List Viterbi Algorithm Research Articles

A Low-Complexity Ordered Statistic Decoding of Short Block Codes

This letter is concerned with a generalized ordered statistic decoding (OSD) algorithm, called locally constrained OSD (LC-OSD). Instead of order- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> reprocessing on the most reliable independent bits, the LC-OSD searches for test error patterns using the serial list Viterbi algorithm (SLVA) over a trellis specified by a local parity-check matrix. We derive several early stopping criteria that can be used to reduce the number of searches. Numerical results show that the LC-OSD algorithm with the proposed stopping criteria has much lower time complexity than the original OSD but incurs negligible performance loss.

List Viterbi Decoding of PAC Codes

Polarization-adjusted convolutional (PAC) codes are special concatenated codes in which we employ a one-to-one convolutional transform as a pre-coding step before the polar transform. In this scheme, the polar transform (as a mapper) and the successive cancellation process (as a demapper) present a synthetic vector channel to the convolutional transformation. The numerical results show that this concatenation improves the Hamming distance properties of polar codes. Motivated by the fact that the parallel list Viterbi algorithm (LVA) sorts the candidate paths locally at each trellis node, in this work, we adapt the trellis, path metric, and the local sorter of LVA to PAC codes and show how the error correction performance moves from the poor performance of the Viterbi algorithm (VA) to the superior performance of list decoding by changing the constraint length, list size, and the sorting strategy (local sorting and global sorting) in the LVA. Also, we analyze the complexity of the local sorting of the paths in LVA relative to the global sorting in the list decoding and we show that LVA has a significantly lower sorting complexity compared with list decoding.

Multiple Model Method for Aircraft Conflict Detection and Resolution in Intent and Weather Uncertainty

This paper presents a novel multiple model (MM) method for aircraft conflict detection and resolution (CDR) in intent and weather uncertainty for the next generation air transportation system. It is based on probabilistic MM aircraft trajectory prediction. Conflict detection is performed through the use of predicted probability of conflict (PC). An improved algorithm for estimating PC is proposed and compared with a commonly used method. Conflict resolution (CR) is formulated as a stochastic model predictive control (MPC) problem subject to a constraint on the predicted PC to guarantee safety of the optimized CR trajectories. The cost function to be minimized is tailored to the CR problem and includes the cost of performing evasive maneuvers as well as the average cost incurred by extra travel distance to the destination due to the maneuvers. An efficient algorithm for finding the optimal path (maneuver sequence), with respect to the maneuver cost, is proposed and extended to an overall CDR optimization algorithm for the total cost, in order to produce optimized conflict-free CR trajectories. The proposed search algorithm is essentially a generalization of an optimal list Viterbi algorithm (for unconstrained minimization through a trellis) to the constrained case of our MPC-based CDR problem. The capability and computational efficiency of the proposed MM-CDR method (including PC prediction, optimal search, and overall CDR) are evaluated via comprehensive simulation of a large variety of unmanned aerial vehicle “sense-and-avoid” encounter scenarios, and are compared with existing methods in the literature.

A Form of List Viterbi Algorithm for Decoding Convolutional Codes

Viterbi algorithm is a maximum likelihood decoding algorithm. It is used to decode convolutional code in several wireless communication systems, including Wi-Fi. The standard Viterbi algorithm gives just one decoded output, which may be correct or incorrect. Incorrect packets are normally discarded thereby necessitating retransmission and hence resulting in considerable energy loss and delay. Some real-time applications such as Voice over Internet Protocol (VoIP) telephony do not tolerate excessive delay. This makes the conventional Viterbi decoding strategy sub-optimal. In this regard, a modified approach, which involves a form of List Viterbi for decoding the convolutional code is investigated. The technique employed combines the bit-error correction capabilities of both the Viterbi algorithm and the Cyclic Redundancy Check (CRC) procedures. It first uses a form of ‘List Viterbi Algorithm’ (LVA), which generates a list of possible decoded output candidates after the trellis search. The CRC check is then used to determine the presence of correct outcome. Results of experiments conducted using simulation shows considerable improvement in bit-error performance when compared to classical approach.

A New List Decoding Algorithm for Short-Length TBCCs With CRC

In this paper, a new list decoding algorithm for tail-biting convolutional codes (TBCCs) with a cyclic redundancy check (CRC) is proposed, where the CRC is considered as a concatenated outer code. The main idea of the proposed algorithm is to modify the list decoding procedure of the TBCC by using the CRC. Two algorithms are proposed for the list decoding of the TBCC with the CRC. The first proposed algorithm is a new initial state estimating algorithm using re-encoded CRC bits and having the low computational complexity. The other proposed algorithm is a modified list Viterbi algorithm, where trellis paths are fixed by re-encoded CRC bits and some CRC bits are used for the error correction. For the TBCC concatenated with the CRC code defined in the long-term evolution standard, the proposed decoding scheme by partially using CRC bits outperforms the conventional list decoding algorithms for the list size $L=4$ even though the proposed algorithm has the lower decoding complexity.

Maximum likelihood detection for coded combinerless LINC-OFDM systems

Owning to the high peak-to-average power ratio problem, the power efficiency of orthogonal-frequency-division-multiplexing (OFDM) systems is usually low. It deteriorates in millimeter wave systems in which the design of an efficient linear power amplifier is much more challenging. The linear-amplification-with-nonlinear-component (LINC) technique can serve as a remedy, decomposing the input signal into two constant-envelop component signals followed by high-efficient nonlinear amplifiers. However, the power combiner, a key component used to combine the amplified signals, is difficult to implement. Combinerless LINC systems employ two transmit antennas such that two component signals can be naturally combined at the receiver. Unfortunately, the performance of combinerless LINC-OFDM systems is seriously degraded if difference, even small, exists between the two channels. The maximum likelihood (ML) receiver can effectively solve the problem; however, its computational complexity is prohibitedly high. We propose a coded combinerless LINC-OFDM system, including a convolutional encoder and a list Viterbi algorithm (LVA) decoder, to solve the problem. The LVA can provide a small number of candidates for the ML detector, dramatically reducing the required computational complexity. We also utilize an enhanced zero-forcing equalizer such that the soft-demapping operation can be effectively conducted. Finally, we propose a simple iterative interference cancellation scheme to further enhance the performance. Simulations show that the proposed combinerless LINC-OFDM system can outperform the conventional OFDM while the consumed power is much lower.

Speech Quality Improvement Based on List Viterbi and Joint Source-Channel Decoding in UMTS

In this letter, we propose a simple and efficient method, called `Dual-CRC', to improve speech quality based on the list Viterbi algorithm (LVA) in the Universal Mobile Telecommunications System (UMTS). We also employ the well-known joint source-channel decoding (JSCD) scheme together with LVA decoding to further improve the speech quality. Simulation results show that the two proposed decoders, the Dual-CRC LVA and the combination of the LVA and the JSCD, can significantly improve the speech quality for UMTS, especially in low signal-to-noise ratio and low mean opinion score regions.

CRC-assisted error correction in a convolutionally coded system

In communication systems employing a serially concatenated cyclic redundancy check (CRC) code along with a convolutional code (CC), erroneous packets after CC decoding are usually discarded. The list Viterbi algorithm (LVA) and the iterative Viterbi algorithm (IVA) are two existing approaches capable of recovering erroneously decoded packets. We here employ a soft decoding algorithm for CC decoding, and introduce several schemes to identify error patterns using the posterior information from the CC soft decoding module. The resultant iterative decoding-detecting (IDD) algorithm improves error performance by iteratively updating the extrinsic information based on the CRC parity check matrix. Assuming errors only happen in unreliable bits characterized by small absolute values of the log-likelihood ratio (LLR), we also develop a partial IDD (P-IDD) alternative which exhibits comparable performance to IDD by updating only a subset of unreliable bits. We further derive a soft-decision syndrome decoding (SDSD) algorithm, which identifies error patterns from a set of binary linear equations derived from CRC syndrome equations. Being noniterative, SDSD is able to estimate error patterns directly from the decoder output. The packet error rate (PER) performance of SDSD is analyzed following the union bound approach on pairwise errors. Simulations indicate that both IDD and IVA are better tailored for single parity check (PC) codes than for CRC codes. SDSD outperforms both IDD and LVA with weak CC and strong CRC. Applicable to AWGN and flat fading channels, our algorithms can also be extended to turbo coded systems.

Joint Erasure Marking and List Viterbi Algorithm for Decoding in Unknown Non-Gaussian Noise

In many real-world communication systems, the channel noise is non-Gaussian due to the presence of impulsive noise as well as the background Gaussian noise. In such situations, the conventional Euclidean distance based decoder may suffer from the problem of severe metric mismatch. To overcome the problem, we recently proposed the joint erasure marking and Viterbi algorithm (JEVA) as a robust trellis decoder that does not require an estimate of the impulsive noise distribution. In this work, two ways to further improve JEVA are presented for systems with an error detecting code. Specifically, the JEVA is integrated with the list Viterbi algorithm (LVA) to form the two-dimensional joint erasure marking and list Viterbi algorithm (JELVA) and the switched JELVA, respectively. By combining the respective strengths of the JEVA and the LVA, the integrated decoding schemes are able to achieve significant performance gains over the original JEVA and achieve a wide range of performance-complexity-delay tradeoffs.

Designing Algebraic Trellis Code as a New Fixed Codebook Module for ACELP Coder

In this paper, a block-constrained trellis coded quantization (BC-TCQ) algorithm is combined with an algebraic codebook to produce an algebraic trellis code (ATC) to be used in ACELP coding. In ATC, the set of allowed algebraic codebook pulse positions is expanded, and the expanded set is partitioned into subsets of pulse positions; the trellis branches are labeled with these subsets. The list Viterbi algorithm (LVA) is used to select the excitation codevector. The combination of an ATC codebook and LVA trellis search algorithm is denoted as an ATC-LVA block code. The ATC-LVA block code is used as the fixed codebook of the AMRWB 8.85kbps mode, reducing complexity compared to the conventional algebraic codebook.

Fast tree-trellis list Viterbi decoding

A list Viterbi algorithm (LVA) finds the n most likely paths in a trellis diagram of a convolutional code. One of the most efficient LVAs is the tree-trellis algorithm of Soong and Huang. We propose a new implementation of this algorithm. Instead of storing the candidate paths in a single list sorted according to the metrics of the paths, we show that it is computationally more efficient to use several unsorted lists, where all paths of the same list have the same metric. For an arbitrary integer bit metric, both the time and space complexity of our implementation are linear in n. Experimental results for a binary symmetric channel and an additive white Gaussian noise channel show that our implementation is much faster than all previous LVAs.

Performance Evaluation of List Sequence MAP Decoding

List-sequence (LS) decoding has the potential to yield significant coding gain additional to that of conventional single-sequence decoding, and it can be implemented with full backward compatibility in systems where an error-detecting code is concatenated with an error-correcting code. LS maximum-likelihood (ML) decoding provides a list of estimated sequences in likelihood order. For convolutional codes, this list can be obtained with the serial list Viterbi algorithm (SLVA). Through modification of the metric increments of the SLVA, an LS maximum a posteriori (MAP) probability decoding algorithm is obtained that takes into account bitwise a priori probabilities and produces an ordered list of sequence MAP estimates. The performance of the resulting LS-MAP decoding algorithm is studied in this paper. Computer simulations and approximate analytical expressions, based on geometrical considerations of the decision domains of LS decoders, are presented. We focus on the frame-error performance of LS-MAP decoding, with genie-assisted error detection, on the additive white Gaussian noise channel. It is concluded that LS-MAP decoding exploits a priori information more efficiently, in order to achieve performance improvements, than does conventional single-sequence MAP decoding. Interestingly, LS-MAP decoding can provide significant improvements at low signal-to-noise ratios, compared with LS-ML decoding. In this environment, it is furthermore observed that feedback convolutional codes offer performance improvements over their feedforward counterparts. Since LS-MAP decoding can be implemented in existing systems at a modest complexity increase, it should have a wide area of applications, such as joint source-channel decoding and other kinds of iterative decoding.

An efficient parallel algorithm for list Viterbi decoding

There is nowadays an increasing interest in list Viterbi decoding, especially for transmission of audio and video over wireless channels. List Viterbi decoding outperforms conventional Viterbi decoding at the expense of an increase in complexity. In this paper, we propose an efficient parallel list Viterbi algorithm with lower computational complexity and memory requirements.

List Viterbi algorithms for continuous transmission

The conventional list Viterbi algorithm (LVA) produces a list of the L best output sequences over a certain block length in decoding a terminated convolutional code. We show in this paper that the LVA with a sufficiently long list is an optimum maximum-likelihood decoder for the concatenated pair of a convolutional code and a cyclic redundancy check (CRC) block code with error detection. The CRC is used to select the output. New LVAs for continuous transmission are proposed and evaluated, where no termination bits are required for the convolutional code for every CRC block. We also present optimum and suboptimum LVAs for tailbiting convolutional codes. Convolutional codes with Viterbi decoding were proposed for so-called hybrid in band on channel (hybrid IBOC) systems for digital audio broadcasting compatible with the frequency modulation band. For high-quality audio signals, it is beneficial to use error concealment/error mitigation techniques to avoid the worst type of channel errors. This requires a reliable error flag mechanism (error detection feature) in the channel decoder. A CRC on a block of audio information bits provides this mechanism. We demonstrate how the LVA can significantly reduce the flag rate compared to the regular Viterbi algorithm (VA) for the same transmission parameters. At the expense of complexity, a receiver optional LVA can reduce the flag rate by more than an order of magnitude. The difference in audio quality is dramatic. The LVA is backward compatible with a VA.

A concatenated coding technique for partial response channels

A new concatenated coding technique has been developed for high-order PRML channels. Its first key feature is a pre-error-correction-coding (pre-ECC) scheme comprising cyclic-redundancy-check ECC (CRCC) coding and simplified soft-output decoding. The CRCC coding, a very-low-redundancy inner-block ECC concatenated to the PRML channel, specifically corrects dominant short error-events in the ML-detector. The soft-output decoding enhances the CRCC coding capability through the list and soft-symbol output Viterbi-algorithm (list-SOVA). A second key feature is an iterative decoding scheme to ensure efficient cooperation between an outer Reed-Solomon (RS) ECC and the ML-detector. By using error-free decoded bit-information feedback from the outer RS-ECC decoder, the iterative scheme employs "state pinning" in the ML trellis-detector. This enables long error-events remaining after the CRCC decoding to be corrected efficiently without increasing the coding redundancy and the decoding complexity. Complementary use of the iterative scheme for long error-events and the CRCC decoding for dominant short error-events improves the total system error-rate performance. Simulation showed that the concatenated coding scheme could significantly improve the RS-ECC error-rate performance of a 16/17-rate quasi-MTR-coded ME/sup 2/PRML channel when used in conjunction with CRCC coding.

An integrated error correction and detection system for digital audio broadcasting

Hybrid in-band on-channel digital audio broadcasting systems deliver digital audio signals in such a way that is backward compatible with existing analog FM transmission. We present a channel error correction and detection system that is well-suited for use with audio source coders, such as the so-called perceptual audio coder (PAC), that have error concealment/mitigation capabilities. Such error mitigation is quite beneficial for high quality audio signals. The proposed system involves an outer cyclic redundancy check (CRC) code that is concatenated with an inner convolutional code. The outer CRC code is used for error detection, providing flags to trigger the error mitigation routines of the audio decoder. The inner convolutional code consists of so-called complementary punctured-pair convolutional codes, which are specifically tailored to combat the unique adjacent channel interference characteristics of the FM band. We introduce a novel decoding method based on the so-called list Viterbi algorithm (LVA). This LVA-based decoding method, which may be viewed as a type of joint or integrated error correction and detection, exploits the concatenated structure of the channel code to provide enhanced decoding performance relative to decoding methods based on the conventional Viterbi algorithm (VA). We also present results of informal listening tests and other simulations on the Gaussian channel. These results include the preferred length of the outer CRC code for 96-kb/s audio coding and demonstrate that LVA-based decoding can significantly reduce the error flag rate relative to conventional VA-based decoding, resulting in dramatically improved decoded audio quality. Finally, we propose a number of methods for screening undetected errors in the audio domain.

High-rate coding system for magnetic recording

A coding system for magnetic recording channels combining a high-rate error detection code with a list Viterbi algorithm (LVA) is proposed. This coding system can provide a coding gain of up to 2-3 dB for a modified extended extended partial response class IV (EEPR4) channel. A pipelined implementation of the LVA is presented, and an accurate estimation technique for the LVA performance is developed.

Multiple symbol differential detection for trellis-coded MPSK over Rayleigh fading channels

This paper presents a multiple-symbol differential detection scheme for coded and interleaved transmission of MPSK data. The performance of this scheme is then evaluated for transmission of digitized voice over a Rayleigh fading channel. It is found that in terms of bit error rate, the improvement given by using multiple-symbol differential detection is minimal, but when evaluated in terms of frame-error rate, the multiple-symbol scheme gives about 1.25-dB improvement. Another 0.75-dB improvement can be obtained by also using a serial list Viterbi algorithm.