Smooth side-match classified vector quantizer with variable blocksize

Although the side-match vector quantizer (SMVQ) reduces the bit rate, the image coding quality by SMVQ generally degenerates as the gray level transition across the boundaries of the neighboring blocks is increasing or decreasing. This study presents a smooth side-match method to select a state codebook according to the smoothness of the gray levels between neighboring blocks. This method achieves a higher PSNR and better visual perception than SMVQ does for the same bit rate. Moreover, to design codebooks, a genetic clustering algorithm that automatically finds the appropriate number of clusters is proposed. The proposed smooth side-match classified vector quantizer (SSM-CVQ) is thus a combination of three techniques: the classified vector quantization, the variable block size segmentation and the smooth side-match method. Experimental results indicate that SSM-CVQ has a higher PSNR and a lower bit rate than other methods. Furthermore, the Lena image can be coded by SSM-CVQ with 0.172 bpp and 32.49 dB in PSNR.     

1000 BASE-T收发器中的Viterbi译码算法研究

采用4维8状态网格编码和Viterbi译码相结合的方法，理论上可以获得6dB的编码增益，用于补偿采用PAM-5编码所带来的噪声容限损失。文章给出了针对4维8状态网格编码的Viterbi译码算法的译码过程，并就译码深度、量化精度和溢出处理方法对译码器性能的影响进行了算法仿真，确定出适合1000 BASE-T收发器应用的译码器参数。     

An effective simplifying scheme for Viterbi decoder

A Viterbi decoding algorithm with a scarce-state transition-type circuit configuration, namely the probability selecting states (PSS) mode decoder, is presented. The algorithm has reduced complexity compared to a conventional Viterbi decoder. It is shown that this method has three advantages over the general Viterbi algorithm: it is suitable to the quick look-in code, it applies the optimum decoding in a PSS-type decoder, and it makes full use of the likelihood concentration property. The bit-error-rate (BER) performance of a r=1/2, k=7 (147,135) code and PSS-type Viterbi decoder approximates the optimum performance of the standard Viterbi decoder and reduces the hardware of the conventional Viterbi decoder to about half     

Modification of branch metric calculation to improve iterative SOVA decoding of turbo codes

It is known that the performance of a SOVA (soft output Viterbi algorithm) turbo decoder can be improved, as the extrinsic information that is produced at its output is over-optimistic. A new parameter associated with the branch metrics calculation in the standard Viterbi algorithm is introduced that affects the turbo code performance. Different parameter values show a simulation improvement in the AWGN channel as well as in an uncorrelated Rayleigh fading channel. By choosing the best value of this parameter, a coding gain improvement of 0.25 dB at BER of 10/sup -5/ is achieved compared to existing schemes.     

Viterbi decoding of the (63, 57) Hamming code-implementation andperformance results

Use of the Viterbi decoder to decode the (63, 57) Hamming code is considered, Implementation and performance of systematic and nonsystematic codes are addressed. It is shown that a Viterbi decoder for the constraint length seven, rate-½ convolutional code can be used to decode both systematic and nonsystematic (63, 57) Hamming codes, but an additional step is needed to complete the decoding of the systematic code. Bounds and simulation results for postdecoding bit-error probability are given and it is shown that the systematic code performs 0.4 dB better than the nonsystematic code. A heuristic explanation is provided     

Quantization loss in convolutional decoding

The loss in quantizing coded symbols in the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) modulation is discussed. A quantization scheme and branch metric calculation method are presented. For the uniformly quantized AWGN channel, cutoff rate is used to determine the step size and the smallest number of quantization bits needed for a given bit-signal-to-noise ratio (E_b/N₀) loss. A nine-level quantizer is presented, along with 3-b branch metrics for a rate-1/2 code, which causes an E_b/N₀ loss of only 0.14 dB. These results also apply to soft-decision decoding of block codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the memory-14, rate-1/4 or -1/6 codes used by the big Viterbi decoders at JPL     

一种高速Viterbi译码器的设计与实现

Viterbi算法是卷积码的最优译码算法.设计并实现了一种高速(3,1,7)Viterbi译码器,该译码器由分支度量单元(BMU)、加比选单元(ACSU)、幸存路径存储单元(SMU)、控制单元(CU)组成.在StratixⅡ FPGA上实现、验证了该Viterbi译码器.验证结果表明,该译码器数据吞吐率达到231Mbit/s,在加性高斯白噪声(AWGN)信道下的误码率十分接近理论仿真值.与同类型Viterbi译码器比较,该译码器具有高速、硬件实现代价低的特点.     

Image coding using variable-rate side-match finite-state vectorquantization

Future B-ISDN (broadband integrated services digital network) users will be able to send various kinds of information, such as voice, data, and image, over the same network and send information only when necessary. It has been recognized that variable-rate encoding techniques are more suitable than fixed-rate techniques for encoding images in a B-ISDN environment. A new variable-rate side-match finite-state vector quantization with a block classifier (CSMVQ) algorithm is described. In an ordinary fixed-rate SMVQ, the size of the state codebook is fixed. In the CSMVQ algorithm presented, the size of the state codebook is changed according to the characteristics of the current vector which can be predicted by a block classifier. In experiments, the improvement over SMVQ was up to 1.761 dB at a lower bit rate. Moreover, the improvement over VQ can be up to 3 dB at nearly the same bit rate.     

An artificial neural net Viterbi decoder

The Viterbi algorithm is a maximum likelihood means for decoding convolutional codes and has thus played an important role in applications ranging from satellite communications to cellular telephony. In the past, Viterbi decoders have usually been implemented using digital circuits. The speed of these digital decoders is directly related to the amount of parallelism in the design. As the constraint length of the code increases, parallelism becomes problematic due to the complexity of the decoder. In this paper an artificial neural network (ANN) Viterbi decoder is presented. The ANN decoder is significantly faster than comparable digital-only designs due to its fully parallel architecture. The fully parallel structure is obtained by implementing most of the Viterbi algorithm using analog neurons as opposed to digital circuits. Several modifications to the ANN decoder are considered, including an analog/digital hybrid design that results in an extremely fast and efficient decoder. The ANN decoder requires one-sixth the number of transistors required by the digital decoder. The connection weights of the ANN decoder are either +1 or -1, so weight considerations in the implementation are eliminated. This, together with the design's modularity and local connectivity, makes the ANN Viterbi decoder a natural fit for VLSI implementation. Simulation results are provided to show that the performance of the ANN decoder matches that of an ideal Viterbi decoder     

(2,1,7)卷积编码及其维特比译码算法的软件实现

提出了一种（2，1，7）卷积编码及其维特（Viterbi）译码的软件实现方案，在Matlab环境中应用软件技术实现了（2，1，7）卷积码的Viterbi译码器功能。测试证明，该Viterbi译码算法在低信噪比下的误码率仍能达到10^-6。     

A coded 8-PSK system for 140 Mb/s information rate transmission over 80 MHz non-linear transponders

A combined 8-PSK modulation and rate 7/9 convolutional coding technique is proposed for 140 Mb/s information rate transmission over the 80 MHz INTELSAT transponders, thus achieving a bandwidth efficiency of 1.75 b/s/Hz of allocated bandwidth. The desired power efficiency is to achieve a bit error rate of 10^?6 at an E_b/N₀ of 11 dB, including modem and codec implementation losses. The proposed system employs an 8-PSK modem operating at a 60 MHz symbol rate (or 180 Mb/s bit rate), as well as a rate 7/9 convolutional encoder and a 16-state Viterbi algorithm decoder operating at 60 MHz. The rate 7/9 code is periodically time varying and is designed to maximize the Euclidean distance between the modulated codeword sequences, thereby achieving a 3 dB asymptotic coding gain relative to the conventional QPSK system over an AWGN channel. This code is also designed to reduce decoder complexity for high-speed operations. The performance of the proposed system over INTELSAT V and VI non-linear transponders was evaluated by Monte Carlo computer simulation. The 180 Mb/s 8 PSK modem, including the automatic frequency control, automatic gain control, carrier recovery and clock recovery circuits, has been implemented and tested. The complete Viterbi decoder is being implemented on five boards, and the critical add-compare-select (ACS) circuit of the high-speed Viterbi algorithm decoder is being implemented with hybrid technology employing 100-K series emitter-coupled logic dies on specially designed ceramic substrates. The ACS circuit operates at a speed exceeding 120 MHz, well over the design goal of 60 MHz. Construction of this codec is almost complete.     

基于FPGA的卷积码译码器设计

针对目前卷积码译码器占用资源较多,最高工作频率较低的缺点,设计了基于FPGA的（2,1,8）卷积码译码器。该译码器采用硬判决维特比译码算法。为有效提高译码器的工作频率,采用寄存器存储路径度量和幸存路径。通过分析译码启动过程中状态转移图上各个状态与其前一状态的关系,找到了硬件实现该过程的一种简单方法。通过分析译码过程中各个状态路径度量值之间的差值的变化规律,找到了采用硬判决维特比译码算法时,存储各个状态路径度量值的寄存器的最小位宽。在Quartus2集成开发平台上用Verilog HDL语言编写了译码器的源代码,并进行了编译、综合、仿真。结果表明所设计的卷积码译码器工作频率高,且输出时延小,占用资源较少。具有一定的实用价值。     

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 robust Viterbi decoder and its application to terrestrial HDTVbroadcasting

The conventional Viterbi (1967) decoder employing the Euclidean distance has been widely used and considered as the optimum one in the sense of maximum likelihood sequence decoding under the hypothesis of additive white Gaussian noise (AWGN). However, what will happen if the noise distributions of actual channels deviate from the assumed AWGN? A robust Viterbi decoder utilizing absolute distance is carefully examined. Analytical and numerical results show that this Viterbi decoder is more advantageous than the conventional Viterbi decoder for actual channels with various kinds of interference, particularly in the presence of impulsive noise. Finally the robust Viterbi decoder is applied to TCM-8VSB terrestrial HDTV broadcasting, achieving 0.5-1.0 dB SNR gains over the conventional Viterbi decoder on contaminated AWGN channels     

A two-dimensional product code with robust soft-decision decoding

The performance of a relatively simple two-dimensional (2-D) product code is considered. The row code is a short constraint length convolutional code, and the column code is a high-rate block code. Both the rows and columns are decoded with soft-decision maximum likelihood decoding. The soft output Viterbi algorithm (SOVA) is used to decode the rows. In one case, the same decoder may be used for the rows and the columns. It is shown that, depending on the rate of the row code, reliable signaling is achieved within about 1.0 to 1.5 dB of the R₀ limit. Results are given for a particular impulsive noise channel; it is seen that performance is robust over a wide range of channel conditions     

Iterative Viterbi algorithm: implementation issues

We address several issues for implementing the iterative Viterbi decoder. We show that 3-bit branch metric quantization, 7- or 8-bit state metric precision, and a survivor length of five times the constraint length yields little degradation for the iterative Viterbi algorithm (IVA). Our results show that without changing the VA hardware (except adding some additional circuits), the error performance of several standard systems can be significantly improved.     

Performance Bounds for Convolutional Codes with Digital Viterbi Decoders in Gaussian Noise

With digital implementations of the Viterbi decoding algorithm for convolutional codes, soft quantization is preferred over hard quantization because it generally yields superior performance. Since the decoder needs to know the signal energy and channel noise variance with soft quantization, inaccurate information can result in a mismatch between the channel and decoder. Bounds which are tight for high signal-to-noise ratios are obtained on the bit error probability using the generating function approach. Automatic gain control level inaccuracies, imperfect carrier phase, symbol timing synchronization error, and path metric digitization are discussed in the context of a mismatch between the channel and decoder.     

Image-adaptive vector quantization in an entropy-constrainedframework

An adaptive vector quantization (VQ) scheme with codebook transmission is derived for the variable-rate source coding of image data using an entropy-constrained Lagrangian framework. Starting from an arbitrary initial codebook C(I) available to both the encoder and decoder, the proposed algorithm iteratively generates an improved operational codebook C(0) that is well adapted to the statistics of a particular image or subimage. Unlike other approaches, the rate-distortion trade-offs associated with the transmission of updated code vectors to the decoder are explicitly considered in the design. In all cases, the algorithm guarantees that the operational codebook C(0) will have rate-distortion performance (including all side-information) better than or equal to that of any initial codebook C(I). When coding the Barbara image, improvement at all rates is demonstrated with observed gains of up to 3 dB in peak signal-to-noise ratio (PSNR). Whereas in general the algorithm is multipass in nature, encoding complexity can be mitigated without an exorbitant rate-distortion penalty by restricting the total number of iterations. Experiments are provided that demonstrate substantial rate-distortion improvement can be achieved with just a single pass of the algorithm.     

Dynamic adaptation of quantization thresholds for soft-decision viterbi decoding with a reinforcement learning neural network

Two reinforcement learning neural network architectures which enhance the performance of a soft-decision Viterbi decoder used for forward error-correction in a digital communication system have been investigated and compared. Each reinforcement learning neural network is designed to work as a co-processor to a demodulator dynamically adapting the soft quantization thresholds toward optimal settings in varying noise environments. The soft quantization thresholds of the demodulator are dynamically adjusted according to the previous performance of the Viterbi decoder, with updates occurring in fixed intervals (every 200 decoded bits out of the Viterbi decoder.) To facilitate implementaiton in digital hardware, each weight of the neural network and related parameters are specified as binary numbers. Computer simulation results demonstrate that, on average, the performance of a Viterbi decoder on an AWGN channel with nonuniformly-spaced soft decision thresholds dynamically adjusted by these neural networks is better than the performance of a Viterbi decoder with uniformly-spaced thresholds. This approach may be used for a variety of other digital communication applications such as channel estimation, adaptive equalization, and signal acquisition.     

Frame error rates for convolutional codes on fading channels andthe concept of effective Eb/N0

Estimation of Viterbi decoder performance over channels with time-varying received signal levels is the subject of this paper. This work is motivated by a desire to obtain good estimates of the frame error rate (FER) for convolutional codes with bit-level interleaving over fading channels subject to practical power control algorithms. The convolutional code performance is quantified through the FER and effective E_b/N₀. where the latter is defined as the E_b/N₀ on an additive white Gaussian noise (AWGN) channel that results in the same FER. Given a received vector of (time-varying) E_b/N₀ values, we compute analytic estimates for the probability of frame error and the effective E_b /N₀ for a Viterbi decoder and interleaver combination. In particular, we validate our analysis using the R=1/3 convolutional code and interleaver used on the IS-95 CDMA reverse channel. Comparisons with simulations show that even for E_b/N₀ vectors with very large variations, our proposed estimates are good to within 0.2 dB for the effective E_b/N₀, giving FER estimates within a factor of two-five of the simulations