A soft decoding scheme for vector quantization over a CDMA channel

The optimal decoding of vector quantization (VQ) over a code-division multiple-access (CDMA) channel is too complicated for systems with a medium-to-large number of users. This paper presents a low-complexity, suboptimal decoder for VQ over a CDMA channel. The proposed decoder is built from a soft-output multiuser detector, a soft bit estimator, and the optimal soft VQ decoding of an individual user. Simulation results obtained over both additive white Gaussian noise and flat Rayleigh fading channels show that with a lower complexity and good performance, the proposed decoding scheme is an attractive alternative to the more complicated optimal decoder.     

Soft multiuser decoding for vector quantization over a CDMA channel

An approach to optimal soft decoding for vector quantization (VQ) over a code-division multiple-access (CDMA) channel is presented. The decoder of the system is soft in the sense that the unquantized outputs of the matched filters are utilized directly for decoding (no decisions are taken), and optimal according to the minimum mean-squared error (MMSE) criterion. The derived decoder utilizes a priori source information and knowledge of the channel characteristics to combat channel noise and multiuser interference in an optimal fashion. Hadamard transform representations for the user VQs are employed in the derivation and for the implementation of the decoder. The advantages of this approach are emphasized. Suboptimal versions of the optimal decoder are also considered. Simulations show the soft decoders to outperform decoding based on maximum-likelihood (ML) multiuser detection. Furthermore, the suboptimal versions are demonstrated to perform close to the optimal, at a significantly lower complexity in the number of users. The introduced decoders are, moreover, shown to exhibit near-far resistance. Simulations also demonstrate that combined source-channel encoding, with joint source-channel and multiuser decoding, can significantly outperform a tandem source-channel coding scheme employing multiuser detection plus table lookup source decoding     

On finite-state vector quantization for noisy channels

Finite-state vector quantization (FSVQ) over a noisy channel is studied. A major drawback of a finite-state decoder is its inability to track the encoder in the presence of channel noise. In order to overcome this problem, we propose a nontracking decoder which directly estimates the code vectors used by a finite-state encoder. The design of channel-matched finite-state vector quantizers for noisy channels, using an iterative scheme resembling the generalized Lloyd algorithm, is also investigated. Simulation results based on encoding a Gauss-Markov source over a memoryless Gaussian channel show that the proposed decoder exhibits graceful degradation of performance with increasing channel noise, as compared with a finite-state decoder. Also, the channel-matched finite-state vector quantizers are shown to outperform channel-optimized vector quantizers having the same vector dimension and rate. However, the nontracking decoder used in the channel-matched finite-state quantizer has a higher computational complexity, compared with a channel-optimized vector-quantizer decoder. Thus, if they are allowed to have the same overall complexity (encoding and decoding), the channel-optimized vector quantizer can use a longer encoding delay and achieve similar or better performance. Finally, an example of using the channel-matched finite-state quantizer as a backward-adaptive quantizer for nonstationary signals is also presented.     

Bit-estimate based decoding for vector quantization over noisychannels with intersymbol interference

We introduce new techniques for quantization over noisy channels with intersymbol interference. We focus on the decoding problem, and present a decoder structure that allows the decoding to be based on soft minimum mean square-error estimates of the transmitted bits. The new bit-estimate based decoder provides a structured lower-complexity approximation of optimal decoding for general codebooks, and for so-called linear mapping codebooks, it is shown that its implementation becomes particularly simple. We investigate decoding based on optimal bit-estimates, and on suboptimal estimates of lower computational complexity. We also consider encoder optimization and combined source-channel code design. Numerical simulations demonstrate that bit-estimate based decoding is able to outperform a two-stage decision-based approach implemented using Viterbi sequence detection plus table look-up source decoding. The simulations also show that decoding based on suboptimal bit-estimates performs well, at a considerably lowered complexity     

Turbo decoding of quantized data

Much of the work on turbo decoding assumes that the decoder has access to infinitely soft (unquantized) channel data. In practice, however, a quantizer is used at the receiver and the turbo decoder must operate on finite precision, quantized data. Hence, the maximum a posteriori (MAP) component decoder which was designed assuming infinitely soft data is not necessarily optimum when operating on quantized data. We modify the well-known normalized MAP algorithm taking into account the presence of the quantizer. This algorithm is optimum given any quantizer and is no more complex than quantized implementations of the MAP algorithm derived based on unquantized data. Simulation results on an additive white Gaussian noise channel show that, even with four bits of quantization, the new algorithm based on quantized data achieves a performance practically equal to the MAP algorithm operating on infinite precision data     

Iterative decoding of serially concatenated arithmetic and channel codes with JPEG 2000 applications.

In this paper, an innovative joint-source channel coding scheme is presented. The proposed approach enables iterative soft decoding of arithmetic codes by means of a soft-in soft- out decoder based on suboptimal search and pruning of a binary tree. An error-resilient arithmetic coder with a forbidden symbol is used in order to improve the performance of the joint source/channel scheme. The performance in the case of transmission across the AWGN channel is evaluated in terms of word error probability and compared to a traditional separated approach. The interleaver gain, the convergence property of the system, and the optimal source/channel rate allocation are investigated. Finally, the practical relevance of the proposed joint decoding approach is demonstrated within the JPEG 2000 coding standard. In particular, an iterative channel and JPEG 2000 decoder is designed and tested in the case of image transmission across the AWGN channel.     

Joint source-channel and multiuser decoding for Rayleigh fadingCDMA channels

We consider joint source-channel and multiuser decoding for frequency selective Rayleigh fading code-division multiple-access channels. The block source-channel encoder is defined by a vector quantizer. We investigate optimal (minimum mean-square error) decoding and “user-separated” decoding of lower complexity. The studied decoders are soft in the sense that they utilize all soft information available at the receiver. Simulations indicate significant performance gains of the introduced decoders compared with a tandem approach that uses maximum-likelihood multiuser detection plus table-lookup decoding     

The Hadamard transform-a tool for index assignment

We show that the channel distortion for maximum-entropy encoders, due to noise on a binary-symmetric channel, is minimized if the vector quantizer can be expressed as a linear transform of a hypercube. The index assignment problem is regarded as a problem of linearizing the vector quantizer. We define classes of index assignments with related properties, within which the best index assignment is found by sorting, not searching. Two powerful algorithms for assigning indices to the codevectors of nonredundant coding systems are presented. One algorithm finds the optimal solution in terms of linearity, whereas the other finds a very good, but suboptimal, solution in a very short time     

Soft-decision decoding of fixed-rate entropy-coded trellis-coded quantizer over a noisy channel

This paper presents new techniques to improve the performance of a fixed-rate entropy-coded trellis-coded quantizer (FE-TCQ) in transmission over a noisy channel. In this respect, we first present the optimal decoder for a fixed-rate entropy-coded vector quantizer (FEVQ). We show that the optimal decoder for the FEVQ can be a maximum likelihood decoder where a trellis structure is used to model the set of possible code words and the Viterbi algorithm is subsequently applied to select the most likely path through this trellis. In order to add quantization packing gain to the FEVQ, we take advantage of a trellis-coded quantization (TCQ) scheme. To prevent error propagation, it is necessary to use a block structure obtained through a truncation of the corresponding trellis. To perform this task in an efficient manner, we apply the idea of tail biting to the trellis structure of the underlying TCQ. It is shown that the use of a tail-biting trellis significantly reduces the required block length with respect to some other possible alternatives known for trellis truncation. This results in a smaller delay and also mitigates the effect of error propagation in signaling over a noisy channel. Finally, we present methods and numerical results for the combination of the proposed FEVQ soft decoder and a tail-biting TCQ. These results show that, by an appropriate design of the underlying components, one can obtain a substantial improvement in the overall performance of such a fixed-rate entropy-coded scheme.     

A generalized framework for iterative source-channel decoding

Joint source-channel decoding is considered for a transmission system, in which the quantizer indices of several autocorrelated source signals are bit-interleaved, commonly channel encoded, and transmitted in parallel. Since the optimal decoding algorithm is not feasible in most practical situations, iterative source-channel decoding has been introduced. The latter is generalized in the present paper. Furthermore, it is shown in detail, that iterative source-channel decoding can be derived by insertion of appropriate approximations into the optimal joint decoding algorithm. The approximations allow the decomposition of the optimal decoder into two parts, which can be identified as the constituent decoders for the channel-code and the source-code redundancies. Similar as in other concatenated coding systems, the constituent decoders are applied in an iterative decoding scheme. Its performance is analyzed by simulation results.     

Universal decoding for frequency-selective fading channels

We address the problem of universal decoding in unknown frequency-selective fading channels, using an orthogonal frequency-division multiplexing (OFDM) signaling scheme. A block-fading model is adopted, where the bands' fading coefficients are unknown yet assumed constant throughout the block. Given a codebook, we seek a decoder independent of the channel parameters whose worst case performance relative to a maximum-likelihood (ML) decoder that knows the channel is optimal. Specifically, the decoder is selected from a family of quadratic decoders, and the optimal decoder is referred to as a quadratic minimax (QMM) decoder for that family. As the QMM decoder is generally difficult to find, a suboptimal QMM decoder is derived instead. Despite its suboptimality, the proposed decoder is shown to outperform the generalized likelihood ratio test (GLRT), which is commonly used when the channel is unknown, while maintaining a comparable complexity. The QMM decoder is also derived for the practical case where the fading coefficients are not entirely independent but rather satisfy some general constraints. Simulations verify the superiority of the proposed QMM decoder over the GLRT and over the practically used training sequence approach.     

Soft-decoding vector quantizer using reliability information fromturbo-codes

The optimum soft-decoding vector quantizer using the reliability information from turbo-codes is derived for combined source-channel coding. The encoder and decoder of the quantizer are optimized iteratively. For a four-dimensional vector quantizer having a rate of 1 bit/sample transmitted through a noisy channel, the soft-decoding channel-optimized quantizer can achieve about 3-3.7 dB performance improvement over conventional source-optimized quantizer     

Nonrecursive decoding algorithm for PR4 channel

The Viterbi algorithm (VA) is a recursive optimal solution to the state sequence estimation problem. The recursive nature of this algorithm puts limitations on high-speed implementations of Viterbi decoders. The authors propose a nonrecursive suboptimal decoding algorithm for the PR4 channel. The new decoder has negligible performance loss     

Nonrecursive decoding algorithm for PR4 channel

The Viterbi algorithm (VA) is a recursive optimal solution to the state sequence estimation problem. The recursive nature of this algorithm puts limitations on high-speed implementations of Viterbi decoders. The authors propose a nonrecursive suboptimal decoding algorithm for the PR4 channel. The new decoder has negligible performance loss     

Optimal soft decoding for combined trellis-codedquantization/modulation

The maximum a posteriori (MAP) algorithm is used as a minimum mean-squared-error decoder for combined trellis-coded quantization and modulation. The optimal trellis-coded quantizer is derived when the soft-decoding MAP algorithm is used as a decoder. The trellis-coded quantizer and the soft decoder are optimized iteratively for minimum overall distortion from transmitter input to receiver output. Significant performance improvement is achieved for both memoryless Gaussian and uniform source, especially for very noisy channels     

Channel-Optimized Quantization With Soft-Decision Demodulation for Space–Time Orthogonal Block-Coded Channels

We introduce three soft-decision demodulation channel-optimized vector quantizers (COVQs) to transmit analog sources over space–time orthogonal block (STOB)-coded flat Rayleigh fading channels with binary phase-shift keying (BPSK) modulation. One main objective is to judiciously utilize the soft information of the STOB-coded channel in the design of the vector quantizers while keeping a low system complexity. To meet this objective, we introduce a simple space–time decoding structure that consists of a space–time soft detector, followed by a linear combiner and a scalar uniform quantizer with resolution$q$. The concatenation of the space–time encoder/modulator, fading channel, and space–time receiver can be described by a binary-input,$2^q$-output discrete memoryless channel (DMC). The scalar uniform quantizer is chosen so that the capacity of the equivalent DMC is maximized to fully exploit and capture the system's soft information by the DMC. We next determine the statistics of the DMC in closed form and use them to design three COVQ schemes with various degrees of knowledge of the channel noise power and fading coefficients at the transmitter and/or receiver. The performance of each quantization scheme is evaluated for memoryless Gaussian and Gauss–Markov sources and various STOB codes, and the benefits of each scheme is illustrated as a function of the antenna-diversity and soft-decision resolution$q$. Comparisons to traditional coding schemes, which perform separate source and channel coding operations, are also provided.     

Twin-stack decoding of recursive systematic convolutional codes

We present a method for soft-in/soft-out sequential decoding of recursive systematic convolutional codes. The proposed decoder, the twin-stack decoder, is an extension of the well-known ZJ stack decoder, and it uses two stacks. The use of the two stacks lends itself to the generation of soft outputs, and the decoder is easily incorporated into the iterative “turbo” configuration. Under thresholded decoding, it is observed that the decoder is capable of achieving near-maximum a posteriori bit-error rate performance at moderate to high signal-to-noise ratios (SNRs). Also, in the iterative (turbo) configuration, at moderate SNRs (above 2.0 dB), the performance of the proposed decoder is within 1.5 dB of the BCJR algorithm for a 16-state, R=1/3, recursive code, but this difference narrows progressively at higher SNRs. The complexity of the decoder asymptotically decreases (with SNR) as 1/(number of states), providing a good tradeoff between computational burden and performance. The proposed decoder is also within 1.0 dB of other well-known suboptimal soft-out decoding techniques     

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     

Analysis and performance of bidirectional decoding of convolutionalcodes over fading channels

The performance of suboptimal convolutional decoding over fading channels is explored. The suboptimal decoding algorithm used is the bidirectional algorithm. By estimating a “decoder weight spectrum” for the decoder, an “equivalent free distance” may be observed. Furthermore, by using this “decoder weight spectrum”, useful estimations of the error probabilities are obtained and compared to computer-simulation results in the case of very slow and very fast fading. The resultant curves are shown to be very tightly related. Computer-simulation results are also shown for various signal-to-noise ratios, normalized Doppler spreads, and frame length on three typical fading channels: the Rayleigh fading channel with exponential and Bessel autocorrelation functions and the Rician fading channel with exponential autocorrelation function. We show that considerable gains (up to 4 dB) can be obtained with respect to a similar-complexity Viterbi decoder at a frame error probability P_e =10^-3 and a slightly smaller gain (up to 1.8 dB) at a bit error probability P_b=10^-5     

一种确定Turbo乘积码迭代因子的方法

提出一种确定Turbo乘积码迭代因子的算法。建立信道模型,生成测试软信息R;生成一组备选迭代因子向量,在备选迭代因子空间里用MATLAB仿真Chase-Pyndiah迭代译码算法流程,选择最优的迭代因子;迭代因子优劣的判据为迭代译码器的误码率以及迭代次数。实验结果表明,最优迭代因子有效地加速了迭代译码器的收敛速度,降低了译码的功耗。