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Neural network implementation of the bcjr algorithm

DIGITAL SIGNAL PROCESSING 2007年第1期17卷 353-359页

作者： Sazli, Murat Husnu Isik, Can Ankara Univ Fac Engn Dept Elect Engn TR-06100 Ankara Turkey Syracuse Univ LC Smith Coll Engn & Comp Sci Dept Elect Engn Syracuse NY 13244 USA

In this paper, we first show that the bcjr algorithm (or Bahl algorithm) can be implemented via some matrix manipulations. As a direct result of this, we also show that this algorithm is equivalent to a feedforward neural network structure. We verified through computer simulations that this novel neural network implementation yields identical results with the BOR algorithm. (c) 2006 Elsevier Inc. All rights reserved.

关键词： turbo codes turbo coding/decoding channel coding Bahl algorithm bcjr algorithm MAP algorithm neural networks

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On memory redundancy in the bcjr algorithm for nonrecursive shift register processes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第4期46卷 1580-1584页

作者： Schmidt, M Fettweis, GP Dresden Univ Technol Mannesmann Mobilfunk Chair Chair Mobile Commun Syst D-01062 Dresden Germany

For computation of a posteriori probabilities (APP's), the well-known bcjr algorithm is often applied. If the underlying model is a nonrecursive shift register process, it will be shown that this algorithm obtains a general memory redundancy if the computation is performed over a commutative semiring with an absorbing zero element. The result is of particular interest for the bcjr algorithm carried out in the mau-log domain.

关键词： APP decoding bcjr algorithm log domain max-log domain semiring

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A modification of the bcjr algorithm over the flat fading channel and its application to turbo decoding

A modification of the BCJR algorithm over the flat fading ch...

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IEEE/CIC International Conference on Communications in China (ICCC)

作者： Yuan, Haifeng Wu, Ming-Wei Kam, Pooi-Yuen Natl Univ Singapore Dept Elect & Comp Engn Singapore 117576 Singapore Zhejiang Univ Sci & Technol Sch Informat & Elect Engn Hangzhou 310023 Peoples R China Natl Univ Singapore Res Inst Ctr Adv Microelect Devices Suzhou 215123 Peoples R China

ISBN: (纸本)9781538645024

A modification of the bcjr algorithm is derived for convolutionally-coded transmissions over the time-selective, frequency-flat, Rayleigh fading channel with pilot-symbol-assisted channel estimation. The derivation demonstrates why the minimum mean-square error (MMSE) channel estimator is required and how the acquired channel estimate and the estimation error variance should be used in the maximum a posteriori probability decoding. Using the LTE turbo code as an example, we show that the newly derived algorithm outperforms the conventional bcjr algorithm in both standard turbo decoding and iterative channel estimation and decoding. The work demonstrates the importance of incorporating channel estimation accuracy in turbo decoding.

关键词： bcjr algorithm fading channel LTE turbo code iterative decoding channel estimation accuracy

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Reduced complexity equalization of MIMO systems with a fixed-lag smoothed M-bcjr algorithm

Reduced complexity equalization of MIMO systems with a fixed...

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6th IEEE Workshop on Signal Processing Advances in Wireless Communications

作者： Vithanage, CM Andrieu, C Piechocki, RJ Yee, MS Univ Bristol Dept Math Bristol BS8 1TW Avon England

ISBN: (纸本)0780388674

M-bcjr algorithm is a reduced state version of the bcjr algorithm and selects a set of active states in the forward recursion based on an estimation of the filtered probability distribution of states at each time. We propose to use instead an estimation of the fixed-lag smoothed probability distribution of states with a non zero lag. Our-implementation uses a Gaussian approximation to estimate these distributions with a low complexity, using the principle of Probabilistic Data Association (PDA). The performance of the M-bcjr can be seen to be greatly improved as a result while remaining robust against changes in the channel multipath profile.

关键词： bcjr algorithm M algorithm probabilistic data association MIMO equalization

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RNN bcjr: a fully trainable version of the additive bcjr algorithm

RNN BCJR: a fully trainable version of the additive BCJR alg...

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IEEE International Conference on Communications (IEEE ICC)

作者： Montorsi, Guido Ripani, Barbara Politecn Torino DET Turin Italy

ISBN: (纸本)9781538674628

We present a new version of the additive bcjr algorithm based on a recurrent neural network whose structure reflects an underlying trellis diagram. Starting from a matrix version of the equations of the additive bcjr algorithm, we derive the equivalent trainable recurrent neural network model, named Recurrent Neural Network (RNN) bcjr. The RNN bcjr consists of a linear layer to form the edge metrics from the state and input metrics, followed by a SOFTMAX/max* layer to marginalize the edge metrics back to the state and output spaces. We derive the recursions for delta propagation to train the two-layer mixing matrices from the output cost function. Unlike the previous approaches, the proposed RNN bcjr can completely replace the bcjr and is trainable from the cost functions of the outputs. The trained RNN bcjr achieves the same optimal performance as the bcjr when the model is known but at the same time can adapt itself to model mismatch, thus outperforming bcjr.

关键词： Additive SISO bcjr algorithm model-driven recurrent neural networks

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Neural Network-Aided bcjr algorithm for Joint Symbol Detection and Channel Decoding 34

Neural Network-Aided BCJR Algorithm for Joint Symbol Detecti...

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34th IEEE Workshop on Signal Processing Systems (SiPS)

作者： Tsai, Wen-Chiao Teng, Chieh-Fang Ou, Han-Mo Wu, An-Yeu (Andy) Natl Taiwan Univ Dept Elect Engn Taipei Taiwan Natl Taiwan Univ Grad Inst Elect Engn Taipei Taiwan

ISBN: (纸本)9781728180991

Recently, deep learning-assisted communication systems have achieved many eye-catching results and attracted more and more researchers in this emerging field. Instead of completely replacing the functional blocks of communication systems with neural networks, a hybrid manner of bcjrNet symbol detection is proposed to combine the advantages of the bcjr algorithm and neural networks. However, its separate block design not only degrades the system performance but also results in additional hardware complexity. In this work, we propose a bcjr receiver for joint symbol detection and channel decoding. It can simultaneously utilize the trellis diagram and channel state information for a more accurate calculation of branch probability and thus achieve global optimum with 2.3 dB gain over separate block design. Furthermore, a dedicated neural network model is proposed to replace the channel-model-based computation of the bcjr receiver, which can avoid the requirements of perfect CSI and is more robust under CSI uncertainty with 1.0 dB gain.

关键词： bcjr algorithm Neural network Symbol detection Channel decoding Turbo codes

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FPGA IMPLEMENTATION OF TURBO DECODERS USING bcjr algorithm

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GA...

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JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY 2011年第4期26卷 823-832页

作者： Atar, Onur Sazli, Murat H. Tubitak UZAY TR-06531 Ankara Turkey Ankara Univ Elekt Muhendisligi TR-06100 Ankara Turkey

The most difficult design issue for turbo codes, which is the most recent and successful channel coding method to approach the channel capacity limit, is the design of the iterative decoders which perform calculations for all possible states of the encoders. bcjr (MAP) algorithm, which is used for turbo decoders, embodies complex mathematical operations such as division, exponential and logarithm calculations. Therefore, bcjr algorithm was avoided and the sub-optimal derivatives of this algorithm such as Log-MAP and Max-Log-MAP were preferred for turbo decoder implementations. bcjr algorithm was reformulated and wrapped into a suitable structure for FPGA implementations at previous works [1]. Reformulated bcjr algorithm is implemented in this work. Complex mathematical operations which run slowly on hardware (division, exponential and logarithm calculations) are read from look-up-tables and high performance calculation structures are established. Implemented system is verified through simulations. It is observed that the BER performance obtained is better than the Log-MAP algorithm as expected.

关键词： bcjr algorithm MAP algorithm Turbo decoder FPGA

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Reduced state bcjr algorithms for one- and two-dimensional equalization

Reduced state BCJR algorithms for one- and two-dimensional e...

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33rd IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Zhu, Ying Belzer, Benjamin Sivakumar, Krishnamoorthy Washington State Univ Sch EECS Pullman WA 99164 USA

ISBN: (纸本)9781424414833

We consider bcjr-like soft-input soft-output (SISO) iterative detection algorithms for 1D and 2D binary-input ISI channels with AWGN. The complexity of bcjr algorithms grows exponentially with the size of the ISI mask and is an important concern with their implementation. We consider new techniques to reduce the complexity of bcjr algorithms by decreasing the effective number of states in the trellis. The proposed state reduction technique does particularly well for mixed phase sequence ISI masks, which have higher weights for the center taps and lower weights for the peripheral taps. Other complexity reduction techniques proposed in the literature perform poorly for such masks. Moreover, the complexity of the proposed state reduction technique is comparable to other reduced complexity techniques reported in the literature. Experimental results are provided to demonstrate the advantages of the proposed state reduction technique.

关键词： intersymbol interference equalization bcjr algorithm reduced complexity

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An efficient MAP decoding algorithm which uses the bcjr and the recursive techniques

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2001年第10期E84A卷 2389-2396页

作者： Shibuya, R Kaji, Y Nara Inst Sci & Technol Grad Sch Informat Sci Ikoma 6300101 Japan

A new algorithm for the maximum a posteriori (MAP) decoding of linear block codes is presented. The proposed algorithm can be regarded as a conventional bcjr algorithm for a section trellis diagram, where branch metrics of the trellis are computed by the recursive MAP algorithm proposed by the authors. The decoding complexity of the proposed algorithm depends on the sectionalization of the trellis. A systematic way to find the optimum sectionalization which minimizes the complexity is also presented. Since the algorithm can be regarded as a generalization of both of the bcjr and the recursive MAP algorithms, the complexity of the proposed algorithm cannot be larger than those algorithms, as far as the sectionalization is chosen appropriately.

关键词： MAP decoding bcjr algorithm recursive algorithm section trellis diagram optimum sectionalization

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Prefiltered space-time M-bcjr equalizer for frequency-selective channels

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IEEE TRANSACTIONS ON COMMUNICATIONS 2002年第5期50卷 742-753页

作者： Fragouli, C Al-Dhahir, N Diggavi, SN Turin, W Natl Capodistrian Univ Athens Athens 17373 Greece AT&T Labs Res Shannon Lab Florham Pk NJ 07932 USA

This paper addresses the problem of soft equalization for space-time-coded transmissions over frequency-selective fading channels. The structure of the space-time code is embedded in the channel impulse response for efficient joint equalization and decoding. The proposed equalization/decoding approach uses a prefliter to concentrate the effective channel power in a small number of taps followed by a reduced-complexity maximum a posteriori probability (MAP) equalizer/decoder to produce soft decisions. The prefilter introduces residual intersymbol interference which degrades the performance of MAP when applied to the trellis of the shortened channel. However, the shape of the overall shortened channel impulse response allows the M-algorithm to approximate the prefiltered MAP performance with a small number of states. Based on this general framework, we investigate several enhancements such as using different prefilters for the forward and backward recursions, concatenating two trellis steps during decoding, and temporal oversampling. The performance is evaluated through simulations over the EDGE typical urban channel.

关键词： bcjr algorithm equalization FIR prefilters space-time coding

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