Soft-input Soft-output Research Articles

An Adaptive Zero Forcing Maximum Likelihood Soft Input Soft Output MIMO Detectorabs

An adaptive zero forcing maximum likelihood soft input soft output (AZFML-SISO) detector for multiple input multiple output (MIMO) wireless systems is presented. Its performance in an iterative MIMO receiver is analyzed. The AZFML-SISO detector calculates the soft outputs, applying the ML approach to the list that contains only those signal vectors limited by a hypersphere around the zero forcing (ZF) solution. The performance of the algorithm is evaluated on a communication system based on the standard for single carrier broadband wireless communication IEEE 802.16, with three transmit and three receive antennas. It is shown by computer simulation that the computational complexity in an average sense of the receiver running the AZFML-SISO algorithm is reduced by 90% at the SNR values of 30dB and by 50% for SNR values of 15dB in comparison to the receiver with an ML detector, while the system performance degrades by less than 1dB.

Stochastic Decoding of Linear Block Codes With High-Density Parity-Check Matrices

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This correspondence extends the application of the recently proposed stochastic decoding approach to decode linear block codes with high-density parity-check matrices and discusses its hardware complexity. Results demonstrate decoding performance close to floating-point iterative soft-input soft-output (SISO) decoding while offering nodes with considerably lower complexity compared to fixed-point SISO decoding. </para>

Novel decoding of square QAM modulated mimo systems based on turbo multiuser detection

By introducing the bit-level multi-stream coded Layered Space-Time (LST) transmitter along with a novel iterative MultiStage Decoding (MSD) at the receiver, the paper shows how to achieve the near-capacity performance of the Multiple-Input Multiple-Output (MIMO) systems with square Quadrature Amplitude Modulation (QAM). In the proposed iterative MSD scheme, the detection at each stage is equivalent to multiuser detection of synchronous Code Division Multiple Access (CDMA) multiuser systems with the aid of the binary representation of the transmitted symbols. Therefore, the optimal Soft-Input Soft-Output (SISO) multiuser detection and low-complexity SISO multiuser detection can be utilized herein. And the proposed scheme with low-complexity SISO multiuser detection has polynomial complexity in the number of transmit antennas M, the number of receive antennas N, and the number of bits per constellation point M c . Simulation results demonstrate that the proposed scheme has similar Bit Error Rate (BER) performance to that of the known Iterative Tree Search (ITS) detection.

Soft-Output BEAST Decoding With Application to Product Codes

A bidirectional efficient algorithm for searching code trees (BEAST) is proposed for efficient soft-output decoding of block codes and concatenated block codes. BEAST operates on trees corresponding to the minimal trellis of a block code and finds a list of the most probable codewords. The complexity of the BEAST search is significantly lower than the complexity of trellis-based algorithms, such as the Viterbi algorithm and its list generalizations. The outputs of BEAST, a list of best codewords and their metrics, are used to obtain approximate a posteriori probabilities (APPs) of the transmitted symbols, yielding a soft-input soft-output (SISO) symbol decoder referred to as the BEAST-APP decoder. This decoder is employed as a component decoder in iterative schemes for decoding of product and incomplete product codes. Its performance and convergence behavior are investigated using extrinsic information transfer (EXIT) charts and compared to existing decoding schemes. It is shown that the BEAST-APP decoder achieves performances close to the Bahl-Cocke-Jelinek-Raviv (BCJR) decoder with a substantially lower computational complexity.

Graph-based detection algorithms for layered space-time architectures

We consider a unified framework to develop various graph-based detection algorithms for layered space-time architectures. We start with a factor graph representation for the communication channel, apply a belief propagation (BP) based algorithm for channel detection, and show that the detector achieves a near optimal performance even when number of receive antennas is smaller than number of transmit antennas. Based on this baseline algorithm, we further develop three different extensions of the BP detector that provide a good complexity/performance trade-off, which are especially useful for systems with a large number of antennas or when we encounter a frequency-selective fading channel with a long ISI span. Moreover, all the proposed detectors are soft-input soft-output in nature and they can be directly applied for use in turbo processing without any additional modifications. We study the performance of the new detectors via both simulations and convergence analysis using the measure of average mutual information.

Low complexity soft-input soft-output block decision feedback equalization

A low complexity soft-input soft-output (SISO) block decision feedback equalizer (BDFE) is presented for turbo equalization. The proposed method employs a sub-optimum sequence-based detection, where the soft-output of the equalizer is calculated by evaluating an approximation of the sequence-based a posteriori probability (APP) of the data symbol. The sequence-based APP approximation is enabled by the adoption of both soft a priori information and soft decision feedback, and it leads to better performance and faster convergence compared to symbol-based detection methods as used by most other low complexity equalizers. The performance and convergence property of the proposed algorithm is analyzed by using extrinsic information transfer (EXIT) chart. Both analytical and simulation results show that the new equalizer can achieve a performance similar to that of trellis-based equalization algorithms, with a complexity similar to linear SISO minimum mean square error equalizers.

Improved BDFE Using A Priori Information for Turbo Equalization

Turbo equalization improves communication system performance by iteratively exchanging information between soft-input soft-output (SISO) equalizer and SISO channel decoder. The trellis-based maximum a posteriori probability (MAP) algorithm serves as the optimum SISO equalizer for turbo equalization. However, MAP algorithm is unsuitable for systems with large modulation constellation size and severe inter-symbol interference (ISI) due to its prohibitively high computational complexity. In this paper, an improved SISO block decision feedback equalizer (BDFE) is proposed for low complexity turbo equalization. Unlike other sub-optimum equalizers which perform symbol by symbol detection, the proposed equalizer generates the soft output for each data bit by collecting information from a sequence of samples as in MAP algorithm. The sequence-based equalization is enabled by using not only soft a priori input from channel decoder, but also hard a priori information obtained from BDFE in previous iteration. The combination of soft a priori information and hard a priori information renders better performance with less iterations compared to other sub-optimum algorithms. In addition, the computational complexity of the proposed algorithm is on the same order as conventional SISO BDFE algorithm, and is much lower compared to the trellis-based MAP algorithm.

Double-Binary Circular Turbo Decoding Based on Border Metric Encoding

This brief presents an energy-efficient soft-input soft-output (SISO) decoder based on border metric encoding, which is especially suitable for nonbinary circular turbo codes. In the proposed method, the size of the branch memory is reduced to half and the dummy calculation is removed at the cost of a small-sized memory that holds encoded border metrics. Due to the infrequent accesses to the border memory and its small size, the energy consumed for SISO decoding is reduced by 26.2%. Based on the proposed SISO decoder and the dedicated hardware interleaver, a double-binary tail-biting turbo decoder is designed for the WiMAX standard using a 0.18-mum CMOS process, which can support 24.26 Mbps at 200 MHz.

Iterative Decoding Based on Error Pattern Correction

The error-pattern correction code is a code specialized to correct dominant error patterns observed at the channel detector output in heavy intersymbol interference channels. In this paper, we consider a turbo-equalizer system that utilizes the error-pattern correcting code (EPCC) as a building component. A soft-input soft-output (SISO) decoder for the EPCC is described, and the performance of the proposed turbo equalizer is compared with those of the conventional turbo equalizer and a low density parity check (LDPC) code system.

Block Iterative/Adaptive Frequency-Domain Channel Estimation for Cyclic-Prefixed Single-Carrier Broadband Wireless Systems

This paper presents a new block iterative/adaptive frequency-domain channel estimation scheme, in which a channel frequency response (CFR) is estimated iteratively by the proposed weighted element-wise block adaptive frequency-domain channel estimation (WEB-CE) scheme using the soft information obtained by a soft-input soft-output (SISO) decoder. In the WEB-CE, an equalizer coefficient is calculated by minimizing a weighted conditional squared-norm of the a posteriori error vector with respect to its correction term. Simulation results verify the superiority of the WEB-CE in a time-varying typical urban (TU) channel.

Low-complexity soft-input soft-output demodulation of orthogonal modulation

This letter is concerned with the soft-input soft-output (SISO) demodulation of M-ary (M = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> ) orthogonal modulation. We prove that the SISO orthogonal demodulation (SISO-OD) is equivalent to the SISO decoding of orthogonal Hadamard codes, for which we deduct a posteriori probability fast Hadamard transform (APP-FHT) algorithm. With FHT and the proposed APP-FHT, the demodulation complexity can be reduced from O(r2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> ) to O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> ) exponential/logarithm operations and O(r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> ) to O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> ) additions, respectively.

A Novel Quadratic Programming Model for Soft-Input Soft-Output MIMO Detection

In this letter, we propose a novel quadratic programming model for soft-input soft-output (SISO) multiple-input multiple-output (MIMO) detection that is compact for QAM constellations and easy to analyze. A semidefinite relaxation for this model is derived that can be solved by the interior-point method. We also give the sufficient conditions and necessary conditions to speed up the interior-point method.

Doubly Iterative Equalization of Continuous-Phase Modulation

In this paper, a doubly iterative receiver is proposed for joint turbo equalization, demodulation, and decoding of coded binary continuous-phase modulation (CPM) in multipath fading channels. The proposed receiver consists of three soft-input soft-output (SISO) blocks: a front-end soft-information-aided minimum mean square error (MMSE) equalizer followed by a CPM demodulator and a back-end channel decoder. The MMSE equalizer, combined with an a priori soft-interference canceler (SIC) and an a posteriori probability mapper, forms a SISO processor suitable for iterative processing that considers discrete-time CPM symbols which belong to a finite alphabet. The SISO CPM demodulator and the SISO channel decoder are both implemented by the a posteriori probability algorithm. The proposed doubly iterative receiver has a central demodulator coupled with both the front-end equalizer and the back-end channel decoder. A few back-end demodulation/decoding iterations are performed for each equalization iteration so as to improve the a priori information for the equalizer. As presented in the extrinsic information transfer (EXIT) chart analysis and simulation results for different multipath fading channels, this provides not only faster convergence to low bit error rates, but also lower computational complexity.

Turbo Decision Aided Receivers for Clipping Noise Mitigation in Coded OFDM

Orthogonal frequency division multiplexing (OFDM) is the modulation technique used in most of the high-rate communication standards. However, OFDM signals exhibit high peak average to power ratio (PAPR) that makes them particularly sensitive to nonlinear distortions caused by high-power amplifiers. Hence, the amplifier needs to operate at large output backoff, thereby decreasing the average efficiency of the transmitter. One way to reduce PAPR consists in clipping the amplitude of the OFDM signal introducing an additional noise that degrades the overall system performance. In that case, the receiver needs to set up an algorithm that compensates this clipping noise. In this paper, we propose three new iterative receivers with growing complexity and performance that operate at severe clipping: the first and simplest receiver uses a Viterbi algorithm as channel decoder whereas the other two implement a soft-input soft-output (SISO) decoder. Each soft receiver is analyzed through EXIT charts for different mappings. Finally, the performances of the receivers are simulated on both short time-varying channel and AWGN channel.

A SiGe BiCMOS analog SISO decoder with I/O interface

Although recent implementations of analog iterative decoders have proven their potential for higher decoding speed and less power consumption than their digital counterparts, the CMOS or conventional BiCMOS technologies used so far seem to be incapable to cope with the need for high throughput that high-speed applications require. Within this context this work presents the design and test results of a high-speed analog SISO (Soft-Input Soft-Output) channel decoder for an 8-bit trellis code by exploiting the high-speed features of SiGe heterojunction bipolar transistors (HBTs). It is one of the first successful implementations of an error-correcting decoder in SiGe BiCMOS technology, which incorporates a high-speed I/O interface. A high-level model of the mismatch effects indicates that there is no significant performance penalty. Moreover, simulations and performance evaluations of an analog Turbo decoder based on the designed SISO decoder are provided. Even though the IC of the SISO module was tested at a throughput up to 3 Mbps, simulation results show that the decoder is capable to operate at 50 Mbps. The measured power consumption is 860 mW and the die area is 3.4 × 3 mm2.

A reduced state SISO iterative decoding algorithm for serially concatenated continuous phase modulation

In this paper, serially concatenated continuous phase modulation (SCCPM) system is analyzed and a reduced state soft input soft output (SISO) a posteriori probability algorithm is proposed. Based on the reduced state sequence detection (RSSD), it has the more general form compared with other reduced state SISO algorithms. The proposed algorithm can greatly reduce the state number, thus leads to the computation complexity reduction. It also minimizes the degradation in Euclidean distance with decision feedback in the reduced state trellis. Analysis and simulation results show that the performance degradation is little with proper reduction scheme.

Performance Investigation of Soft-Decodable Runlength-Limited Codes With Different Minimum Runlength Constraints in High-Density Optical Recording

This paper investigates the performance of runlength-limited (RLL) codes with different d constraints in high-density optical recording, for both the low-density parity-check (LDPC)-coded Bliss scheme and the standard concatenation scheme. For the d = 5 constraint, we propose a low-complexity compression/decompression scenario that maps each 6-bit channel to a 3-bit compressed codeword by Gray-alike coding of the position of the transition in the 6-bit codeword, to compensate the density loss introduced by the redundancy of LDPC coding in the LDPC-coded Bliss scheme. Using a scalar diffraction channel model, we ran simulations to compare the performance of RLL codes with four different d constraints: d = 0,1,2, and 5, in near-field optical recording systems. The simulation results address the average bit error number in erroneous symbols after soft-input soft-output channel detection. Further, we evaluated the net density with different sets of simulation parameters, for both the LDPC-coded Bliss scheme and the standard concatenation scheme, considering jitter noise and additive white Gaussian noise, respectively.

Soft-Input Soft-Output Equalizers for Turbo Receivers: A Statistical Physics Perspective

Many algorithms in signal processing and digital communications must deal with the problem of computing the probabilities of the hidden state variables given the observations, i.e., the inference problem, as well as with the problem of estimating the model parameters. Such an inference and estimation problem is encountered, for e.g., in adaptive turbo equalization/demodulation where soft information about the transmitted data symbols has to be inferred in the presence of the channel uncertainty, given the received signal samples and a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> information provided by the decoder. An exact inference algorithm computes the a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">posteriori</i> probability (APP) values for all transmitted symbols, but the computation of APPs is known to be an NP-hard problem, thus, rendering this approach computationally prohibitive in most cases. In this paper, we show how many of the well-known low-complexity soft-input soft-output (SISO) equalizers, including the channel-matched filter-based linear SISO equalizers and minimum mean square error (MMSE) SISO equalizers, as well as the expectation-maximization (EM) algorithm-based SISO demodulators in the presence of the Rayleigh fading channel, can be formulated as solutions to a variational optimization problem. The variational optimization is a well-established methodology for low-complexity inference and estimation, originating from statistical physics. Importantly, the imposed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">variational</i> optimization framework provides an interesting link between the APP demodulators and the linear SISO equalizers. Moreover, it provides a new set of insights into the structure and performance of these widely celebrated linear SISO equalizers while suggesting their fine tuning as well.

A LOW-COMPLEXITY ITERATIVE RECEIVER FOR MULTIUSER SPACE-TIME BLOCK CODING SYSTEMS

In an iterative receiver of a bandwidth-efficient multiuser space-time block coding (STBC) system, the extrinsic information is iteratively exchanged among the soft-input soft-output (SISO) channel decoders, the soft-output multiuser detector and the soft-output M-ary demodulators. Error performance, complexity and efficiency of the extrinsic information exchange are the most important properties of an iterative receiver. Taking these factors into account, sigma mapping is first applied to M-QAM constellations to yield a low-complexity soft-output minimum mean squared error (MMSE) demodulator to be used in the iterative receiver. Then a low-complexity two-loop iterative receiver is proposed for the multiuser STBC systems. It is shown that by running an additional inner iteration (between the channel decoders and the M-ary demodulators) for every outer iteration (between the channel decoders and the multiuser detector), the proposed receiver is superior to the conventional one, in which only one inner iteration is executed per one outer iteration. The results in this paper are therefore useful for wireless applications that employ space-time coding and require a very high bandwidth efficiency.

Design issues in the implementation of versatile, high‐speed iterative decoders

AbstractThe ever increasing demand for high data rate communication, and the use of radio resource management techniques requiring frame‐by‐frame adaptive coding/modulation to match user demands and channel conditions, pose a number of crucial problems to the design of versatile, high‐speed iterative decoders, for both turbo‐like and low‐density parity‐check codes. Among them, we mention: The modification of the Soft‐Input Soft‐Output (SISO) algorithm in a way that permits its implementation using several parallel processors working independently on segments of the received frame. The collisions in the process of reading/writing into/from the memory by the parallel processors. The design of prunable interleavers covering a wide range of information and/or code words lengths while keeping good spreading properties. The design of codes yielding a wide range of code rates with good performance for the range of probability of error of interest. The paper will touch all the previous points, offering state‐of‐the art solutions and examples showing their performance. Copyright © 2007 John Wiley &amp; Sons, Ltd.