Turbo codes and turbo algorithms

In the first part of this paper, several basic ideas that prompted the coming of turbo codes are commented on. We then present some personal points of view on the main advances obtained in past years on turbo coding and decoding such as the circular trellis termination of recursive systematic convolutional codes and double-binary turbo codes associated with Max-Log-MAP decoding. A novel evaluation method, called genieinitialised iterative processing (GIIP), is introduced to assess the error performance of iterative processing. We show that using GIIP produces a result that can be viewed as a lower bound of the maximum likelihood iterative decoding and detection performance. Finally, two wireless communication systems are presented to illustrate recent applications of the turbo principle, the first one being multiple-input/multiple-output channel iterative detection and the second one multi-carrier modulation with linear precoding

Doctor of Philosophy

dissertationMultiple-input and multiple-output (MIMO) technique has emerged as a key feature for future generations of wireless communication systems. It increases the channel capacity proportionate to the minimum number of transmit and receive antennas. This dissertation addresses the receiver design for high-rate MIMO communications in at fading environments. The emphasis of the thesis is on the cases where channel state information (CSI) is not available and thus, clever channel estimation algorithms have to be developed to bene t from the maximum available channel capacity. The thesis makes four distinct novel contributions. First, we note that the conventional MCMC-MIMO detector presented in the prior work may deteriorate as SNR increases. We suggest and show through computer simulations that this problem to a great extent can be solved by initializing the MCMC detector with regulated states which are found through linear detectors. We also introduce the novel concept of staged-MCMC in a turbo receiver, where we start the detection process at a lower complexity and increase complexity only if the data could not be correctly detected in the present stage of data detection. Second, we note that in high-rate MIMO communications, joint data detection and channel estimation poses new challenges when a turbo loop is used to improve the quality of the estimated channel and the detected data. Erroneous detected data may propagate in the turbo loop and, thus, degrade the performance of the receiver signi cantly. This is referred to as error propagation. We propose a novel receiver that decorrelates channel estimation and the detected data to avoid the detrimental e ect of error propagation. Third, the dissertation studies joint channel estimation and MIMO detection over a continuously time-varying channel and proposes a new dual-layer channel estimator to overcome the complexity of optimal channel estimators. The proposed dual-layer channel estimator reduces the complexity of the MIMO detector with optimal channel estimator by an order of magnitude at a cost of a negligible performance degradation, on the order of 0.1 to 0.2 dB. The fourth contribution of this dissertation is to note that the Wiener ltering techniques that are discussed in this dissertation and elsewhere in the literature assume that channel (time-varying) statistics are available. We propose a new method that estimates such statistics using the coarse channel estimates obtained through pilot symbols. The dissertation also makes an additional contribution revealing di erences between the MCMC-MIMO and LMMSE-MIMO detectors. We nd that under the realistic condition where CSI has to be estimated, hence the available channel estimate will be noisy, the MCMC-MIMO detector outperforms the LMMSE-MIMO detector with a signi cant margin

A Study on the Iterative Decoding Method based on Layered Space Time Codes in Underwater Communications

The transmission of acoustic waves is limited because of various factors such as water temperature, salinity, depth in the underwater acoustic communication with a multi-path channel environment. And the performance is limited because the underwater acoustic communication uses low frequency band relative to wireless communication. In the underwater acoustic communication, the performance greatly depends on the characteristics of multi-path channel and the distortion of the received signal is increased due to reverberation and multi-path. Such channel characteristics cause ISI. It is necessary to study on equalizer technique and channel coding to correct error by multi-path and ISI because the optimal communication method has to be designed based on characteristics of multi-path channel. Therefore, in this paper, the performance according to various channel codes is analyzed by simulation. As a result, the turbo encoder based on iteration is suitable for underwater acoustic communication. We analyze a turbo pi code by permutation pattern, CRSC code, Puncturing pattern to improve BER performance and to solve a problem of error floor at high SNR. In the result of BER performance analysis, error floor phenomenon that occurs in the turbo encoder is removed and the performance is enhanced by 0.3 [dB]. And we proposed a low-power iterative decoding algorithm for turbo decoder basThe transmission of acoustic waves is limited because of various factors such as water temperature, salinity, and water depth in the underwater communications with a multi-path channel environments. The performance is also limited due to low frequency bands relative to wireless communications. The excessive multipath encountered in underwater communications channel is creating inter symbol interference (ISI), which is limiting factor to achieve a high data rate and bit error rate performance. Various different methods to cope with multipath situation have been developed. In addition to ISI. Removal of ISI is a challenging problem in view of difficult channel conditions. The optimal detector is a maximum likelihood detector, which can be realized for example by a soft Viterbi algorithm. Due to the length of the impulse response in the underwater communication channel, the number of states in the decoder will be increased. One well proven method to counteract ISI is the decision feedback equalized (DFE), which has been used in many underwater communication links. The other way to cope with ISI, iterative equalizer is used which constitutes an outer loop in the receiver. An inner loop consists of iterative decoder. This thesis proposed iterative coding based equalization for single carrier underwater communication channels. Among the iterative coding schemes, turbo pi coding scheme is optimal for underwater communications in aspect to performance, packet size, and underwater environments. As an outer code, DFE is used in the thesis. As an inner code, the turbo pi codes are used. In simulation results, this thesis confirms that the performance is the better as iteration numbers are increased. In the range of iteration number is three or four, we can achieve BER performance enhancement by 3.5 [dB] compared to non-iteration. However, performance gain can’t be achieved after third iterations, and we conclude the optimal iteration numbers are three. Based on the results of single input single output (SISO) systems, our focus expands to multiple input multiple output (MIMO) system. MIMO technique is being studied in underwater communications because of increasing the data rates. MIMO communication systems employ multiple sensors at the transmitter and receiver sides. They can yield significantly increased data rates and improved link reliability without additional bandwidth. Representative method is space-time trellis codes (STTCs). Normally, the candidate of outer codes are space-time block codes (STBCs) and STTCs. Representative method of STBCs is V-BLAST (Vertical-Bell Labs lAyered Space-Time). This system is obtained diversity or spatial multiplexing effect. However, STBCs for MIMO turbo equalization can’t obtain coding gain even if increasing number of iteration. This is the reason that the outputs of STBCs are not soft type symbols. The types of input symbols and output symbols must be soft symbols in order to improve performance by increasing number of iterations. This thesis proposes an efficient iterative layered STTC based on soft decision information with DFE equalizer for MIMO system in the underwater communication channel. As same as SISO turbo equalization models, two codes are concatenated in the serial fashion in MIMO system. The inner codes are turbo pi codes with 16 states and outer codes are STTCs with optimal generator polynomial. The symbols of outer decoder are then subtracted from the input and interleaved. The interleaved symbols are canceled a posteriori from the proceeding received symbol. Interleaving helps receiver convergence. There are two kinds of iterative models. The first model is outer iteration which is done between DFE and STTC decoder. The second one is inner iteration which is done between STTC and turbo pi decoder. Outer iteration type is conventional model and inner iteration model is proposed model in the thesis. To confirm the performance improvement of proposed inner iteration model for MIMO system, the simulation was conducted. The performance of inner iteration model is better than that of outer iteration model. Finally, based on proposed decoder model, this thesis confirms that the coding gain of 1 [dB] can be achieved compared to conventional decoder model in the MIMO system.제 1 장 서론 1 제 2 장 수중 통신에서 고려되는 채널 부호화 기법 6 2.1 채널 부호화 기법 6 2.1.1 강판정 기반 부호화 기술 8 2.1.2 연판정 기반 부호화 기술 17 2.2 성능 분석기반 최적의 부호화 기법 24 2.2.1 수중 채널 모델링 및 시뮬레이션 결과 24 2.2.2 Error floor 및 성능 향상을 위한 터보 Pi 부호화 기법 38 제 3 장 저전력 고속 터보 Pi 복호 알고리즘 44 3.1 Radix-4 알고리즘 44 3.2 Center-to-Top 알고리즘 46 3.3 Early-Stop 알고리즘 46 3.4 병렬 복호기 알고리즘 47 제 4 장 SISO 수중채널에서 반복기반의 최적의 복호 구조 50 4.1 채널 등화 기법 51 4.2 반복 기반의 터보 등화기 제안 55 4.3 제안된 반복 기반 터보 등화기의 최적 파라메타 설정 57 4.3.1 위상 오차에 따른 최적의 패킷 구조 제시 58 4.3.2 최적의 반복 횟수 분석 64 제 5 장 MIMO 수중채널에서 계층적 시공간 부호를 이용한 최적의 복호 구조 70 5.1 시공간 부호화 방식 71 5.1.1 시공간 블록 부호 71 5.1.2 시공간 격자 부호 74 5.1.3 계층적 시공간 부호 76 5.1.4 성능분석을 통한 최적의 계층적 시공간 부호화 방식 설정 78 5.2 MIMO에서의 채널 등화 기법 80 5.3 수중환경에서의 최적의 계층적 시공간 복호 구조 제안 83 5.3.1 시공간 부호화 방식의 강판정 및 연판정에 따른 성능 85 5.3.2 MIMO 수중환경에 적합한 최적의 등화 기법 86 5.3.3 반복 기반의 최적의 복호 구조 제안 및 성능 분석 88 제 6 장 결론 90 참고문헌 9

Bandwidth-efficient communication systems based on finite-length low density parity check codes

Low density parity check (LDPC) codes are linear block codes constructed by pseudo-random parity check matrices. These codes are powerful in terms of error performance and, especially, have low decoding complexity. While infinite-length LDPC codes approach the capacity of communication channels, finite-length LDPC codes also perform well, and simultaneously meet the delay requirement of many communication applications such as voice and backbone transmissions. Therefore, finite-length LDPC codes are attractive to employ in low-latency communication systems. This thesis mainly focuses on the bandwidth-efficient communication systems using finite-length LDPC codes. Such bandwidth-efficient systems are realized by mapping a group of LDPC coded bits to a symbol of a high-order signal constellation. Depending on the systems' infrastructure and knowledge of the channel state information (CSI), the signal constellations in different coded modulation systems can be two-dimensional multilevel/multiphase constellations or multi-dimensional space-time constellations. In the first part of the thesis, two basic bandwidth-efficient coded modulation systems, namely LDPC coded modulation and multilevel LDPC coded modulation, are investigated for both additive white Gaussian noise (AWGN) and frequency-flat Rayleigh fading channels. The bounds on the bit error rate (BER) performance are derived for these systems based on the maximum likelihood (ML) criterion. The derivation of these bounds relies on the union bounding and combinatoric techniques. In particular, for the LDPC coded modulation, the ML bound is computed from the Hamming distance spectrum of the LDPC code and the Euclidian distance profile of the two-dimensional constellation. For the multilevel LDPC coded modulation, the bound of each decoding stage is obtained for a generalized multilevel coded modulation, where more than one coded bit is considered for level. For both systems, the bounds are confirmed by the simulation results of ML decoding and/or the performance of the ordered-statistic decoding (OSD) and the sum-product decoding. It is demonstrated that these bounds can be efficiently used to evaluate the error performance and select appropriate parameters (such as the code rate, constellation and mapping) for the two communication systems.The second part of the thesis studies bandwidth-efficient LDPC coded systems that employ multiple transmit and multiple receive antennas, i.e., multiple-input multiple-output (MIMO) systems. Two scenarios of CSI availability considered are: (i) the CSI is unknown at both the transmitter and the receiver; (ii) the CSI is known at both the transmitter and the receiver. For the first scenario, LDPC coded unitary space-time modulation systems are most suitable and the ML performance bound is derived for these non-coherent systems. To derive the bound, the summation of chordal distances is obtained and used instead of the Euclidean distances. For the second case of CSI, adaptive LDPC coded MIMO modulation systems are studied, where three adaptive schemes with antenna beamforming and/or antenna selection are investigated and compared in terms of the bandwidth efficiency. For uncoded discrete-rate adaptive modulation, the computation of the bandwidth efficiency shows that the scheme with antenna selection at the transmitter and antenna combining at the receiver performs the best when the number of antennas is small. For adaptive LDPC coded MIMO modulation systems, an achievable threshold of the bandwidth efficiency is also computed from the ML bound of LDPC coded modulation derived in the first part

Estimation and detection techniques for doubly-selective channels in wireless communications

A fundamental problem in communications is the estimation of the channel. The signal transmitted through a communications channel undergoes distortions so that it is often received in an unrecognizable form at the receiver. The receiver must expend significant signal processing effort in order to be able to decode the transmit signal from this received signal. This signal processing requires knowledge of how the channel distorts the transmit signal, i.e. channel knowledge. To maintain a reliable link, the channel must be estimated and tracked by the receiver. The estimation of the channel at the receiver often proceeds by transmission of a signal called the 'pilot' which is known a priori to the receiver. The receiver forms its estimate of the transmitted signal based on how this known signal is distorted by the channel, i.e. it estimates the channel from the received signal and the pilot. This design of the pilot is a function of the modulation, the type of training and the channel. [Continues.

Design of a simulation platform to test next generation of terrestrial DVB

Digital Terrestrial Television Broadcasting (DTTB) is a member of our daily life routine, and nonetheless, according to new users’ necessities in the fields of communications and leisure, new challenges are coming up. Moreover, the current Standard is not able to satisfy all the potential requirements. For that reason, first of all, a review of the current Standard has been performed within this work. Then, it has been identified the needing of developing a new version of the standard, ready to support enhanced services, as for example broadcasting transmissions to moving terminals or High Definition Television (HDTV) transmissions, among others. The main objective of this project is the design and development of a physical layer simulator of the whole DVB-T standard, including both the complete transmission and reception procedures. The simulator has been developed in Matlab. A detailed description of the simulator both from a functional and an architectural point of view is included. The simulator is the base for testing any possible modifications that may be included into the DVB-T2 future standard. In fact, several proposed enhancements have already been carried out and their performance has been evaluated. Specifically, the use of higher order modulation schemes, and the corresponding modifications in all the system blocks, have been included and evaluated. Furthermore, the simulator will allow testing other enhancements as the use of more efficient encoders and interleavers, MIMO technologies, and so on. A complete set of numerical results showing the performance of the different parts of the system, are presented in order to validate the correctness of the implementation and to evaluate both the current standard performance and the proposed enhancements. This work has been performed within the context of a project called FURIA, which is a strategic research project funded by the Spanish Ministry of Industry, Tourism and Commerce. A brief description of this project and its consortium has been also included herein, together with an introduction to the current situation of the DTTB in Spain (called TDT in Spanish)

Wireless receiver designs: from information theory to VLSI implementation

Receiver design, especially equalizer design, in communications is a major concern in both academia and industry. It is a problem with both theoretical challenges and severe implementation hurdles. While much research has been focused on reducing complexity for optimal or near-optimal schemes, it is still common practice in industry to use simple techniques (such as linear equalization) that are generally significantly inferior. Although digital signal processing (DSP) technologies have been applied to wireless communications to enhance the throughput, the users' demands for more data and higher rate have revealed new challenges. For example, to collect the diversity and combat fading channels, in addition to the transmitter designs that enable the diversity, we also require the receiver to be able to collect the prepared diversity. Most wireless transmissions can be modeled as a linear block transmission system. Given a linear block transmission model assumption, maximum likelihood equalizers (MLEs) or near-ML decoders have been adopted at the receiver to collect diversity which is an important metric for performance, but these decoders exhibit high complexity. To reduce the decoding complexity, low-complexity equalizers, such as linear equalizers (LEs) and decision feedback equalizers (DFEs) are often adopted. These methods, however, may not utilize the diversity enabled by the transmitter and as a result have degraded performance compared to MLEs. In this dissertation, we will present efficient receiver designs that achieve low bit-error-rate (BER), high mutual information, and low decoding complexity. Our approach is to first investigate the error performance and mutual information of existing low-complexity equalizers to reveal the fundamental condition to achieve full diversity with LEs. We show that the fundamental condition for LEs to collect the same (outage) diversity as MLE is that the channels need to be constrained within a certain distance from orthogonality. The orthogonality deficiency (od) is adopted to quantify the distance of channels to orthogonality while other existing metrics are also introduced and compared. To meet the fundamental condition and achieve full diversity, a hybrid equalizer framework is proposed. The performance-complexity trade-off of hybrid equalizers is quantified by deriving the distribution of od. Another approach is to apply lattice reduction (LR) techniques to improve the ``quality' of channel matrices. We present two widely adopted LR methods in wireless communications, the Lenstra-Lenstra-Lovasz (LLL) algorithm [51] and Seysen's algorithm (SA), by providing detailed descriptions and pseudo codes. The properties of output matrices of the LLL algorithm and SA are also quantified. Furthermore, other LR algorithms are also briefly introduced. After introducing LR algorithms, we show how to adopt them into the wireless communication decoding process by presenting LR-aided hard-output detectors and LR-aided soft-output detectors for coded systems, respectively. We also analyze the performance of proposed efficient receivers from the perspective of diversity, mutual information, and complexity. We prove that LR techniques help to restore the diversity of low-complexity equalizers without increasing the complexity significantly. When it comes to practical systems and simulation tool, e.g., MATLAB, only finite bits are adopted to represent numbers. Therefore, we revisit the diversity analysis for finite-bit represented systems. We illustrate that the diversity of MLE for systems with finite-bit representation is determined by the number of non-vanishing eigenvalues. It is also shown that although theoretically LR-aided detectors collect the same diversity as MLE in the real/complex field, it may show different diversity orders when finite-bit representation exists. Finally, the VLSI implementation of the complex LLL algorithms is provided to verify the practicality of our proposed designs.Ph.D.Committee Chair: Ma, Xiaoli; Committee Member: Anderson, David; Committee Member: Barry, John; Committee Member: Chen, Xu-Yan; Committee Member: Kornegay, Kevi

Design of a simulation platform to test next generation of terrestrial DVB

Digital Terrestrial Television Broadcasting (DTTB) is a member of our daily life routine, and nonetheless, according to new users’ necessities in the fields of communications and leisure, new challenges are coming up. Moreover, the current Standard is not able to satisfy all the potential requirements. For that reason, first of all, a review of the current Standard has been performed within this work. Then, it has been identified the needing of developing a new version of the standard, ready to support enhanced services, as for example broadcasting transmissions to moving terminals or High Definition Television (HDTV) transmissions, among others. The main objective of this project is the design and development of a physical layer simulator of the whole DVB-T standard, including both the complete transmission and reception procedures. The simulator has been developed in Matlab. A detailed description of the simulator both from a functional and an architectural point of view is included. The simulator is the base for testing any possible modifications that may be included into the DVB-T2 future standard. In fact, several proposed enhancements have already been carried out and their performance has been evaluated. Specifically, the use of higher order modulation schemes, and the corresponding modifications in all the system blocks, have been included and evaluated. Furthermore, the simulator will allow testing other enhancements as the use of more efficient encoders and interleavers, MIMO technologies, and so on. A complete set of numerical results showing the performance of the different parts of the system, are presented in order to validate the correctness of the implementation and to evaluate both the current standard performance and the proposed enhancements. This work has been performed within the context of a project called FURIA, which is a strategic research project funded by the Spanish Ministry of Industry, Tourism and Commerce. A brief description of this project and its consortium has been also included herein, together with an introduction to the current situation of the DTTB in Spain (called TDT in Spanish)