorial designs, the improved code design focuses on high-rate structured codes with constant column weights 3 and higher. The proposed codes are efficiently encodable and exhibit good structural properties. Experimental results on decoding performance with the sum-product algorithm show that the novel codes offer substantial practical application potential, for instance, in high-speed applications in magnetic recording and optical communications channels.Comment: 10 pages; to appear in "IEEE Transactions on Communications

Construction of low-density parity-check codes based on balanced incomplete block designs

This correspondence presents a method for constructing structured regular low-density parity-check (LDPC) codes based on a special type of combinatoric designs, known as balance incomplete block designs. Codes constructed by this method have girths at least 6 and they perform well with iterative decoding. Furthermore, several classes of these codes are quasi-cyclic and hence their encoding can be implemented with simple feedback shift registers

Comparação de algoritmos para detecção de erros na transmissão

In order to mitigate errors caused by noise or interference in a data transmission system, several techniques are applied. A very effective method for detecting errors in digital transmissions, the Viterbi algorithm, together the concepts of convolutional encoders were and still are quite used in communication systems. This work seeks, through various scientific studies, bringing further explanation on the performance of convolutional encoders, as well as show its operation through simulations, with the purpose of illustrate the great improvement that has to insert an encoder like this in a transmission system. Through the applied techniques, it was possible to reduce the error rate by up to 10 times in the error rate in the transmission system with Additive White Gaussian Noise channel.Com intuito de atenuar erros causados por ruídos ou interferências em um sistema de transmissão de dados, são aplicadas diversas técnicas. Um método bastante eficaz para detecção de erros em transmissões digitais, o Algoritmo de Viterbi, agregado aos conceitos de codificadores convolucionais foram e ainda são bastante utilizados em sistemas de comunicações. Este trabalho procura, através de vários estudos científicos, trazer maiores esclarecimentos sobre o desempenho dos codificadores convolucionais, bem como mostrar seu funcionamento através de simulações, com o objetivo de ilustrar a grande melhoria que se tem ao inserir um codificador deste tipo em um sistema de transmissão. Através das técnicas aplicadas, foi possível reduzir a taxa de erros em até 10 vezes na taxa de erros no sistema de transmissão com canal com ruído aditivo gaussiano branco

Codes and Designs Related to Lifted MRD Codes

Lifted maximum rank distance (MRD) codes, which are constant dimension codes, are considered. It is shown that a lifted MRD code can be represented in such a way that it forms a block design known as a transversal design. A slightly different representation of this design makes it similar to a $q-$analog of a transversal design. The structure of these designs is used to obtain upper bounds on the sizes of constant dimension codes which contain a lifted MRD code. Codes which attain these bounds are constructed. These codes are the largest known codes for the given parameters. These transversal designs can be also used to derive a new family of linear codes in the Hamming space. Bounds on the minimum distance and the dimension of such codes are given.Comment: Submitted to IEEE Transactions on Information Theory. The material in this paper was presented in part in the 2011 IEEE International Symposium on Information Theory, Saint Petersburg, Russia, August 201

High-Rate Quantum Low-Density Parity-Check Codes Assisted by Reliable Qubits

Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find