Synchronisation detection in an M-ary PSK system with arate-selectable punctured convolutional code

The authors propose an efficient algorithm for detecting synchronisation in a Viterbi decoder. By monitoring the `back-traceability' between two trellis states with the minimum metric at adjacent time units, over a specified span, the proposed algorithm can efficiently detect synchronisation. Experimental results confirm the efficiency of the proposed algorithm     

Low-Density Parity-Check Codes with 2-State Trellis Decoding

A class of low-density parity-check (LDPC) codes with a simple 2-state trellis structure is presented. For LDPC decoding, the conventional belief propagation (BP) algorithm consists of numerous sub-decoders of single-parity check codes and exchanges information between sub-decoders in an iterative manner. If the single-parity check codes can be constructed and grouped in a proper way, the decoder can be decomposed into few identical 2-state trellis decoders. Therefore, instead of numerous sub-decoders of single-parity check codes, an iterative decoding algorithm based on few sub-decoders over 2-state trellis is proposed. The proposed decoding algorithm improves the efficiency of message passing between sub-decoders and hence provides a fast convergent rate as compared to the standard BP algorithm. Simulation results show that the proposed scheme provides a better performance and a fast convergent rate as compared to those of standard BP algorithm. The result also shows that the proposed algorithm has a similar performance as that of asynchronous replica shuffled BP algorithm and has a slightly inferior performance than that of synchronous replica shuffled BP algorithm. However, complexity analysis shows that our proposed algorithm has complexity that is lower than that of the replica shuffled BP algorithm.     

Achieving Single-User Performance in an FEC-Coded DS-CDMA System for Frequency Selective and Flat Fading Channels

This paper presents a reduced-complexity soft-input soft-output trellis/tree multiuser equalizer for an iterative DS-CDMA system undergoing Rayleigh frequency selective fading. The algorithm first expands the equalizer-trellis to an equivalent trellis/tree structure. Then it applies the M-algorithm to the equivalent structure twice, once to reduce the number of states in the trellis and the other to reduce the number of branches emanating from each state. To compute soft-information, the algorithm utilizes not only those fully-extended paths reaching the end of the trellis but also paths that are traversed and discarded in the pruned trellis. Through a simple update-and-discard procedure, reliable soft-information is extracted from discarded paths which enables an extremely large trellis to be successfully decoded with modest complexity. BER performance is presented for a convolutional-coded DS-CDMA system employing random spreading sequences. Our results demonstrate that the proposed algorithm is capable of achieving single-user performance with a much reduced complexity. The proposed algorithm can also be applied to reduce the complexity of multiuser detection where the transmission channel is frequency flat. Single-user performance can also be achieved with the proposed technique.     

On dualizing trellis-based APP decoding algorithms

The trellis of a finite Abelian group code is locally (i.e., trellis section by trellis section) related to the trellis of the corresponding dual group code which allows one to express the basic operations of the a posteriori probability (APP) decoding algorithm (defined on a single trellis section of the primal trellis) in terms of the corresponding dual trellis section. Using this local approach, any algorithm employing the same type of operations as the APP algorithm can, thus, be dualized, even if the global dual code does not exist (e.g., nongroup codes represented by a group trellis). Given this, the complexity advantage of the dual approach for high-rate codes can be generalized to a broader class of APP decoding algorithms, including suboptimum algorithms approximating the true APP, which may be more attractive in practical applications due to their reduced complexity. Moreover, the local approach opens the way for mixed approaches where the operations of the APP algorithm are not exclusively performed on the primal or dual trellis. This is inevitable if the code does not possess a trellis consisting solely of group trellis sections as, e.g., for certain terminated group or ring codes. The complexity reduction offered by applying dualization is evaluated. As examples, we give a dual implementation of a suboptimum APP decoding algorithm for tailbiting convolutional codes, as well as dual implementations of APP algorithms of the sliding-window type. Moreover, we evaluate their performance for decoding usual tailbiting codes or convolutional codes, respectively, as well as their performance as component decoders in iteratively decoded parallel concatenated schemes.     

Optimal sectionalization of a trellis

While the complexity of trellis decoding for a given block code is essentially a function of the number of states and branches in its trellis, the decoding complexity may be often reduced by means of an appropriate sectionalization of the trellis. Notwithstanding the many examples of such sectionalizations for particular codes that appeared in the literature, no systematic method for finding the best sectionalization of a given trellis is presently known. We present a polynomial-time algorithm which produces the optimal sectionalization of a given trellis T in time O(n²), where n is the length of the code generated by T. The algorithm is developed in a general setting of certain operations and functions defined on the set of trellises; it therefore applies to both linear and nonlinear codes, and easily accommodates a broad range of optimality criteria. The particular optimality criterion based on minimizing the total number of additions and comparisons required for maximum-likelihood trellis decoding is investigated in detail: several different methods for decoding a given trellis are discussed and compared in a number of examples. Finally, analysis of the dynamical properties of certain optimal sectionalizations is presented     

Reduced-complexity equalization techniques for ISI and MIMO wireless channels in iterative decoding

Two reduced-complexity soft-input soft-output trellis decoding techniques are presented in this paper for equalizing single-input single-output intersymbol interference (ISI) channels and multiple-input multiple-output (MIMO) frequency selective fading channels. Given a trellis representing an ISI channel, the soft-output M-algorithm (SOMA) reduces the complexity of equalization by retaining only the best M survivors at each trellis interval. The remaining survivors are discarded. The novelty of the SOMA is the use of discarded paths to obtain soft-information. Through a simple update-and-discard procedure, the SOMA extracts reliable soft-information from discarded paths which enables a large trellis to be successfully decoded with a relatively small value of M. To decode a trellis representing a MIMO frequency selective fading channel, two challenges are faced. Not only that the trellis has a large number of states, the number of branches per trellis interval is also enormous. The soft-output trellis/tree M-algorithm (SOTTMA) expands each trellis interval into a tree-like structure and performs the M-algorithm twice: once at each trellis interval to reduce the number of states and the other at each tree sub-level to remove unwanted branches. With the proposed technique, high-order trellises with million of branches per interval can be decoded with modest complexity.     

A new decoding algorithm for geometrically uniform trellis codes

A new decoding algorithm for geometrically uniform trellis codes is presented. The group structure of the codes is exploited in order to improve the decoding process. Analytical bounds to the algorithm performance and to its computational complexity are derived. The algorithm complexity does not depend on the number of states of the trellis describing the code. Extensive simulations yield results on the algorithm performance and complexity, and permit a comparison with the Viterbi algorithm and the sequential Fano algorithm     

On the BCJR trellis for linear block codes

In this semi-tutorial paper, we will investigate the computational complexity of an abstract version of the Viterbi algorithm on a trellis, and show that if the trellis has e edges, the complexity of the Viterbi algorithm is Θ(e). This result suggests that the “best” trellis representation for a given linear block code is the one with the fewest edges. We will then show that, among all trellises that represent a given code, the original trellis introduced by Bahl, Cocke, Jelinek, and Raviv in 1974, and later rediscovered by Wolf (1978), Massey (1978), and Forney (1988), uniquely minimizes the edge count, as well as several other figures of merit. Following Forney and Kschischang and Sorokine (1995), we will also discuss “trellis-oriented” or “minimal-span” generator matrices, which facilitate the calculation of the size of the BCJR trellis, as well as the actual construction of it     

A cyclic redundancy check‐based non‐coherent receiver for automatic identification system signals

A non‐coherent receiver for automatic identification system (AIS) signals is proposed in this paper. The proposed receiver is based on the Viterbi algorithm with cyclic redundancy check (CRC) trellis. It takes bit stuffing into consideration and is designed to simultaneously demodulate decode and correct the received messages. The complexity of the proposed receiver has been reduced with state‐complexity reduction. Simulations prove that the proposed receiver outperforms those AIS receivers without CRC trellis error correction in terms of BER and packet error rate. Copyright © 2015 John Wiley & Sons, Ltd.     

Trellis coded self-synchronous multi-h CPM

Trellis coded multi-h CPM schemes have been shown in the literature to have attractive power-bandwidth performance at the expense of increased receiver complexity. In this Letter, a combined trellis coding with self-synchronous multi-h CPM technique is described which eliminates the need for the multi-h synchronisation overhead and maximises the minimum distance. In this method, the multi-h pattern is made to be associated with the encoder state transitions and repeated rather than cyclically changed in time for successive symbol intervals, resulting in a simpler receiver with better performance     

Cyclic redundancy check‐based detection algorithms for automatic identification system signals received by satellite

This paper addresses the problem of demodulating signals transmitted in the automatic identification system. The main characteristics of such signals consist of two points: (i) they are modulated using a trellis‐coded modulation, more precisely a Gaussian minimum shift keying modulation; and (ii) they are submitted to a bit stuffing procedure, which makes more difficult the detection of the transmitted information bits. This paper presents several demodulation algorithms developed in different contexts: mono‐user and multi‐user transmissions, and known/unknown phase shift. The proposed receiver uses the cyclic redundancy check (CRC) present in the automatic identification system signals for error correction and not for error detection only. By using this CRC, a particular Viterbi algorithm, on the basis of a so‐called extended trellis, is developed. This trellis is defined by extended states composed of a trellis code state and a CRC state. Moreover, specific conditional transitions are defined to take into account the possible presence of stuffing bits. The algorithms proposed in the multi‐user scenario present a small increase of computation complexity with respect to the mono‐user algorithms. Some performance results are presented for several scenarios in the context of the automatic identification system and compared with those of existing techniques developed in similar scenarios. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive state allocation algorithm in MLSD receiver for multipathfading channels: structure and strategy

This paper presents the adaptive state allocation (ASA) algorithm, a new scheme based on maximum likelihood sequence detection (MLSD) of signals transmitted over Rayleigh fading channels. Although MLSD is an optimal scheme, its computational complexity limits many applications. The ASA algorithm is a detection method whose performance is close to that of MLSD, but with greatly reduced computational complexity. Adaptive state partitioning in the trellis diagram is used in this algorithm by measuring the short-term received signal power. Also, an adaptive threshold for selecting only a few states of the trellis is employed in this algorithm based on the Chernoff distance between the probability density functions (PDFs) of correct and incorrect branch metrics. The ASA-DF, a special case of ASA using decision feedback, shows a very good tradeoff between the performance and computational complexity for selective fading channels. Using ASA with diversity reception not only improves the performance, but also decreases the computational complexity in comparison with the computational complexity of using MLSD with diversity reception     

Non‐binary SOVA algorithms for decoding of block codes on a sectionalized trellis

In this paper, we explore computationally efficient implementations of the soft output viterbi algorithm (SOVA) applied to Soft‐Input Soft‐Output (SISO) decoding of linear block codes. In order to simplify the trellis‐based decoding of binary block codes with SOVA, we use the technique of sectionalization of the trellis, which has been successfully applied to the simplification of the MAP and Max‐Log‐MAP algorithms. Due to the branch complexity of the sectionalized trellis, we define a generalization of a non‐binary version of SOVA. However, the computational complexity of directly applying this approach remains too high for efficient implementation; we thus introduce the concept of non‐binary SOVA (NSOVA) with propagation of bit‐level reliabilities (BLR). This new algorithm is analyzed from a computational complexity viewpoint. Both serial and parallel implementations are explored. Finally, optimal sectionalizations are derived for selected codes; since the normal SOVA decoding is a particular case of NSOVA with BLR, we show that our approach is more efficient than a bit‐level trellis by showing that, for all the codes tested, the optimal trellis is a sectionalized one. Copyright © 2007 John Wiley & Sons, Ltd.     

基于额外列多元LDPC码网格最小最大译码算法

为了降低多元LDPC(Low Density Parity Check Code)码网格最小最大(Trellis Min-Max,T-MM)译码算法复杂度,减少译码过程中所需存储空间,提出一种基于额外列的T-MM译码算法(Extra-Column-based Trellis Min-Max,EC-T-MM).选取网格中可靠度最高的信息构造出优化的配置集,生成一列用于更新校验节点的q维额外列信息,再根据网格路径中偏移量信息,从最小值、次小值和额外列信息中得到校验节点的外在输出信息,通过网格的路径优化降低校验节点的更新复杂度.在译码过程中,用偏移量信息代替所有变量节点输入信息,减少存储空间.仿真结果表明:该算法在几乎不损失性能的前提下,降低了计算复杂度及所需的存储空间.     

Efficient performance computations for trellis-coded modulation

The algorithm given by Rouanne and Costello (1989) for the computation of the distance spectrum is improved for trellis-coded modulation schemes having uncoded bits, i.e., for trellis diagrams having parallel paths. It is shown that, when through a trellis corresponding to such kind of codes, all parallel transitions (labeled by signal selectors) between states are considered as a single branch labeled by a subset, then defining subset selector distance polynomials makes the computational complexity of the distance spectrum dependent on the number of states as compared to the complexity of Rouanne and Costello algorithm which depends on the number of paths to be extended     

A trellis-based recursive maximum-likelihood decoding algorithm forbinary linear block codes

This paper presents an efficient trellis-based maximum-likelihood decoding algorithm for binary linear block codes. This algorithm is recursive in nature and is devised based on the structural properties and optimum sectionalization of a code trellis. The complexity of the proposed decoding algorithm is analyzed. Numerical results show that the proposed decoding algorithm significantly reduces the decoding complexity. A recursive method for finding the optimum sectionalization of a trellis in terms of computational complexity is given     

Analysis and Comparison of Multimedia Inter-stream and Group Synchronisation Algorithms

In this paper an analysis and comparison of multimedia synchronisation algorithms is presented. After presenting the three types of multimedia synchronisation (intra-stream, inter-stream and group synchronisation), only inter-stream and group synchronisation algorithms are considered. The main synchronisation techniques included in most of the analysed algorithms have also been classified. Finally, a table is presented with the main characteristics of each algorithm according to the techniques included and other critical parameters such as the use of global or locally available clocks, the suitability for stored contents or live contents, the synchronisation information added to the data packets, the use of Real Time Transport Protocol, etc. This work provides a good starting point to all the new researchers interested in multimedia synchronisation and multimedia systems.     

Parallel trellis Viterbi algorithm for sparse channels

The Viterbi algorithm (VA), which normally operates using a single trellis, can be optimally reformulated into a set of independent trellises for a special class of sparse intersymbol interference (ISI) channels. These independent trellises operate in parallel and have less overall complexity than a single trellis. This trellis decomposition can be applied to a more general class of sparse channels approximately resulting in a suboptimal reduced complexity equalizer     

Reduced-Complexity Time-Domain Equalization for Turbo-MIMO Systems

A reduced-complexity time-domain equalization scheme for wideband turbo-multiple-input multiple-output (turbo-MIMO) systems is presented. This scheme, called iterative trellis search equalization, is based on a modified version of the M-Bahl-Cocke-Jelinek-Raviv (M-BCJR) algorithm, applied to a suitably chosen trellis representation of the wideband MIMO channel process. Exploiting the properties of quadrature amplitude modulation (QAM) signal constellations with block-partitionable labels, this modified M-BCJR algorithm has complexity per bit that is independent of the constellation size, and polynomial in the number of transmit antennas and channel memory. Results from computer simulations show that the new scheme successfully mitigates intersymbol interference even if only a very small fraction of trellis state transitions is considered. It is also demonstrated that asynchronous transmission of the spatially multiplexed symbol streams can result in considerable performance improvement compared to synchronous MIMO systems.     

MAP algorithms for decoding linear block codes based onsectionalized trellis diagrams

The maximum a posterioriprobability (MAP) algorithm is a trellis-based MAP decoding algorithm. It is the heart of turbo (or iterative) decoding that achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in a long decoding delay. For practical applications, this decoding algorithm must be simplifled and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variation's, such as log-MAP and max-log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bidirectional and parallel MAP decodings