Parallel decoding of turbo codes using multi-point trellis termination and collision-free interleavers

The UMTS turbo encoder is composed of parallel concatenation of two Recursive Systematic Convolutional (RSC) encoders which start and end at a known state. This trellis termination directly affects the performance of turbo codes. This paper presents performance analysis of multi-point trellis termination of turbo codes which is to terminate RSC encoders at more than one point of the current frame while keeping the interleaver length the same. For long interleaver lengths, this approach provides dividing a data frame into sub-frames which can be treated as independent blocks. A novel decoding architecture using multi-point trellis termination and collision-free interleavers is presented. Collision-free interleavers are used to solve memory collision problems encountered by parallel decoding of turbo codes. The proposed parallel decoding architecture reduces the decoding delay caused by the iterative nature and forward-backward metric computations of turbo decoding algorithms. Our simulations verified that this turbo encoding and decoding scheme shows Bit Error Rate (BER) performance very close to that of the UMTS turbo coding while providing almost %50 time saving for the 2-point termination and %80 time saving for the 5-point termination.

Increasing the speed of parallel decoding of turbo codes

Turbo codes experience a significant decoding delay because of the iterative nature of the decoding algorithms, the high number of metric computations and the complexity added by the (de)interleaver. The extrinsic information is exchanged sequentially between two Soft-Input Soft-Output (SISO) decoders. Instead of this sequential process, a received frame can be divided into smaller windows to be processed in parallel. In this paper, a novel parallel processing methodology is proposed based on the previous parallel decoding techniques. A novel Contention-Free (CF) interleaver is proposed as part of the decoding architecture which allows using extrinsic Log-Likelihood Ratios (LLRs) immediately as a-priori LLRs to start the second half of the iterative turbo decoding. The simulation case studies performed in this paper show that our parallel decoding method can provide %80 time saving compared to the standard decoding and %30 time saving compared to the previous parallel decoding methods at the expense of 0.3 dB Bit Error Rate (BER) performance degradation.

The modified Max-Log-MAP turbo decoding algorithm by extrinsic information scaling for wireless applications

The iterative nature of turbo-decoding algorithms increases their complexity compare to conventional FEC decoding algorithms. Two iterative decoding algorithms, Soft-Output-Viterbi Algorithm (SOVA) and Maximum A posteriori Probability (MAP) Algorithm require complex decoding operations over several iteration cycles. So, for real-time implementation of turbo codes, reducing the decoder complexity while preserving bit-error-rate (BER) performance is an important design consideration. In this chapter, a modification to the Max-Log-MAP algorithm is presented. This modification is to scale the extrinsic information exchange between the constituent decoders. The remainder of this chapter is organized as follows: An overview of the turbo encoding and decoding processes, the MAP algorithm and its simplified versions the Log-MAP and Max-Log-MAP algorithms are presented in section 1. The extrinsic information scaling is introduced, simulation results are presented, and the performance of different methods to choose the best scaling factor is discussed in Section 2. Section 3 discusses trends and applications of turbo coding from the perspective of wireless applications.

Enumeração de espectro de distâncias de esquemas de modulação codificada em treliça empregando codificação turbo

In this work, a performance analysis of transmission schemes employing turbo trellis coded modulation. In general, the performance analysis of such schemes is guided by evaluating the error probability of these schemes. The exact evaluation of this probability is very complex and inefficient from the computational point of view, a widely used alternative is the use of union bound of error probability, because of its easy implementation and computational produce bounds that converge quickly. Since it is the union bound, it should use to expurge some elements of distance spectrum to obtain a tight bound. The main contribution of this work is that the listing proposal is carried out from the puncturing at the level of symbol rather than bit-level as in most works of literature. The main reason for using the symbol level puncturing lies in the fact that the enummerating function of the turbo scheme is obtained directly from complex sequences of signals through the trellis and not indirectly from the binary sequences that require further binary to complex mapping, as proposed by previous works. Thus, algorithms can be applied through matrix from the adjacency matrix, which is obtained by calculating the distances of the complex sequences of the trellis. This work also presents two matrix algorithms for state reduction and the evaluation of the transfer function of this. The results presented in comparisons of the bounds obtained using the proposed technique with some turbo codes of the literature corroborate the proposition of this paper that the expurgated bounds obtained are quite tight and matrix algorithms are easily implemented in any programming software language

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.

Approaching near-capacity on a multi-antenna channel using successive decoding and interference cancellation receivers

In this paper, we address the problem of designing multirate codes for a multiple-input and multiple-output (MIMO) system by restricting the receiver to be a successive decoding and interference cancellation type, when each of the antennas is encoded independently. Furthermore, it is assumed that the receiver knows the instantaneous fading channel states but the transmitter does not have access to them. It is well known that, in theory, minimum-mean-square error (MMSE) based successive decoding of multiple access (in multi-user communications) and MIMO channels achieves the total channel capacity. However, for this scheme to perform optimally, the optimal rates of each antenna (per-antenna rates) must be known at the transmitter. We show that the optimal per-antenna rates at the transmitter can be estimated using only the statistical characteristics of the MIMO channel in time-varying Rayleigh MIMO channel environments. Based on the results, multirate codes are designed using punctured turbo codes for a horizontal coded MIMO system. Simulation results show performances within about one to two dBs of MIMO channel capacity.

Detecção multiutilizador do domínio da frequência para sistemas DS-CDMA

Os Sinais de Espalhamento de Espectro de Sequência Directa exibem propriedades cicloestacionárias que implicam redundância entre componentes de frequência espaçadas por múltiplos da taxa de símbolo. Nesta tese, é apresentado um cancelador de interferência multiutilizador (Cancelador por translação na frequência - FSC) que tira partido desta propriedade. Este cancelador linear opera no domínio da frequência no sinal espalhado de tal forma que minimiza a interferência e ruído na saída (Critério do Mínimo Erro Quadrado Médio). Além de testado para o caso de antena única, são avaliadas as performances das configurações de antenas múltiplas para o caso de beamforming e canais espacialmente descorrelacionados considerando sistemas síncronos e sistemas com desalinhamento no tempo dos perfis de canais (ambos UMTS-TDD). Essas configurações divergiam na ordem da combinação temporal, combinação espacial e detecção multiutilizador. As configurações FSC foram avaliadas quando concatenadas com o PIC-2D. Os resultados das simulações mostram consideráveis melhorias nos resultados relativamente ao RAKE-2D convencional e PIC-2D. Foi atingida performance próximo ao RAKE de utilizador único quando o FSC foi avaliado concatenado com PIC-2D em quase todas as configurações. Todas as configurações foram avaliadas com modulação QPSK, 8-PSK e 16-QAM. Foi introduzida codificação Turbo e identificou-se as situações da vantagem de utilização do FSC antes do PIC-2D. As modulações 8-PSK e 16-QAM foram igualmente testadas com codificação.

Ecualización y optimización de la codificación para la simulación de sistemas OFDM

Los sistemas basados en la técnica OFDM (Multiplexación por División de Frecuencias Ortogonales) son una evolución de los tradicionales sistemas FDM (Multiplexación por División de Frecuencia), gracias a la cual se consigue un mejor aprovechamiento del ancho de banda. En la actualidad los sistemas OFDM y sus variantes ocupan un lugar muy importante en las comunicaciones, estando implementados en diversos estándares como pueden ser: DVB-T (estándar de la TDT), ADSL, LTE, WIMAX, DAB (radio digital), etc. Debido a ello, en este proyecto se implementa un sistema OFDM en el que poder realizar diversas simulaciones para entender mejor su funcionamiento. Para ello nos vamos a valer de la herramienta Matlab. Los objetivos fundamentales dentro de la simulación del sistema es poner a prueba el empleo de turbo códigos (comparándolo con los códigos convolucionales tradicionales) y de un ecualizador. Todo ello con la intención de mejorar la calidad de nuestro sistema (recibir menos bits erróneos) en condiciones cada vez más adversas: relaciones señal a ruido bajas y multitrayectos. Para ello se han implementado las funciones necesarias en Matlab, así como una interfaz gráfica para que sea más sencillo de utilizar el programa y más didáctico. En los capítulos segundo y tercero de este proyecto se efectúa un estudio de las bases de los sistemas OFDM. En el segundo nos centramos más en un estudio teórico puro para después pasar en el tercero a centrarnos únicamente en la teoría de los bloques implementados en el sistema OFDM que se desarrolla en este proyecto. En el capítulo cuarto se explican las distintas opciones que se pueden llevar a cabo mediante la interfaz implementada, a la vez que se elabora un manual para el correcto uso de la misma. El quinto capítulo se divide en dos partes, en la primera se muestran las representaciones que puede realizar el programa, y en la segunda únicamente se realizan simulaciones para comprobar que tal responde nuestra sistema a distintas configuraciones de canal, y las a distintas configuraciones que hagamos nosotros de nuestro sistema (utilicemos una codificación u otra, utilicemos el ecualizador o el prefijo cíclico, etc…). Para finalizar, en el último capítulo se exponen las conclusiones obtenidas en este proyecto, así como posibles líneas de trabajo que seguir en próximas versiones del mismo. ABSTRACT. Systems based on OFDM (Orthogonal Frequency Division Multiplexing) technique are an evolution of traditional FDM (Frequency Division Multiplexing). Due to the use of OFDM systems are achieved by more efficient use of bandwidth. Nowadays, OFDM systems and variants of OFDM systems occupy a very important place in the world of communications, being implemented in standards such as DVB-T, ADSL, LTE, WiMAX, DAB (digital radio) and another more. For all these reasons, this project implements a OFDM system for performing various simulations for better understanding of OFDM system operation. The system has been simulated using Matlab. With system simulation we search to get two key objectives: to test the use of turbo codes (compared to traditional convolutional codes) and an equalizer. We do so with the intention of improving the quality of our system (receive fewer rates of bit error) in increasingly adverse conditions: lower signal-to-noise and multipath. For these reasons necessaries Matlab´s functions have been developed, and a GUI (User Graphical Interface) has been integrated so the program can be used in a easier and more didactic way. This project is divided into five chapters. In the second and third chapter of this project are developed the basis of OFDM systems. Being developed in the second one a pure theoretical study, while focusing only on block theory implemented in the OFDM system in the third one. The fourth chapter describes the options that can be carried out by the interface implemented. Furthermore the chapter is developed for the correct use of the interface. The fifth chapter is divided into two parts, the first part shows to us the representations that the program can perform, and the second one just makes simulations to check that our system responds to differents channel configurations (use of convolutional codes or turbo codes, the use of equalizer or cyclic prefix…). Finally, the last chapter presents the conclusions of this project and possible lines of work to follow in future versions.

On the performance of LDPC and turbo decoder architectures with unreliable memories

In this paper, we investigate the impact of faulty memory bit-cells on the performance of LDPC and Turbo channel decoders based on realistic memory failure models. Our study investigates the inherent error resilience of such codes to potential memory faults affecting the decoding process. We develop two mitigation mechanisms that reduce the impact of memory faults rather than correcting every single error. We show how protection of only few bit-cells is sufficient to deal with high defect rates. In addition, we show how the use of repair-iterations specifically helps mitigating the impact of faults that occur inside the decoder itself.