Iterative Decoding and Turbo Equalization: The Z-Crease Phenomenon

Iterative probabilistic inference, popularly dubbed the soft-iterative paradigm, has found great use in a wide range of communication applications, including turbo decoding and turbo equalization. The classic approach of analyzing the iterative approach inevitably use the statistical and information-theoretical tools that bear ensemble-average flavors. This paper consider the per-block error rate performance, and analyzes it using nonlinear dynamical theory. By modeling the iterative processor as a nonlinear dynamical system, we report a universal "Z-crease phenomenon:" the zig-zag or up-and-down fluctuation -- rather than the monotonic decrease -- of the per-block errors, as the number of iteration increases. Using the turbo decoder as an example, we also report several interesting motion phenomenons which were not previously reported, and which appear to correspond well with the notion of "pseudo codewords" and "stopping/trapping sets." We further propose a heuristic stopping criterion to control Z-crease and identify the best iteration. Our stopping criterion is most useful for controlling the worst-case per-block errors, and helps to significantly reduce the average-iteration numbers.Comment: 6 page

Interleaving Gains for Receive Diversity Schemes of Distributed Turbo Codes in Wireless Half–Duplex Relay Channels

This paper proposes the interleaving gain in two different distributed turbo-coding schemes: Distributed Turbo Codes (DTC) and Distributed Multiple Turbo Codes (DMTC) for half-duplex relay system as an extension of our previous work on turbo coding interleaver design for direct communication channel. For these schemes with half-duplex constraint, the source node transmits its information with the parity bit sequence(s) to both the relay and the destination nodes during the first phase. The relay received the data from the source and process it by using decode and forward protocol. For the second transmission period, the decoded systematic data at relay is interleaved and re-encoded by a Recursive Systematic Convolutional (RSC) encoder and forwarded to the destination. At destination node, the signals received from the source and relay are processed by using turbo log-MAP iterative decoding for retrieving the original information bits. We demonstrate via simulations that the interleaving gain has a large effect with DTC scheme when we use only one RSC encoder at both the source and relay with best performance when using Modified Matched S-Random (MMSR) interleaver. Furthermore, by designing a Chaotic Pseudo Random Interleaver (CPRI) as an outer interleaver at the source node instead of classical interleavers, our scheme can add more secure channel conditions

Turbo codes: the phase transition

Turbo codes are a very efficient method for communicating reliably through a noisy channel. There is no theoretical understanding of their effectiveness. In [1] they are mapped onto a class of disordered spin models. The analytical calculations concerning these models are reported here. We prove the existence of a no-error phase and compute its local stability threshold. As a byproduct, we gain some insight into the dynamics of the decoding algorithm.Comment: 26 pages, 3 eps figure

A Continuous-Time Recurrent Neural Network for Joint Equalization and Decoding – Analog Hardware Implementation Aspects

Equalization and channel decoding are “traditionally” two cascade processes at the receiver side of a digital transmission. They aim to achieve a reliable and efficient transmission. For high data rates, the energy consumption of their corresponding algorithms is expected to become a limiting factor. For mobile devices with limited battery’s size, the energy consumption, mirrored in the lifetime of the battery, becomes even more crucial. Therefore, an energy-efficient implementation of equalization and decoding algorithms is desirable. The prevailing way is by increasing the energy efficiency of the underlying digital circuits. However, we address here promising alternatives offered by mixed (analog/digital) circuits. We are concerned with modeling joint equalization and decoding as a whole in a continuous-time framework. In doing so, continuous-time recurrent neural networks play an essential role because of their nonlinear characteristic and special suitability for analog very-large-scale integration (VLSI). Based on the proposed model, we show that the superiority of joint equalization and decoding (a well-known fact from the discrete-time case) preserves in analog. Additionally, analog circuit design related aspects such as adaptivity, connectivity and accuracy are discussed and linked to theoretical aspects of recurrent neural networks such as Lyapunov stability and simulated annealing

Optical Time-Frequency Packing: Principles, Design, Implementation, and Experimental Demonstration

Time-frequency packing (TFP) transmission provides the highest achievable spectral efficiency with a constrained symbol alphabet and detector complexity. In this work, the application of the TFP technique to fiber-optic systems is investigated and experimentally demonstrated. The main theoretical aspects, design guidelines, and implementation issues are discussed, focusing on those aspects which are peculiar to TFP systems. In particular, adaptive compensation of propagation impairments, matched filtering, and maximum a posteriori probability detection are obtained by a combination of a butterfly equalizer and four 8-state parallel Bahl-Cocke-Jelinek-Raviv (BCJR) detectors. A novel algorithm that ensures adaptive equalization, channel estimation, and a proper distribution of tasks between the equalizer and BCJR detectors is proposed. A set of irregular low-density parity-check codes with different rates is designed to operate at low error rates and approach the spectral efficiency limit achievable by TFP at different signal-to-noise ratios. An experimental demonstration of the designed system is finally provided with five dual-polarization QPSK-modulated optical carriers, densely packed in a 100 GHz bandwidth, employing a recirculating loop to test the performance of the system at different transmission distances.Comment: This paper has been accepted for publication in the IEEE/OSA Journal of Lightwave Technolog

Decoding the `Nature Encoded\u27 Messages for Wireless Networked Control Systems

Because of low installation and reconfiguration cost wireless communication has been widely applied in networked control system (NCS). NCS is a control system which uses multi-purpose shared network as communication medium to connect spatially distributed components of control system including sensors, actuator, and controller. The integration of wireless communication in NCS is challenging due to channel unreliability such as fading, shadowing, interference, mobility and receiver thermal noise leading to packet corruption, packet dropout and packet transmission delay. In this dissertation, the study is focused on the design of wireless receiver in order to exploit the redundancy in the system state, which can be considered as a `nature encoding\u27 for the messages. Firstly, for systems with or without explicit channel coding, a decoding procedures based on Pearl\u27s Belief Propagation (BP), in a similar manner to Turbo processing in traditional data communication systems, is proposed to exploit the redundancy in the system state. Numerical simulations have demonstrated the validity of the proposed schemes, using a linear model of electric generator dynamic system. Secondly, we propose a quickest detection based scheme to detect error propagation, which may happen in the proposed decoding scheme when channel condition is bad. Then we combine this proposed error propagation detection scheme with the proposed BP based channel decoding and state estimation algorithm. The validity of the proposed schemes has been shown by numerical simulations. Finally, we propose to use MSE-based transfer chart to evaluate the performance of the proposed BP based channel decoding and state estimation scheme. We focus on two models to evaluate the performance of BP based sequential and iterative channel decoding and state estimation. The numerical results show that MSE-based transfer chart can provide much insight about the performance of the proposed channel decoding and state estimation scheme. In this dissertation, the study is focused on the design of wireless receiver in order to exploit the redundancy in the system state, which can be considered as a `nature encoding\u27 for the messages. Firstly, for systems with or without explicit channel coding, a decoding procedures based on Pearl\u27s Belief Propagation (BP), in a similar manner to Turbo processing in traditional data communication systems, is proposed to exploit the redundancy in the system state. Numerical simulations have demonstrated the validity of the proposed schemes, using a linear model of electric generator dynamic system. Secondly, we propose a quickest detection based scheme to detect error propagation, which may happen in the proposed decoding scheme when channel condition is bad. Then we combine this proposed error propagation detection scheme with the proposed BP based channel decoding and state estimation algorithm. The validity of the proposed schemes has been shown by numerical simulations. Finally, we propose to use MSE-based transfer chart to evaluate the performance of the proposed BP based channel decoding and state estimation scheme. We focus on two models to evaluate the performance of BP based sequential and iterative channel decoding and state estimation. The numerical results show that MSE-based transfer chart can provide much insight about the performance of the proposed channel decoding and state estimation scheme