Iterative multiuser interference reduction: turbo CDMA

We view the asynchronous random code division multiple-access (CDMA) channel as a time-varying convolutional code. We study the case where the users encode their data, and, therefore, the single user transmitters and the CDMA channel appear as the concatenation of two coding systems. At the receiver we employ serial turbo decoding strategies. Unlike conventional turbo codes where both the inner and outer code may be selected, in our case, the inner code is due to the CDMA channel which we assume to be random. Nevertheless, the decoding system resembles the decoder of a serial turbo code and single-user performance is obtained even for numbers of users approaching the spreading code length     

SVD iterative decision feedback demodulation and detection of coded space-time unitary differential modulation

A new suboptimal demodulator based on iterative decision feedback demodulation (DFD), and a singular value decomposition (SVD) for estimation of unitary matrices, is introduced. Noncoherent communication over the Rayleigh flat-fading channel with multiple transmit and receive antennas, where no channel state information (CSI) is available at the receiver is investigated. With four transmit antennas, codes achieving bit-error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub o/) of -0.25 dB up to 3.5 dB, with coding rates of 1.6875 to 5.06 bits per channel use were found. The performance is compared to the mutual information upper bound of the capacity attaining isotropically random (IR) unitary transmit matrices. The codes achieve BER lower than 10/sup -4/ at E/sub b//N/sub o/ of 3.2 dB to 5.8 dB from this bound. System performance including the iterative DFD algorithm is compared to the one using Euclidean distance, as a reliability measure for demodulation . The DFD system presents a performance gain of up to 1.5 dB. Uncoded systems doing iterative DFD demodulation and idealized pilot sequence assisted modulation (PSAM) detection are compared. Iterative DFD introduces a gain of more than 1.2 dB. The coded system comprises a serial concatenation of turbo code and a unitary matrix differential modulation code. The receiver employs the high-performance coupled iterative decoding of the turbo code and the modulation code. Information-theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.     

Complexity Reduction in SISO Decoding of Block Codes

SISO decoding for block codes can be carried out based on a trellis representation of the code. However, the complexity entailed by such decoding is most often prohibitive and thus prevents practical implementation. This paper examines a new decoding scheme based on the soft-output Viterbi algorithm (SOVA) applied to a sectionalized trellis for linear block codes. The computational complexities of the new SOVA decoder and of the conventional SOVA decoder, based on a bit-level trellis, are theoretically analyzed and derived for different linear block codes. These results are used to obtain optimum sectionalizations of a trellis for SOVA. For comparisons, the optimum sectionalizations for Maximum A Posteriori (MAP) and Maximum Logarithm MAP (Max-Log-MAP) algorithms, and their corresponding computational complexities are included. The results confirm that the new SOVA decoder is the most computationally efficient SISO decoder, in comparisons to MAP and Max-Log-MAP algorithms. The simulation results of the bit error rate (BER) performance, assuming binary phase -- shift keying (BPSK) and additive white Gaussian noise (AWGN) channel, demonstrate that the performance of the new decoding scheme is not degraded. The BER performance of iterative SOVA decoding of serially concatenated block codes shows no difference in the quality of the soft outputs of the new decoding scheme and of the conventional SOVA.     

Bandwidth-efficient turbo trellis-coded modulation using puncturedcomponent codes

We present a bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes. The combination of turbo codes with powerful bandwidth-efficient component codes leads to a straightforward encoder structure, and allows iterative decoding in analogy to the binary turbo decoder. However, certain special conditions may need to be met at the encoder, and the iterative decoder needs to be adapted to the decoding of the component TCM codes. The scheme has been investigated for 8-PSK, 16-QAM, and 64-QAM modulation schemes with varying overall bandwidth efficiencies. A simple code choice based on the minimal distance of the punctured component code has also been performed. The interset distances of the partitioning tree can be used to fix the number of coded and uncoded bits. We derive the symbol-by-symbol MAP component decoder operating in the log domain, and apply methods of reducing decoder complexity. Simulation results are presented and compare the scheme with traditional TCM as well as turbo codes with Gray mapping. The results show that the novel scheme is very powerful, yet of modest complexity since simple component codes are used     

SVD iterative detection of turbo-coded multiantenna unitary differential modulation

A new suboptimal demodulator based on a singular value decomposition for estimation of unitary matrices is introduced. Noncoherent communication over the Rayleigh flat fading channel with multiple transmit and receive antennas, where no channel state information is available at the receiver is investigated. Codes achieving bit-error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 1.6-1.9 dB from code restricted capacity limit were found. At higher data rates, computation of code restricted capacity is impractical. Therefore, the mutual information upper bound of the capacity attaining isotropically random unitary transmit matrices was used. The codes achieve BER lower than 10/sup -4/ at E/sub b//N/sub 0/ of 3.2-6 dB from this bound, with coding rates of 1.125-5.06 bits per channel use, and different modulation decoding complexities. The codes comprise a serial concatenation of turbo code and a unitary matrix differential modulation code. The receiver employs the high-performance coupled iterative decoding of the turbo code and the modulation code. Information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.     

Adaptive Generator Sequence Selection in Multilevel Space–Time Trellis Codes

It has been shown that multilevel space–time trellis codes (MLSTTCs) designed by combining multilevel coding (MLC) with space–time trellis codes (STTCs) can provide improvement in diversity gain and coding gain of the STTCs. MLSTTCs assume perfect channel state information (CSI) at receiver and no knowledge of CSI at transmitter. Weighted multilevel space–time trellis codes (WMLSTTCs), designed by combining MLSTTCs and perfect CSI at transmitter are capable of providing improvement in coding gain of MLSTTCs. In this paper, we present improvement in performance of MLSTTCs by using channel feedback information from the receiver for adaptive selection of generator sequences. The selected generator sequences are used for encoding the component STTCs. The receiver compares current channel profile at receiver with a set of predetermined channel profiles, and sends an index of a predefined channel profile closest to the current channel profile to the transmitter. The transmitter selects a code set that matches best with the current channel profile at receiver using the index. The selected code set having different sets of generator sequences is used by STTC encoders to generate dynamic space–time trellis codes (DSTTCs). The DSTTCs act as component codes in multilevel coding for generating new codes henceforth referred to as multilevel dynamic space–time trellis codes (MLDSTTCs). Analysis and simulation results show that MLDSTTCs provide improvement in performance over MLSTTCs.     

Space-time codes and concatenated channel codes for wirelesscommunications

Following a brief historical perspective on channel coding, an introduction to space-time block codes is given. The various space-time codes considered are then concatenated with a range of channel codecs, such as convolutional and block-based turbo codes as well as conventional and turbo trellis codes. The associated estimated complexity issues and memory requirements are also considered. These discussions are followed by a performance study of various space-time and channel-coded transceivers. Our aim is first to identify a space-time code/channel code combination constituting a good engineering tradeoff in terms of its effective throughput, bit-error-rate performance, and estimated complexity. Specifically, the issue of bit-to-symbol mapping is addressed in the context of convolutional codes (CCs) and convolutional coding as well as Bose-Chaudhuri-Hocquenghem coding-based turbo codes in conjunction with an attractive unity-rate space-time code and multilevel modulation is detailed. It is concluded that over the nondispersive or narrow-band fading channels, the best performance versus complexity tradeoff is constituted by Alamouti's twin-antenna block space-time code concatenated with turbo convolutional codes. Further comparisons with space-time trellis codes result in similar conclusions     

Turbo codes for noncoherent FH-SS with partial band interference

Turbo codes are investigated in a slow frequency-hopped spread spectrum (FH-SS) system with partial band jamming. In addition, full-band thermal noise is present. The channel model is that of a partial-band jammer in which a fraction of the frequency band is jammed and the remaining fraction is unjammed. This paper focuses on the implementation and performance of a modified turbo decoder for this model. We refer to the knowledge that each transmitted bit is jammed as channel state information. We consider cases of known or unknown channel state and variable number of bits per hop. Our approach is to modify the calculation of branch transition probabilities inherent in the original turbo decoder. For the cases with no side information and multiple bits per hop, we iteratively calculate channel state estimates. Analytical bounds are derived and simulation is performed for noncoherent demodulation. The performance of turbo codes is compared with a Reed-Solomon and a concatenated code comprised of a convolutional inner code and Reed-Solomon outer code     

A Bandwidth Efficient Turbo Coding Scheme for VDSL Systems

The current forward error correction (FEC) scheme for very high bit-rate digital subscriber line (VDSL) systems in the ANSI standard employs a 16-state four-dimensional (4D) Wei code as the inner code and the Reed-Solomon (RS) code as the outer code. The major drawback of this scheme is that further improvement cannot be achieved without a substantial increase in the complexity and power penalty. Also, a VDSL system employing the 4D Wei-RS scheme operates far below the channel capacity. In 1993, powerful turbo codes were introduced whose performance closely approaches the Shannon limit. In this paper, we propose a bandwidth and power efficient turbo coding scheme for VDSL modems in order to obtain high data rates, extended loop reach and increased transmission robustness. We also propose a pipelined decoding scheme to reduce the latency at the receiver end. The objective of the proposed scheme is to provide a higher coding gain than that given by the 4D Wei-RS scheme, resulting in an improved performance of the VDSL modems in terms of bit rate, loop length and transmitting power. The scheme is investigated for various values of transmitting power, signaling frequencies and numbers of crosstalkers for a targeted bit error rate of 10⁻⁵ and is implemented in a system with a quadrature amplitude modulation in which a mixed set partitioning mapping is employed to reduce the decoding complexity. The effects of code complexity, interleaver length, the number of decoding iterations and the level of modulation on the performance of VDSL modems are explored. Simulation results are presented and compared to those of the 4D Wei-RS scheme. The results show that the choice of turbo codes not only provides a significant coding gain over the standard FEC scheme but also efficiently maximizes the loop length and bit rate at a very low transmitting power in the presence of dominant far-end crosstalk and intersymbol interference. In order to compare the hardware complexity, we synthesize the proposed and 4D Wei-RS schemes using SYNOPSYS with the target technology of Xilinx 4020e-3. The Xilinx field programmable gate array statistics of the proposed scheme is compared with that of the 4D Wei-RS scheme.     

Space-time turbo trellis codes for two, three, and four transmit antennas

New space-time turbo trellis codes (ST turbo TCs) with 4-phase-shift keying (PSK) and 8-PSK for two, three, and four transmit antennas in slow and fast fading channels are proposed in this paper. The component codes of the space-time turbo schemes are constructed by choosing the feedforward coefficients to maximize the minimum squared Euclidean distance and the feedback coefficients to minimize the iterative decoding threshold. The performance of the proposed ST turbo TCs with various memory orders, transmit antennas, and interleaver structures is evaluated by simulation. It is shown that the new codes achieve better performance than previously designed codes. The impact of antenna correlation and imperfect channel estimation on the code performance is also discussed.     

Design of LDPC-coded BICM using a semi-Gaussian approximation

This paper investigates analysis and design of Low-Density Parity-Check （LDPC） coded Bit Interleaved Coded Modulation （BICM） over Additive White Gaussian Noise （AWGN） channel. It focuses on Gray-labeled 8-ary Phase-Shift-Keying （8PSK） modulation and employs a Maximum A Posteriori （MAP） symbol-to-bit metric calculator at the receiver. An equivalent model of a BICM communication channel with ideal interleaving is presented. The probability distribution function of log-likelihood ratio messages from the MAP receiver can be approximated by a mixture of symmetric Gaussian densities. As a result semi-Gaussian approximation can be used to analyze the decoder. Extrinsic information transfer charts are employed to describe the convergence behavior of LDPC decoder. The design of irregular LDPC codes reduces to a linear programming problem on two-dimensional variable edge-degree distribution. This method allows irregular code design in a wider range of rates without any limit on the maximum node degree and can be used to design irregular codes having rates varying from 0.5275 to 0.9099. The designed convergence thresholds are only a few tenths, even a few hundredths of a decibel from the capacity limits. It is shown by Monte Carlo simulations that, when the block length is 30,000, these codes operate about 0.62-0.75 dB from the capacity limit at a bit error rate of 10s.     

Memory-Reduced Maximum A Posteriori Probability Decoding for High-Throughput Parallel Turbo Decoders

Wireless communication standards make use of parallel turbo decoder for higher data rate at the cost of large hardware resources. This paper presents a memory-reduced back-trace technique, which is based on a new method of estimating backward-recursion factors, for the maximum a posteriori probability (MAP) decoding. Mathematical reformulations of branch-metric equations are performed to reduce the memory requirement of branch metrics for each trellis stage. Subsequently, an architecture of MAP decoder and its scheduling based on the proposed back trace as well as branch-metric reformulation are presented in this work. Comparative analysis of bit-error-rate (BER) performances in additive white Gaussian noise channel environment for MAP as well as parallel turbo decoders are carried out. It has shown that a MAP decoder with a code rate of 1/2 and a parallel turbo decoder with a code rate of 1/3 have achieved coding gains of 1.28 dB at a BER of 10\(^{-5}\) and of 0.4 dB at a BER of 10\(^{-4}\), respectively. In order to meet high-data-rate benchmarks of recently deployed wireless communication standards, very large scale integration implementations of parallel turbo decoder with 8–64 MAP decoders have been reported. Thereby, savings of hardware resources by such parallel turbo decoders based on the suggested memory-reduced techniques are accounted in terms of complementary metal oxide semiconductor transistor count. It has shown that the parallel turbo decoder with 32 and 64 MAP decoders has shown hardware savings of 34 and 44 % respectively.     

Low complexity turbo equalization based on soft feedback interference cancellation

This letter presents a new soft feedback interference cancellation (SFIC) based equalizer suitable for iterative receivers applying turbo equalization. SFIC offers a very low computational complexity depending only linearly on the channel memory length. Despite its low complexity, SFIC shows a very good BER performance. Simulation results for the severely intersymbol interference distorted Proakis C channel show, that our approach performs within 0.5 dB to the powerful turbo equalization scheme based on MMSE linear filtering with time-varying coefficients and fails the mathematical optimum maximum a-posteriori (MAP) equalizer only by 1.2 dB.     

Iterative decoding of space-time differentially coded unitary matrix modulation

Noncoherent communication over the Rayleigh flat fading channel with multiple transmit and receive antennas is investigated. Codes achieving bit error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 0.8 to 2.8 dB from the capacity limit were found with coding rates of 0.5 to 2.25 bits per channel use. The codes are serial concatenation of a turbo code and a unitary matrix differential modulation code. The receiver is based on a high-performance joint iterative decoding of the turbo code and the modulation code. Information-theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.     

Nonhomogeneous Trellis codes for the Quasi-Synchronous Multiple-Access Binary adder channel with Two Users

A trellis code is {em homogeneous} if the number of branches emanating from each node (or state) in the trellis diagram is constant. For example, convolutional codes are linear homogeneous trellis codes. A trellis code is {em nonhomogeneous} if the number of branches emanating from each node in the trellis diagram is not the same. The two-user binary adder channel is a multiple-access channel with two binary inputs,x_{1}andx_{2}, and one ternary output,y = x_{1} + x_{2}, where the addition is done in the real number field. The adder channel is synchronous if both encoders and the decoder maintain block (frame) synchronism. It is quasi-synchronous if the encoders do not start their blocks at the same time, but the decoder knows the position of each block. The difference between the starting times of the blocks is called the slippage. The channel is asynchronous if no block synchronism exists among the encoders and the decoder. Some uniquely decodable code pairs(C_{1}, C_{2})are presented that can be used to transmit information reliably over the quasi-synchronous binary adder channel with two users. One of the codes is a nonhomogeneous trellis code, the other is a common block code. Our code rates are better than Deaett-Wolf codes and are close to or equal to the asymptotic rates of Kasami {em et al}. A method for calculating the rates of nonhomogeneous trellis codes is described. An algorithm for finding more uniquely decodable code pairs for the quasi-synchronous binary adder channel is formulated.     

Near-optimum decoding of product codes: block turbo codes

This paper describes an iterative decoding algorithm for any product code built using linear block codes. It is based on soft-input/soft-output decoders for decoding the component codes so that near-optimum performance is obtained at each iteration. This soft-input/soft-output decoder is a Chase decoder which delivers soft outputs instead of binary decisions. The soft output of the decoder is an estimation of the log-likelihood ratio (LLR) of the binary decisions given by the Chase decoder. The theoretical justifications of this algorithm are developed and the method used for computing the soft output is fully described. The iterative decoding of product codes is also known as the block turbo code (BTC) because the concept is quite similar to turbo codes based on iterative decoding of concatenated recursive convolutional codes. The performance of different Bose-Chaudhuri-Hocquenghem (BCH)-BTCs are given for the Gaussian and the Rayleigh channel. Performance on the Gaussian channel indicates that data transmission at 0.8 dB of Shannon's limit or more than 98% (R/C>0.98) of channel capacity can be achieved with high-code-rate BTC using only four iterations. For the Rayleigh channel, the slope of the bit-error rate (BER) curve is as steep as for the Gaussian channel without using channel state information     

Joint MAP equalization and channel estimation forfrequency-selective and frequency-flat fast-fading channels

This paper presents a new fractionally-spaced maximum a posteriori (MAP) equalizer for data transmission over frequency-selective fading channels. The technique is applicable to any standard modulation technique. The MAP equalizer uses an expanded hypothesis trellis for the purpose of joint channel estimation and equalization. The fading channel is estimated by coupling minimum mean square error techniques with the (fixed size) expanded trellis. The new MAP equalizer is also presented in an iterative (turbo) receiver structure. Both uncoded and conventionally coded systems (including iterative processing) are studied. Even on frequency-flat fading channels, the proposed receiver outperforms conventional techniques. Simulations demonstrate the performance of the proposed equalizer     

Iterative turbo decoder analysis based on density evolution

We track the density of extrinsic information in iterative turbo decoders by actual density evolution, and also approximate it by symmetric Gaussian density functions. The approximate model is verified by experimental measurements. We view the evolution of these density functions through an iterative decoder as a nonlinear dynamical system with feedback. Iterative decoding of turbo codes and of serially concatenated codes is analyzed by examining whether a signal-to-noise ratio (SNR) for the extrinsic information keeps growing with iterations. We define a “noise figure” for the iterative decoder, such that the turbo decoder will converge to the correct codeword if the noise figure is bounded by a number below zero dB. By decomposing the code's noise figure into individual curves of output SNR versus input SNR corresponding to the individual constituent codes, we gain many new insights into the performance of the iterative decoder for different constituents. Many mysteries of turbo codes are explained based on this analysis. For example, we show why certain codes converge better with iterative decoding than more powerful codes which are only suitable for maximum likelihood decoding. The roles of systematic bits and of recursive convolutional codes as constituents of turbo codes are crystallized. The analysis is generalized to serial concatenations of mixtures of complementary outer and inner constituent codes. Design examples are given to optimize mixture codes to achieve low iterative decoding thresholds on the signal-to-noise ratio of the channel     

Turbo codes for image transmission-a joint channel and sourcedecoding approach

This paper studies an application of turbo codes to compressed image/video transmission and presents an approach to improving error control performance through joint channel and source decoding (JCSD). The proposed approach to JCSD includes error-free source information feedback, error-detected source information feedback, and the use of channel soft values (CSV) for source signal postprocessing. These feedback schemes are based on a modification of the extrinsic information passed between the constituent maximum a posteriori probability (MAP) decoders in a turbo decoder. The modification is made according to the source information obtained from the source signal processor. The CSVs are considered as reliability information on the hard decisions and are further used for error recovery in the reconstructed signals. Applications of this joint decoding technique to different visual source coding schemes, such as spatial vector quantization, JPEG coding, and MPEG coding, are examined. Experimental results show that up to 0.6 dB of channel SNR reduction can be achieved by the joint decoder without increasing computational cost for various channel coding rates     

Adaptive multidimensional coded modulation over flat fadingchannels

We introduce a general adaptive coding scheme for Nakagami multipath fading channels. An instance of the coding scheme utilizes a set of 2L-dimensional (2L-D) trellis codes originally designed for additive white Gaussian noise (AWGN) channels. Any set of 2L-D trellis codes for AWGN channels can be used, Sets for which all codes can be generated by the same encoder and decoded by the same decoder are of particular interest. A feedback channel between the transmitter and receiver makes it possible to transmit at high spectral efficiencies under favorable channel conditions and respond to channel degradation through a smooth reduction of the spectral efficiency. We develop a general technique to determine the average spectral efficiency of the coding scheme for any set of 2L-D trellis codes. As an illustrative example, we calculate the average spectral efficiency of an adaptive codec utilizing eight 4-D trellis codes. The example codec is based on the International Telecommunications Union's ITU-T V.34 modem standard