Soft Output Viterbi Algorithm Research Articles

Research on unequal error protection with punctured turbo codes in jpeg image transmission system

An investigation of Unequal Error Protection (UEP) methods applied to JPEG image transmission using turbo codes is presented. The JPEG image is partitioned into two groups, i.e., DC components and AC components according to their respective sensitivity to channel noise. The highly sensitive DC components are better protected with a lower coding rate, while the less sensitive AC components use a higher coding rate. While we use the s-random interleaver and s-random odd-even interleaver combined with odd-even puncturing, we can fix easily the local rate of turbo-code. We propose to modify the design of s-random interleaver to fix the number of parity bits. A new UEP scheme for the Soft Output Viterbi Algorithm (SOVA) is also proposed to improve the performances in terms of Bit Error Rate (BER) and Peak Signal to Noise Ratio (PSNR). Simulation results are given to demonstrate how the UEP schemes outperforms the equal error protection (EEP) scheme in terms of BER and PSNR.

Complexity Reduction in SISO Decoding of Block Codes

SISO decoding for block codes can be carried out based on a trellis representation of the code. However, the complexity entailed by such decoding is most often prohibitive and thus prevents practical implementation. This paper examines a new decoding scheme based on the soft-output Viterbi algorithm (SOVA) applied to a sectionalized trellis for linear block codes. The computational complexities of the new SOVA decoder and of the conventional SOVA decoder, based on a bit-level trellis, are theoretically analyzed and derived for different linear block codes. These results are used to obtain optimum sectionalizations of a trellis for SOVA. For comparisons, the optimum sectionalizations for Maximum A Posteriori (MAP) and Maximum Logarithm MAP (Max-Log-MAP) algorithms, and their corresponding computational complexities are included. The results confirm that the new SOVA decoder is the most computationally efficient SISO decoder, in comparisons to MAP and Max-Log-MAP algorithms. The simulation results of the bit error rate (BER) performance, assuming binary phase -- shift keying (BPSK) and additive white Gaussian noise (AWGN) channel, demonstrate that the performance of the new decoding scheme is not degraded. The BER performance of iterative SOVA decoding of serially concatenated block codes shows no difference in the quality of the soft outputs of the new decoding scheme and of the conventional SOVA.

A simple remedy for the exaggerated extrinsic information produced by the SOVA algorithm

In this paper, we propose a novel and simple approach for dealing with the exaggerated extrinsic information produced by the soft-output Viterbi algorithm (SOVA). The proposed remedy is based on mathematical analysis and it involves using two attenuators, one applied to the immediate output of the SOVA and another applied to the extrinsic information before it is passed to the other decoder (assuming iterative decoding). The use of these attenuators aims at reducing the inherent strong correlation between the intrinsic information (input to the SOVA) and extrinsic information (output of the SOVA). We examine the modified SOVA (MSOVA) on additive white Gaussian noise (AWGN) and flat fading channels for parallel concatenated codes (PCCs) and serial concatenated codes (SCCs). We show that the MSOVA provides substantial performance improvements over both channels. For example, it provides improvements of about 0.8 to 1.0 dB at P/sub b/ = 10/sup -5/ in AWGN, and about 1.4 to 2.0 dB at P/sub b/ = 10/sup -5/ on fading channels. We also show that there are cases where the MSOVA is superior to the a posteriori probability (APP) algorithm. With this motivation, we extend the proposed modification to the APP algorithm with favorable results. We demonstrate that the modified APP (MAPP) provides performance improvements between 0.3 to 0.6 dB at P/sub b/ = 10/sup -5/ relative to the APP. We lastly mention that the proposed modifications, while they provide considerable performance improvements, keep the complexity of these decoders almost the same, which is remarkable.

Turbo equalisation of time varying multipath channel under class-A impulsive noise

The paper explores the problem of turbo equalisation and channel estimation under class-A impulsive noise. The channel is a frequency selective fading channel in which its time varying coefficients are expanded into a finite number of basis sequences and time invariant (TI) expansion parameters. Instead of the application of a maximum likelihood (ML) approach in its standard form, the proposed channel estimator is performed by an iterative approach based on the expectation maximisation (EM) algorithm and the steepest descent algorithm. The proposed estimator reduces the complexity of computations resulting from direct application of the ML approach and provides significant performance gain over the algorithms which are efficient in white Gaussian noise. Also, the proposed estimator is suitable for class-A impulsive noise and utilises the soft information obtained from the soft output Viterbi algorithm (SOVA) which is derived under class-A impulsive noise.

Improved performance SOVA turbo decoder

A novel approach for improving the performance of the soft-output Viterbi algorithm (SOVA) when applied to turbo decoding is proposed. Based upon a modified two-step scaling factor approach for the decoder's extrinsic information, it is shown that the proposed technique reduces significantly the error floor present in previous SOVA-based turbo decoding techniques. Various computer simulated bit error rate (BER) performance evaluation results for binary phase shift keying (BPSK) signals transmitted over the additive white Gaussian noise (AWGN) and flat Rician fading channels clearly indicate that for large interleaver sizes and high numbers of decoding iterations no error floor is observed for BERs as low as 10−6.

Iterative joint source-channel decoding of speech spectrum parameters over an additive white Gaussian noise channel

In this paper, we show how the Gaussian mixture modeling framework used to develop efficient source encoding schemes can be further exploited to model source statistics during channel decoding in an iterative framework to develop an effective joint source-channel decoding scheme. The joint probability density function (PDF) of successive source frames is modeled as a Gaussian mixture model (GMM). Based on previous work, the marginal source statistics provided by the GMM is used at the encoder to design a low-complexity memoryless source encoding scheme. The source encoding scheme has the specific advantage of providing good estimates to the probability of occurrence of a given source code-point based on the GMM. The proposed iterative decoding procedure works with any channel code whose decoder can implement the soft-output Viterbi algorithm that uses a priori information (APRI-SOVA) or the BCJR algorithm to provide extrinsic information on each source encoded bit. The source decoder uses the GMM model and the channel decoder output to provide a priori information back to the channel decoder. Decoding is done in an iterative manner by trading extrinsic information between the source and channel decoders. Experimental results showing improved decoding performance are provided in the application of speech spectrum parameter compression and communication.

Improvements in SOVA-based decoding for turbo-coded storage channels

In this paper, we propose a novel and simple approach for dealing with the exaggerated extrinsic information produced by the soft-output Viterbi algorithm (SOVA). We first identify the reason behind these exaggerated values and then propose a simple remedy for it. We argue that what leads to this optimistic extrinsic information is the inherent strong correlation between the intrinsic information (input to the SOVA) and extrinsic information (output of the SOVA). Our proposed remedy is based on mathematical analysis, and it involves using two attenuators, one applied to the immediate output of the SOVA and another applied to the extrinsic information before it is passed to the other decoder (assuming iterative decoding). We examine the modified SOVA (MSOVA) on idealized partial response (PR) channels and the Lorentzian channel equalized to a PR target. We consider both parallel concatenated codes (PCCs) and serial concatenated codes (SCCs). We show that the MSOVA provides substantial performance improvements over both channels. For example, it provides improvements of about 0.8 to 1.6 dB at P/sub b/=10/sup -5/. Finally, we note that the proposed modifications, while they provide considerable performance improvements, introduce only two additional multipliers to the complexity of the SOVA algorithm, which is remarkable.

Performance of a turbo‐coded CDMA system in a mobile satellite channel

AbstractThe bit error rate (BER) performance of a turbo‐coded code‐division multiple‐access (CDMA) system operating in a satellite channel is analysed and simulated. The system performance is compared for various constituent decoders, including maximum a posteriori probability (MAP) and Max‐Log‐MAP algorithms, and the soft‐output Viterbi algorithm. The simulation results indicate that the Max‐Log‐MAP algorithm is the most promising among these three algorithms in overall terms of performance and complexity. It is also shown that, for fixed code rate, the BER performance is improved substantially by increasing the number of iterations in the turbo decoder, or by increasing the interleaver length in the turbo encoder. The results in this paper are of interest in CDMA‐based satellite communications applications. Copyright © 2005 John Wiley & Sons, Ltd.

Iterative decoding of wrapped space-time codes

We study the iterative decoding of Wrapped Space-Time Codes (WSTCs) employing per-survivor-processing with the soft-output Viterbi-algorithm (SOVA). We use a novel receiver scheme that incorporates extrinsic information delivered by the SOVA. The decision metric of the SOVA is developed, and the performance is analyzed.

RAKE-SOVA Equalization for Multi-Code CDMA System with Low Spreading Factor

In CDMA system, the RAKE receiver is commonly used to attain diversity gain by taking advantage of the good correlation properties of the spreading codes. However, at low spreading gains the good correlation properties of the spreading codes are lost and the RAKE receiver performance is severely degraded by intersymbol interference (ISI) due to the interpath interference (IPI). In case of multi-code CDMA system, there are exist multi-code interference (MCI). In order to suppress ISI and MCI, a novel receiver based on soft-output viterbi algorithm (SOVA) equalization is proposed in this paper. The SOVA equalization is applied to symbol sequences after RAKE combining and MCI cancellation to effectively eliminate the ISI during transmission of high rate data in wideband DS-CDMA systems. Simulation results show that the proposed RAKE-SOVA receiver significantly outperform the traditional RAKE and RAKE-VA receivers.

Adaptive Equalization for Frequency-Selective Channels of Unknown Length

This paper studies adaptive equalization for time-dispersive communication channels whose impulse responses have unknown lengths. This problem is important, because an adaptive equalizer designed for an incorrect is suboptimal; it often estimates an unnecessarily large number of parameters. Some solutions to this problem exist (e.g., attempting to estimate the channel length and then switching between different equalizers); however, these are suboptimal owing to the difficulty of correctly identifying the and the risk associated with an incorrect estimation of this length. Indeed, to determine the is effectively a model order selection problem, for which no optimal solution is known. We propose a novel systematic approach to the problem under study, which circumvents the estimation of the length. The key idea is to model the impulse response via a mixture Gaussian model, which has one component for each possible length. The parameters of the mixture model are estimated from a received pilot sequence. We derive the optimal receiver associated with this mixture model, along with some computationally efficient approximations of it. We also devise a receiver, consisting of a bank of soft-output Viterbi algorithms, which can deliver soft decisions. Via numerical simulations, we show that our new method can outperform conventional adaptive Viterbi equalizers that use a fixed or an estimated length.

Iterative Decoding of Orthogonal Space-Time Coded CPM Systems

We present an iterative decoding/demodulation technique for an orthogonal space-time coded continuous-phase modulation (OST-CPM) system. A low-complexity soft input and soft output (SISO) demodulator is developed based on the bidirectional soft output Viterbi algorithm (BSOVA) for the multiple antennas CPM systems. By taking advantage of the orthogonal structure, the complexity of extrinsic information extraction can be significantly reduced at each iteration.

A concatenated equalizer/trellis decoder architecture for a terrestrial digital television receiver

In the U.S. terrestrial digital television receiver, when the terrestrial channel presents multipath and additive white Gaussian noise, particularly strong multipath, error propagation in the feedback filter of a decision feedback equalizer (DFE) severely affects the performance at the output of the trellis decoder. The performance degradation occurs when incorrectly detected symbols are fed through the feedback filter. Then, instead of mitigating intersymbol interference (ISI) from the cursor symbol, the DFE enhances ISI. Error propagation causes bursts of decision errors and a corresponding increase in the average probability of bit or symbol error. This work evaluates the performance improvement achieved by a concatenated equalizer/trellis decoder architecture for the receiver whereby the re-encoded trellis decoder outputs are used as the input to the DFE feedback filter. In addition, the soft output Viterbi algorithm (SOVA) is proposed for trellis decoding in order to achieve additional gains.

A High-Throughput, Field Programmable Gate Array Implementation of Soft Output Viterbi Algorithm for Magnetic Recording

A high throughput, reconfigurable field programmable gate array (FPGA) implementation of the soft output Viterbi algorithm (SOVA) is described. Such a SOVA module provides the soft information needed by an iterative soft decoder used with Turbo codes and low density parity check (LDPC) codes. The implementation of the SOVA algorithm runs at 100 Mb/s on Xilinx Virtex II 2000 FPGA. Using a higher capacity FPGA and repeating the circuit doubles the throughput. The design can be reconfigured for different partial response (PR) targets. The design requires about 5 kb of memory for the EPR4 channel and may be integrated on a single chip with serially implemented LDPC decoder.

Iterative decoding and channel estimation for space-time bicm over mimo block fading multipath awgn channel

In this paper, we consider a generic model of space-time bit-interleaved coded modulation (ST-BICM) on a multiple-input multiple-output (MIMO) Rayleigh fading multipath channel. A practical low-complexity receiver structure performing iteratively MIMO data detection, channel decoding and channel estimation, is presented. The MIMO data detection, employing a reduced-state list-type soft output Viterbi algorithm enables to cope with severe channel intersymbol interference (ISI) without MIMO prefiltering. Among other results, simulations show that our approach can dramatically improve the downlink performance of time-division multiple access (TDMA) systems with high order modulation, keeping a reasonable complexity at the receiver side.

New siso decoding algorithms

A new maximum a posteriori (MAP)-equivalent soft-input soft-output (SISO) algorithm is derived together with its simplified versions. The proposed SISO algorithms provide a good compromise between complexity and performance. Our simplest SISO algorithm has lower complexity than the log-MAP, the max-log-MAP, and the soft-output Viterbi (1998) algorithm SISO algorithms, and it is an equivalent max-log-MAP algorithm. When this algorithm is used, turbo codes with block length as short as 150 bits will outperform convolutional codes when compared on the basis of equal decoder complexity.

High performance, high throughput turbo/SOVA decoder design

Two efficient approaches are proposed to improve the performance of soft-output Viterbi (1998) algorithm (SOVA)-based turbo decoders. In the first approach, an easily obtainable variable and a simple mapping function are used to compute a target scaling factor to normalize the extrinsic information output from turbo decoders. An extra coding gain of 0.5 dB can be obtained with additive white Gaussian noise channels. This approach does not introduce extra latency and the hardware overhead is negligible. In the second approach, an adaptive upper bound based on the channel reliability is set for computing the metric difference between competing paths. By combining the two approaches, we show that the new SOVA-based turbo decoders can approach maximum a posteriori probability (MAP)-based turbo decoders within 0.1 dB when the target bit-error rate (BER) is moderately low (e.g., BER<10/sup -4/ for 1/2 rate codes). Following this, practical implementation issues are discussed and finite precision simulation results are provided. An area-efficient parallel decoding architecture is presented in this paper as an effective approach to design high-throughput turbo/SOVA decoders. With the efficient parallel architecture, multiple times throughput of a conventional serial decoder can be obtained by increasing the overall hardware by a small percentage. To resolve the problem of multiple memory accesses per cycle for the efficient parallel architecture, a novel two-level hierarchical interleaver architecture is proposed. Simulation results show that the proposed interleaver architecture performs as well as random interleavers, while requiring much less storage of random patterns.

On the SOVA for extremely high code rates over partial response channels

In this paper, we extend the derivation of the iterative soft-output Viterbi algorithm (SOVA) for partial response (PR) channels, and modify its decoding process such that it works consistently for arbitrary high code rates, e.g., rate 64/65. We show that the modified SOVA always outperforms the conventional SOVA that appears in the literature with a significant difference for high code rates. It also offers a significant cut down in the trace-back computations. We further examine its performance for parallel and serial concatenated codes on a precoded Class IV partial response (PR4) channel. Code rates of the form k 0 /k 0 +1 (k 0 = 4, 8, and 64) are considered. Our simulations indicate that the loss suffered by the modified SOVA, relative to the APP algorithm, is consistent for all code rates and is at most 1.2 dB for parallel concatenations and at most 1.6 dB for serial concatenations at P b = 10−5.

Application of the Berrou SOVA algorithm in decoding of a turbo code

We present a turbo decoder that is based on a low complexity soft output Viterbi algorithm (SOVA) introduced by Claude Berrou et al. in ICC'93. It is conceptually different from the conventional turbo decoders, where the iteration is based on the a posteriori probabilities (APP). The constituent Berrou SOVA decoders make the maximum likelihood (ML) decision on the correct path in the trellis, and they have lots of similarities with a conventional hard decision Viterbi decoder—their complexity is double that of the Viterbi due to extraction of the soft output. The iterative Berrou SOVA decoder is able to achieve a relatively high speed: the constituent decoders can work at the same pace as their conventional Viterbi counterparts, and no back tracing is needed. The performance is competitive with the traditional decoding algorithms. In comparison with Max-Log-MAP, we have attained a slightly better performance. Copyright © 2003 AEI.

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 10−5 is achieved compared to existing schemes.