Max Log MAP Research Articles

Fast Two-Stage Max-Log MAP Detection Schemes for the Soft-Input Soft-Output Detection of Coded Generalized Spatial Modulation Signals

Fast Two-Stage Max-Log MAP Detection Schemes for the Soft-Input Soft-Output Detection of Coded Generalized Spatial Modulation Signals

Comparison of single-lane 100 Gb/s PAM-4 and DB-PAM-4 signals transmission based on 12G receiver with FFE and LDPC

Using low-bandwidth receivers to transmit single-wavelength 100 Gb/s data provides a low-cost and high-rate solution for the next generation passive optical networks (PONs). In this paper, we experimentally investigate the transmission of single-wavelength 100 Gb/s four-level pulse–amplitude modulation (PAM-4) and duobinary PAM-4 (DB-PAM-4) signal with a cost-effective 12 GHz PIN receiver. Feed-forward equalization (FFE) in conjunction with low-density parity-check (LDPC) is applied to enhance the bit error rate (BER) performance of the 25-km standard single-mode fiber (SSMF) transmitted signal. The Max-Log-maximum a posteriori (MAP) algorithm is utilized to computing soft information and provide it to LDPC decoding. As a result, under the same limited-bandwidth transmission conditions, DB-PAM-4 shows superior performance compared to PAM-4, reducing BER below the LDPC threshold 10−2. Error-free 25 km-transmission of 100 Gb/s DB-PAM-4 signal is realized employing 35-tap FFE and LDPC. On the contrast, the BER of PAM-4 cannot even be lower than 10−1, even with more taps and longer training sequences.

Model-Driven DNN Decoder for Turbo Codes: Design, Simulation, and Experimental Results

This paper presents a novel model-driven deep learning (DL) architecture, called TurboNet, for turbo decoding that integrates DL into the traditional max-log-maximum a posteriori (MAP) algorithm. The TurboNet inherits the superiority of the max-log-MAP algorithm and DL tools and thus presents excellent error-correction capability with low training cost. To design the TurboNet, the original iterative structure is unfolded as deep neural network (DNN) decoding units, where trainable weights are introduced to the max-log-MAP algorithm and optimized through supervised learning. To efficiently train the TurboNet, a loss function is carefully designed to prevent tricky gradient vanishing issue. To further reduce the computational complexity and training cost of the TurboNet, we can prune it into TurboNet+. Compared with the existing black-box DL approaches, the TurboNet+ has considerable advantage in computational complexity and is conducive to significantly reducing the decoding overhead. Furthermore, we also present a simple training strategy to address the overfitting issue, which enable efficient training of the proposed TurboNet+. Simulation results demonstrate TurboNet+'s superiority in error-correction ability, signal-to-noise ratio generalization, and computational overhead. In addition, an experimental system is established for an over-the-air (OTA) test with the help of a 5G rapid prototyping system and demonstrates TurboNet's strong learning ability and great robustness to various scenarios.

Iterative Interference Cancellation for Non‐orthogonal Multiple Access System

Non-orthogonal multiple access (NOMA) makes multiple users to overload the same wireless resources by utilizing the superposition coding principle, so that it can improve the system capacity and spectral efficiency. Various NOMA schemes are proposed, including the Power-domain NOMA (PD-NOMA). Most of them are using Successive interference cancellation (SIC) for detection, which limits the promised performance gain brought by NOMA due to the error propagation. An Iterative SIC and parallel interference cancellation (ISP) method is proposed for the PD-NOMA system. The MaxLog-MAP (MLM) algorithm (MAP is short for Maximum a posteriori) and SIC are used for performance comparison. Simulation results show that the Bit error rate (BER) performance of ISP is much better than that of SIC, and is close to that of MLM. It can perform even better than MLM at low signal to noise ratio for the user with lower power allocation. The ISP can obtain the promised performance gain brought by NOMA.

Soft MIMO detection through sphere decoding and box optimization

Achieving optimal detection performance with low complexity is one of the major challenges, mainly in multiple-input multiple-output (MIMO) detection. This paper presents three low-complexity Soft-Output MIMO detection algorithms that are based mainly on Box Optimization (BO) techniques. The proposed methods provide good performance with low computational cost using continuous constrained optimization techniques. The first proposed algorithm is a non-optimal Soft-Output detector of reduced complexity. This algorithm has been compared with the Soft-Output Fixed Complexity (SFSD) algorithm, obtaining lower complexity and similar performance. The two remaining algorithms are employed in a turbo receiver, achieving the max-log Maximum a Posteriori (MAP) performance. The two Soft-Input Soft-Output (SISO) algorithms were proposed in a previous work for soft-output MIMO detection. This work presents its extension for iterative decoding. The SISO algorithms presented are developed and compared with the SISO Single Tree Search algorithm (STS), in terms of efficiency and computational cost. The results show that the proposed algorithms are more efficient for high order constellation than the STS algorithm.

Simplified Non-Square Quadrature Amplitude Modulation Demapper for DOCSIS 3.1

A simplified soft demapper for non-square quadrature amplitude modulation (QAM) provided by fifth generation of high-speed data-over-cable systems (DOCSIS 3.1) is proposed. By using the geometric tendency of the non-square QAM constellation and “fold-and-overlap” approach, the non-linear log likelihood ratio (LLR) equation based on the max-log maximum a posteriori (MAP) algorithm can be approximated to linear equations. With this approximation, the proposed method can be applied to high-order non-square QAM, up to 8192 QAM, with negligible bit error rate performance degradation under additive white Gaussian noise and multipath flat-fading channels. Computational complexity is reduced by at least 93% compared to the LLR calculation based on the max-log MAP algorithm.

Low-complexity soft-decision parallel equaliser algorithms for Chinese next-generation-high-performance AV

ABSTRACTThe goals of the Chinese next-generation-high-performance AV (C-NGHPAV) system are to efficiently utilise the precious last 100 m of the coaxial cable of China’s state administration of radio film and television (SARFT) to achieve a gigabit transmission rate. This target demands higher requirements regarding the physical layer (PHY) throughput. The key to high throughput is to devise an effective method for increasing the execution speed of the demodulated soft decision and the adaptive equalisation algorithm. In this paper, the C-NGHPAV system architecture is introduced and the technical details of the key features are described. Firstly, quadrature amplitude modulation (QAM) and the binary phase shift keying (BPSK) soft-decision algorithm known as the max-log-maximum a posteriori (MAP) algorithm with logarithmic complexity (max-log-map-lc) are realised. The algorithm is less complex than other soft-decision algorithms. Secondly, a parallel architecture of adaptive quadrature rectangle-decomposit...

Exact Max-Log MAP Soft-Output Sphere Decoding via Approximate Schnorr–Euchner Enumeration

The complexity gains of sphere decoders (SDs) with Schnorr-Euchner enumeration and nonconstant amplitude constellations are limited by the required node ordering. Aiming at improving the implementation efficiency of SD without compromising optimality, this paper proposes a novel tree traversal for soft-output SDs providing the exact max-log MAP decoder performance. It consists of a predefined visiting order that approximates the exact Schnorr-Euchner enumeration (SEE) and a modified pruning metric that preserves the exact max-log MAP despite the approximate ordering. The proposed approach significantly improves both the computational complexity and the implementation cost of exact soft-output SDs compared with previous techniques. In particular, simulations show gains of 30%-56% in the required calculations for a 4 × 4 multiple-input multiple-output system with 16-quadrature amplitude modulation (QAM), and field-programmable gate array (FPGA) implementations show an average power reduction of 34%-50%.

DESIGN AND IMPLEMENTATION OF TURBO CODER FOR LTE ON FPGA

Recent wireless communication standards such as 3GPP-LTE, WiMax, DVB-SH and HSPA incorporates turbo code for its excellent performance. This work provides an overview of the novel class of channel codes referred to as turbo codes, which have been shown to be capable of performing close to the Shannon Limit. It starts with a brief discussion on turbo encoding, and then move on to describing the form of the iterative decoder most commonly used to decode turbo codes. Here, Turbo decoder uses original MAP algorithm instead of using the approximated Max log-MAP algorithm thereby it reduces the number iterations to decode the transmitted information bits. This paper presents the FPGA (Field Programmable Gate Array) implementation simulation results for Turbo encoder and decoder structure for 3GPP-LTE standard.

Reliability Distributions of Truncated Max-Log-MAP (MLM) Detectors Applied to Binary ISI Channels

The max-log-MAP (MLM) receiver is an approximated version of the well-known Bahl–Cocke–Jelinek-Raviv algorithm. The MLM algorithm is attractive due to its implementation simplicity. In practice, sliding-window implementations are preferred, whereby truncated signaling neighborhoods (around each transmission time instant) are considered. In this paper, we consider binary signaling sliding-window MLM receivers, where the MLM detector is truncated to a length- $m$ signaling neighborhood. Here, truncation is used to ease the burden of analysis. For any number $n$ of chosen times instants, we derive exact expressions for both 1) the joint distribution of the MLM symbol reliabilities, and 2) the joint probability of the erroneous MLM symbol detections. We show that the obtained expressions can be efficiently evaluated using Monte–Carlo techniques. The most computationally expensive operation (in each Monte–Carlo trial) is an eigenvalue decomposition of a size $2mn$ $\times$ $2mn$ matrix. The proposed method handles various scenarios such as correlated noise distributions, modulation coding, etc.

Research and Realization by FPGA of Turbo Codes

Turbo Code is a channel coding with excellent error-correcting performance in the condition of low noise-signal ratio.It has a superior decoding performance approaching the Shannon limit by adopting the random coding and decoding. This paper focuses on Turbo code and its implementation with FPGA and deeply analyzes the decoding theory and algorithm of Turbo code. Firstly, it analyzes the decoding theory of Turbo code. Then, it discusses key issues in the process of implementation with the most excellent and complicated Max—log—MAP algorithm. At last, it ends up with the Turbo encoder and decoding algorithm which hardware is successfully implemented finally.

Reduced-Complexity Iterative-Detection-Aided Generalized Space-Time Shift Keying

A novel reduced-complexity soft decision (SoD)-aided detector is proposed for the recent concept of space-time shift keying (STSK), where the detector's achievable performance is capable of closely approaching that of the optimal maximum a posteriori (MAP) detector. More specifically, we exploit a hybrid combination of the modified matched filtering concept and of reduced-complexity exhaustive search for the sake of reducing the MAP detector's decoding complexity. Furthermore, we extended this detector to support the class of generalized STSK (GSTSK) scheme that subsumes diverse multiple-input–multiple-output (MIMO) arrangements. The proposed reduced-complexity SoD-aided GSTSK detector also attains significantly lower complexity than the MAP detector while imposing only marginal performance degradation, which is in the range of 1–2 dB. As an optional means of further reducing complexity, the Markov Chain Monte Carlo (MCMC) algorithm is invoked for the proposed GSTSK detector. Our EXtrinsic Information Transfer (EXIT) chart analysis reveals that the proposed STSK detector is capable of closely approaching the optimal performance, whereas the GSTSK detector advocated exhibits a modest performance gap with respect to the max-log MAP detector.

Linear-constant log-map, a fast accurate algorithm for map decoding

This paper proposes a new approximation to be used for the correction function in the turbo decoding algorithm, called Linear-Constant-log Map. Max-log Map, Linear-log Map and Constant-log Map are the well known simplified versions of Jacobi-log Map (Maximum a Posteriori) algorithm already in use but they cannot meet a proper performance in term of output BER and clock consumption of the CPU decoding encoded bits. The proposed algorithm first breaks the correction function domain of the Jacobi logarithm to three subsections by determining the border points between these sections and then uses a linear function and two constant values as an approximation of this function. Using an AWGN channel model, simulation results show that the new algorithm is almost more than six times faster than Jacobi-log Map algorithm with a Bit Error Rate (BER) very close to it.

Reconfigurable Architecture For High Performance Turbo Decoder

This paper presents a reconfigurable architecture for high performance turbo decoder based on Max-Log Maximum a Posteriori (ML-MAP) algorithm using sliding window technique. The proposed architecture with branch metric standardization and state metric reallocation techniques improve the speed performance of the soft input soft output (SISO) decoder and is also configured to support three different constraint lengths. The intended reconfigurable decoder architecture has been implemented using Verilog HDL at RTL level and synthesized to investigate its performance in terms of area usage, timing delay and power. The power consumption of the device is measured using Synopsis Design Compiler – Simplicity Premier with DCP 2008 tool. This architecture provides a throughput of 107 Mbit/s with a power consumption of about 66.6mW.

Low-Complexity Multi-Stream Space-Time Codes—Part I: Direct-Sum Codes and Design Criteria

Multi-stream codes are used in wireless broadcast services where two or more priority classes of data are transmitted simultaneously, and a receiving terminal may decode one or more of the streams as a function of its receive signal to noise ratio. Present-day commercial cellular-based broadcast services generally utilize hierarchical modulation, a clever technique for embedding high and low-priority streams in a single modulated quadrature symbol. With many cellular standards moving to multiple-transmit antenna configurations, there are opportunities for designing new multi-stream encoding techniques that exploit these antennas. We examine the design of space-time codes that allow simple encoding and decoding of high and low-priority streams of data. A desirable multi-stream space-time code has a combination of good performance and low complexity. Performance is generally measured as coded bit-error rate, assuming max-log maximum aposteriori decoding. Complexity is measured as the effort needed to compute the aposteriori probabilities for either stream. Hierarchical modulation, for single-antenna transmissions, allows each stream to be decoded simply and independently. The paper comprises two parts. In this first part, we establish a general performance criterion for two-stream space-time codes and derive a formula for the complexity of max-log maximum aposteriori decoding of either stream. We also show how existing space-time codes may be combined with hierarchical modulation in a "direct sum". The direct-sum codes have low complexity, but we show in the second part of this paper that these codes can be significantly outperformed by non-direct-sum codes. One of our proposed two-stream codes performs 4 dB better than the Alamouti direct-sum code; it also has the benefit of decoding complexity in one stream that is a bounded function of the rate of the other.

고속 전력선 통신을 위한 터보 부호화된 OFDM

본 논문은 전력선 통신 채널에서 터보 부호와 OFDM 시스템의 성능을 분석하고 시뮬레이션 하였다. 전력선통신 시스템은 최악의 환경에서 동작되기 때문에 터보 부호는 전송 데이터의 신뢰성을 보장하기 위해서 사용되었다. 시뮬레이션의 성능은 비트 오류 확률로써 표현하였다. 터보 복호 알고리즘으로써 MAP과 Max-Log MAP 알고리즘, 그리고 SOVA를 선택하였고, 이것들의 성능을 비교하였다. 시뮬레이션 결과로부터, Max-Log MAP 알고리즘이 성능과 복잡도면에서 유망하다는 것이 입증되었다. 그리고 터보 부호기의 인터리버 길이가 100에서 5000으로 변할 때와 반복 횟수가 2번에서 8번으로 증가할 때, 각 각 3dB증가하였음을 알 수 있다. 본 논문에서의 결과는 OFDM를 기반으로 하는 전력선 통신 시스템에 적용될 수 있음을 보여준다. In this paper, performance of a turbo-coded OFDM system is analyzed and simulated in a power line communication channel. Since the power line communication system typically operates in a hostile environment, turbo code has been employed to enhance reliability of transmitted data. The performance is evaluated in terms of bit error probability. As turbo decoding algorithms, MAP (maximum a posteriori), Max-Log-MAP, and SOVA (soft decision viterbi output) algorithms are chosen and their performances are compared. From simulation results, it is demonstrated that Max-Log-MAP algorithm is promising in terms of performance and complexity. It is shown that performance is improved 3dB by increasing the number of iterations, 2 to 8, and interleaver length of a turbo encoder, 100 to 5000. The results in this paper can be applied to OFDM-based high-speed power line communication systems.

Design of Voltage Overscaled Low-Power Trellis Decoders in Presence of Process Variations

In hardware implementations of many signal processing functions, timing errors on different circuit signals may have largely different importance with respect to the overall signal processing performance. This motivates us to apply the concept of unequal error tolerance to enable the use of voltage overscaling at minimal signal processing performance degradation. Realization of unequal error tolerance involves two main issues, including how to quantify the importance of each circuit signal and how to incorporate the importance quantification into signal processing circuit design. We developed techniques to tackle these two issues and applied them to two types of trellis decoders including Viterbi decoder for convolutional code decoding and max-log-maximum a posteriori (MAP) decoder for turbo code decoding. Simulation results demonstrated promising energy saving potentials of the proposed design solution on both trellis decoding computation and memory storage at small decoding performance degradation.

Improved Turbo Equalization Schemes Robust to SNR Estimation Errors

An improved Max-Log-Map (MLM) turbo equalization algorithm called Scaled Max-Log-Map (SMLM) iterative equalization is presented. Simulations show that the scheme can dramatically outperform the MLM besides it is insensitive to SNR mismatch. Unfortunately, its performance is still much worse than that of Log-Map (LM) with exact SNR over high-loss channels. Accordingly, we also propose a new SNR estimation algorithm based on the reliability values of soft output extrinsic information of SMLM decoder. Using the new scheme, we obtain good performance close to that of LM with ideal knowledge of SNR.

An Improved Max-Log-MAP Algorithm for Turbo Decoding and Turbo Equalization

This paper proposes an improved Max-Log-maximum a posteriori (MAP) algorithm for turbo decoding and turbo equalization. The proposed algorithm utilizes the MacLaurin Series to expand the logarithmic term in the Jacobian logarithmic function of the Log-MAP algorithm. In terms of complexity, the proposed algorithm can easily be implemented by means of adders and comparators as this is the case for the Max-Log-MAP algorithm. In addition, simulation results show that the proposed algorithm performs very closely to the Log-MAP algorithm for both turbo decoding over additive-white-Gaussian-noise channels and turbo equalization over frequency-selective channels. Further, it is shown than even in a high-loss intersymbol-interference channel, the proposed algorithm preserves its performance close to that of the Log-Map algorithm, while there is a wide gap between the performance of the Log-MAP and Max-Log-MAP turbo equalizers

The Max-Log List Algorithm (MLLA)—A List-Sequence Decoding Algorithm That Provides Soft-Symbol Output

We present a soft decoding algorithm for convolutional codes that simultaneously yields soft-sequence output, i.e., list sequence (LS) decoding, and soft-symbol output. The max-log list algorithm (MLLA) introduced in this paper provides near-optimum soft-symbol output equal to that of the max-log maximum a posteriori (MAP) probability algorithm. Simultaneously, the algorithm produces an ordered list containing LS-MAP estimates. The MLLA exists in an optimum and a suboptimum version that are different in that the optimum version produces optimum LS-MAP decoding for arbitrary list lengths, while the suboptimum low-complexity version only provides the MAP, the second-order MAP, and the third-order MAP sequence estimates. For lists with more than three elements, MAP decoding is not guaranteed, but the LS decoding is close to the optimal. It is demonstrated that the suboptimum/optimum MLLA can be used to obtain the combination of soft-symbol and soft-sequence outputs at lower complexity than a previously published algorithm. Furthermore, the suboptimum MLLA is well suited for operation in an iterative list (turbo) decoder, since it is obtained by only minor modifications of the well-known Max-Log-MAP algorithm frequently used for decoding of the component codes of turbo codes. Another potential area of application for the suboptimum/optimum MLLA is joint source-channel LS decoding. Estimates of complexity and memory use, as well as performance evaluations of the suboptimum/optimum MLLA, are provided in this paper.