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This study proposes a system that employs multilevel coding scheme with dynamic space–time trellis codes (DSTTCs) as component codes in order to cooperatively transmit the information of mobile nodes to a common destination node. Perfect channel state information is available at both transmitter and receiver. Every mobile node has a DSTTC encoder at each information level, which receives feedback information from destination node and adapts to the current channel conditions by modifying its code set of generator sequences. The feedback information is in the form of an index of predefined channel profile with power gain in close proximity to the power gain of current channel profile at destination node. The proposed cooperative multilevel dynamic space–time trellis coding (CMLDSTTC) system has the potential of improving spectral efficiency, system throughput, diversity gain, coding gain with low decoding complexity. The CMLDSTTC system outperforms cooperative multilevel space–time trellis coding (CMLSTTC) system with predefined space–time trellis codes and non-cooperative multilevel dynamic space–time trellis coding system by ∼5 and ∼2.5 dB, respectively, at frame error rate of 10−2 using two transmit and two receive antennas. The performance of CMLDSTTC system improves further with an increase in the bits of feedback information.

Spatial modulation (SM), which employs the indices of multiple transmit antennas to transmit information in addition to the conventional M-ary signal constellations, is a novel transmission technique that has been proposed for multiple-input multiple-output systems. In this study, a new class of space-time trellis codes, called 'super-orthogonal trellis-coded SM' (SOTC-SM), is proposed. These codes combine set partitioning and a super set of space-time block coded SM (STBC-SM) codewords to achieve maximal diversity and coding gains by exploiting both SM and space-time block codes. Unlike super-orthogonal space-time trellis codes (SOSTTCs), which parametrise the orthogonal STBCs, these new codes expand the antenna constellation using the principle of SM. Systematic construction methods are presented for the SOTC-SM scheme and design examples are given for 2, 4 and 8 trellis states, at 2, 3 and 4 bits/s/Hz spectral efficiencies. The approximate bit-error probability performance of SOTC-SM is derived and shown to match computer simulation results. A simplified maximum likelihood detection method for the proposed scheme is given. It is shown through computer simulations that the proposed SOTC-SM schemes achieve significantly better error performance than SOSTTCs with comparable complexity.

A new high-order differential space-time block code (DSTBC) is introduced as an attractive alternative to the well-known coherent space-time block code (STBC) by providing both full space-time diversity and blind detection. A differential detection based on the orthogonal STBC scheme is proposed. The proposed differential scheme is a generalisation of the recent DSTBC already designed for two transmit antennas. The proposed differential encoder consists of a specific trellis diagram that creates a positive correlation between successive differential data. At the receiver side, the well-known Viterbi algorithm is applied using a specific metric that nearly compensates for the 3 dB penalty commonly introduced by the symbol by symbol differential schema, and shows a 0.5 dB performance loss only from the coherent STBC scheme.

In fading channels, the minimum product distance of a trellis code plays an important role in error rate performance. In the Letter, an algorithm for computing the minimum product distance and its multiplicity is introduced. The algorithm is applied to search for best trellis codes on fading channels.

Super-orthogonal space-time trellis (SOSTT) codes provide a significant coding gain with respect to the conventional space-time trellis (STT) codes without increasing the decoding complexity at the receiver. Transmit antenna selection (TAS) is an important technique to solve the implementation complexity problems of multiple-antenna systems that arise from employing a separate RF chain for each antenna. This study treats a scheme combining SOSTT coding with TAS in order to exploit performance improvements provided by SOSTT codes while realising the promises made by the TAS technique. In the proposed scheme, transmit antennas that maximise the signal-to-noise ratio at the receiver are chosen and activated out of all available transmit antennas for transmission of the baseline SOSTT code, whereas all other transmit antennas are silent. The error performance of the proposed structure is investigated by deriving moment generating function (MGF)-based upper bound expressions on the pairwise error probability in quasi-static flat Rayleigh fading channels for both perfect and imperfect antenna subset selection. The performance analysis demonstrates that the proposed scheme provides full diversity order as if all transmit antennas were used when antennas are perfectly selected. Moreover, it is shown that this structure provides better error performance almost at the same decoding complexity compared to the previous STT coding structures with TAS in the literature.

An family of improved trellis coded signaling schemes is provided that by vary the signal constellation to a smaller constellation periodically according to a pre-selected pattern. A set of specific embodiments involving periodically-reduced 4-PAM/2-PAM trellis coded schemes are disclosed that change their signal constellations periodically from 4-PAM to 2-PAM during selected intervals to improve performance. Similar periodically QAM and higher-dimensional coding schemes are also disclosed. Simplified receiver and decoder structures to decode the periodically-reduced trellis codes are also presented. The present invention allows embodiments to be produced that reduce coding complexity, reduce decoding complexity, and simplify symbol timing recovery and equalization. The cost is a moderate increase in the path memory length of the decoder.

An improved design criterion for distributed space-time trellis codes with amplify-and-forward relaying for the case of one relay is derived. The codes found by the new criterion are compared to conventional codes, and the results show that the new codes provide a performance gain over the conventional codes.

All the best known space-time trellis codes (STTCs) belong to the balanced STTC class. The first method to design balanced STTCs is proposed. The exhaustive code search of optimal codes can then be reduced to this class. Finally, the proposed method is used to construct new QPSK codes for three and four transmit antennas, which outperform the best previously published codes of the same complexity.

Conventional space-time turbo trellis coding (STTuTC) schemes allocate transmit power equally to the available antennas. This is not optimal if channel state information (CSI) is available at the transmitter. A STTuTC scheme is considered with partial CSI knowledge that optimally allocates power to the transmit antennas. This scheme is referred to as STTuTC with dynamic transmit power allocation (STTuTC/DTPA). The optimum four-state constituent code and power allocation are presented. Simulation results show that the STTuTC/DTPA scheme with the new code outperforms conventional STTuTC schemes.

The performance analysis of high rate space-time trellis-coded modulation (HR-STTCM) using the Gauss-Chebyshev quadrature technique is presented. HR-STTCM is an example of space-time codes that combine the idea used in trellis coded modulation (TCM) design that is signal set expansion and set partitioning into its construction. HR-STTCM construction is based on the concatenation of an outer TCM encoder and inner space-time block code. This paper evaluates the exact pairwise error probability of HR- STTCM based on the Gauss-Chebyshev quadrature formula. Comparison of numerical and simulation results shows that the proposed method is accurate. The method used is shown to be computationally simpler than those in the literature.

Super-orthogonal space-time trellis codes (SOSTTCs) given in the literature are full rate and provide full spatial diversity with high coding gain in narrowband quasistatic fading channels. The high number of parallel transitions in their trellis structure restricts their performance in wideband channels where the code performance suffers from multipath. Code design criteria are derived and a computer search based method is proposed to design full-rate optimised SOSTTCs exploiting full spatial and multipath diversity for multiple-input multiple-output orthogonal frequency division multiplexing systems. The proposed codes have codewords defined in space, time, and frequency. We evaluate the codeword error rates of the new 16, 32 and 64-state super-orthogonal space-time-frequency trellis codes for quadrature phase shift keying by computer simulation and show that they provide significant error performance improvement compared to their counterparts with equivalent delay length.

A high-rate (rate 1.5) nonlinear orthogonal space-time block code for four transmit antennas is presented. It outperforms previous space-time block codes where there are more than two receive antennas. This high-rate code improves on the performance of a recently proposed nonlinear orthogonal space-time block code of the same rate and without any extra constellation expansion.

Binary continuous phase modulation (CPM) is considered with space-time trellis codes (STTCs) for multiple-input multiple-output systems. Single-h CPM with rectangular, raised cosine and half cycle sinusoid is considered. The upper bound on the minimum product distance of this signalling scheme is determined over a quasi-static Rayleigh fading channel. Based on the rank and determinant criterion, best STTC/CPM combinations are identified for two transmit and an arbitrary number of receive antennas.

In existing space-time trellis codes (STTCs), the transmit power is equally distributed across all transmit antennas. However, this power allocation strategy is not optimum regarding the error performance. A new scheme is proposed, referred to as the weighted space-time trellis codes with dynamic transmit power allocation (WSTTCs/DTPA). Compared with the general open-loop STTCs, WSTTCs/DTPA have better performance and achieve a full diversity order regardless of STTCs adopted at the transmitter.

It has been shown that if perfect channel state information is available at the transmitter, the performance of a space-time coded system can be dramatically improved by weighting the transmitted signals. In this reported work, the performance of combined space-time turbo trellis codes and ideal beamforming is evaluated. Simulation results show that the proposed scheme considerably outperforms the conventional space-time turbo trellis codes without weighting and it approaches the MIMO channel capacity within about 1.5 dB with a moderate interleaver size over quasi-static fading channels.

The authors address the problematic issues in generating space-time trellis codes, and propose novel methods for reducing the exponentially growing full code search. It is proved that by exploiting the symmetry in QAM and PSK constellations, together with the modulo operation in the encoder, the number of possible combinations in the generator matrix can be halved when performing a full search to obtain optimal codes. It is also shown that for a fixed set of columns in the generator matrix, interchanging columns yields identical results, hence reducing the full code search by the factorial of the number of transmit antennas. Furthermore, the existing sub-optimal (but fast) method for obtaining codes is investigated and results from this method are compared with those obtained from the two proposed methods. Using the suggested methods, novel space-time codes for both slow and fast fading environments are generated and their performance is evaluated through frame error probabilities obtained by simulation.

The performance of space-time trellis codes with antenna selection over fast fading channels is studied. A selection criterion is adopted that is based on selecting L out of the available M receive antennas that results in maximising the instantaneous signal-to-noise ratio (SNR) at the receiver, where L/spl les/M. It is shown that the resulting diversity order with antenna selection deteriorates and becomes a function of the number of selected antennas. This is unlike the case for slow fading in which the diversity order is always preserved with antenna selection when the underlying space-time code is full-rank.

A code design criterion for the design of space-time trellis codes in keyhole channels is provided. The code designed according to this criterion is shown to have a better performance compared with previously designed codes for Rayleigh fading channels.

The space-time (ST) trellis code for 2P4PSK orthogonal plane sequence modulation (OPSM) signals is presented when the number of receiver antennas is large. The simulation results shows that the ST codes obtained from the maximising minimum squared Euclidean distance criterion search algorithm achieve a recognisable coding gain (i.e. 1–2 dB) over the codes of Choe , where the coding gain increases for the case of two or more receiver antennas.

The residual redundancy that persists in the transmitted parameters of a low bit rate speech coder are exploited to reduce the computational complexity of a Reed-Solomon (RS) trellis decoder. The use of RS codes for mobile telephony provides the opportunity for avoiding channel interleaving and so reduces one-way delay.

A low-complexity encoding and maximum-likelihood trellis decoding (MLTD) technique for nonlinear balanced codes is presented. The technique is illustrated by the design of a (16, 9, 4) balanced code.

A scheme combining transmit antenna selection (TAS) and space-time trellis code (STTC), which is referred to as the TAS/STTC scheme, is considered. In this scheme, two transmit antennas, which maximise the signal-to-noise ratio (SNR) at the receiver, are chosen to transmit the baseline STTCs designed for two transmit antennas. It is shown by simulation that, similar to two other transmit antenna selection schemes investigated previously by the authors, this scheme also achieves a full diversity order as if all the transmit antennas were used. In addition, this scheme has a fixed low decoding complexity no matter how high the diversity order. Unlike the traditional STTC, this scheme does not have the requirement for minimum memory order to achieve a full diversity order.

Novel space-time trellis codes (STTCs) combined with adaptive weighting at transmitter-weighted space-time trellis codes (WSTTCs) are proposed and a new design criterion is presented. Simulation results show that it outperforms both the optimum beamforming scheme and standard STTCs without weighting.

Punctured space-time trellis codes (STTCs) that preserve the diversity gain for short error sequences are derived. The rate 4/3 and 8/7 punctured STTCs achieve a two-level diversity gain for a frame size of 16, which require 1.3 and 0.7 dB more power to attain the same frame error rate compared with the STTC without puncturing.

New space-time trellis-codes based on a signalling with high dimensionality (= 2n, n = 2, 3....) that are applicable to high rate wireless CDMA systems are presented. Compared to known codes these codes improve coding gain and system adaptability while maintaining the maximum diversity gain, especially at or above 3 bits/s/Hz.

Novel space-time trellis codes for five and six transmit antennas which best satisfy an optimal design criteria for quasi-static flat fading channels are presented. The codes are constructed through a reduced code-search method, and their performance is evaluated in terms of frame error probabilities.

Good 8-PSK space-time trellis codes (STTCs) for two, three and four transmit antennas are reported and the performance is evaluated by simulation. The new STTCs with three and four transmit antennas achieve large performance improvements over those with two transmit antennas.

New non-orthogonal space-time block codes for three transmit antennas are proposed, achieving throughput rates larger than those of currently known orthogonal designs. The proposed codes are found through a code search based on the rank criterion, determinant criterion and rank distribution.

A multiple input, multiple output (MIMO) iterative decoding structure is proposed for serial concatenated codes with space-time trellis code (STTC) as outer code and rate-1 recursive convolutional encoders as inner coder. To preserve the full diversity gain of the space-time code and to achieve additional coding gain, the proposed MIMO iterative decoder decodes jointly the received symbol streams from all the transmit antennas. The bit error rate simulation of four-state STTC employing the proposed scheme shows additional 3 dB coding gain, without reducing the code rate, compared to that achievable by STTC alone.

A reduced-complexity Jacobian redial basis function aided turbo equalisation (TEQ) scheme is proposedm which was found to provide a bit error ratio performance similar to that of the conventional trellis-based TEQ benchmarker at a 14-fold reduced complexity for a serially concatenated systematic convolutional coded and systematic space-time trellis-coded arrangement.

It has been established that the appropriate criteria for space-time trellis coded modulation (STTCM) design on slow Rayleigh fading channels are maximisation of the minimum rank and the minimum determinant of the distance matrices. It is demonstrated that when STTCM is used in systems with a large product (>3) of the numbers of transmit and receive antennas, the design of codes with maximum coding gain is governed by the minimum trace of the distance matrices. A number of new codes based on the proposed design criterion have been constructed and shown to be superior to other known codes.

A simple recursive method for generating weight enumerating functions of trellis codes with finite lengths is presented. The proposed technique is conceptually simple and yet computationally efficient. It provides a convenient means for evaluating the performance of turbo-type concatenated codes.

In the context of per-survivor processing, an adaptive decoder for a space-time trellis code is proposed which exploits the accelerated self-tuning least-mean-square algorithm for tracking the fading channel. The proposed decoder provides good performance on slowly and moderately fast time-varying wireless channels.

The BER performance of a spectrally efficient trellis coded modulation (TCM) scheme, which combines convolutional coding and GMSK, in frequency-selective fading channels, is presented. Computer simulated results show that a significant improvement in the BERs is achievable with the TCM scheme. The TCM scheme also shows less sensitivity to carrier phase errors than the uncoded scheme.

A novel code combining system based on Reed-Muller codes is presented. Because of their simple structure RM codes are simple to decode using a trellis based soft maximum likelihood decoder (SMLD). The decoder exploits the modular structure of the RM code to construct a set of nested trellises which minimise the complexity of the decoder by re-using the results of previous decoding attempts. A protocol utilising this technique to produce an efficient code combining ARQ-scheme is also introduced.

Turbo codes can be naturally extended to bandwidth-efficient applications. A turbo code with powerful bandwidth-efficient component codes is investigated and its application in the discrete multitone environment is considered. Simulation results show that the multidimensional turbo trellis-coded modulation scheme can achieve outstanding performance even at relatively low signal-to-noise ratio.

A receiver structure is proposed for trellis coded signals transmitted through broadband wireless channels based on the generalised Viterbi algorithm (GVA). Simulation results show that the proposed receiver structure is suitable for high bit rate wireless applications and gives close to optimal performances with reasonable complexity.

A novel decoder for a space-time trellis code (STTC) used in a TDMA downlink is developed which performs adaptive decoding with bidirectional per-survivor processing and soft-decision. Simulation results are given, which demonstrate the system performance improvement which can be realised using this proposed decoder.

An efficient reduced search trellis decoding algorithm in which the decoder selects a part of existing paths by using a threshold value of the path metric is proposed. The threshold value at each time stage of the trellis is found by simply investigating the statistics of the path metrics, and does not require any prior knowledge such as the signal-to-noise ratio.

A Chernoff bound is derived on the pairwise error event probability of pilot-symbol aided TCM schemes with L-fold space diversity in a Rayleigh fading channel. In the scheme, pilot-symbols are inserted periodically to estimate the channel characteristics. The fading processes experienced by the pilot-symbols are used to estimate those suffered by the data symbols using interpolation. The estimated fading characteristics are used to compute the symbol metrics of the Viterbi decoder. With the Chernoff bound derived, the cutoff rate of 16QAM and the bit error probability (BEP) of the trellis coded 16QAM scheme are calculated as a function of the signal-to-noise ratio (SNR) and the Doppler shift. New trellis codes are constructed according to the proposed design rule and are shown to result in a performance improvement over the conventional trellis code.

The authors have used a multilevel coding technique to construct run-length limited (RLL) trellis codes with error-correcting capabilities. The constructed codes have better performance than the RLL trellis codes previously proposed, in terms of error-correcting capabilities, coding rates and decoding complexities.

A novel low-complexity trellis design technique for linear binary block codes is introduced. It is shown that, for some linear block codes, the problem of finding the permutation minimal trellis is very simple. For linear binary block codes, a heuristic algorithm for the reduction of trellis complexity is proposed. A reduction in trellis complexity is achieved by the implementation of a new permutation algorithm, which is based on column and row permutations in the minimal weight generator matrix of the code. The ‘permutation-oriented’ generator matrix for obtaining permutation minimal or near-minimal trellises is defined.

A trellis design procedure for the M-user binary-adder channel is introduced. Based on this technique, trellis diagrams for some known 2-user coding schemes have been designed. In addition, a DC-free 2-user binary coding scheme, together with its trellis structure, is introduced and investigated. It is shown that the new technique provides about 2 dB energy gain in comparison with the conventional techniques. A useful and interesting application of this technique would be the token-ring local area network where the number of users can be increased without bandwidth expansion.

Various novel trellis decoding methods are suggested that make it easy to incorporate soft decision methods for Reed-Solomon codes. For each decoding method the advantages and disadvantages are pointed out. The performance and computational efficiency of each decoder are estimated using simulation on an AWGN channel. From the simulation results the best of these trellis decoding schemes is suggested for particular codes and particular applications.

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.

To reduce the decoding complexity efficiently when using a trellis, a criterion is introduced, which can indicate at each stage of decoding whether or not the appropriate permutations on columns of the generator or parity-check matrix of the code are needed to obtain the minimal trellis in terms of its complexity. This criterion can also be used as a guide for finding a way to carry out column permutations more efficiently, as is shown in an example.

A new reduced-state trellis and Viterbi decoding for binary full-response continuous phase modulation (FRCPM) are derived. The theoretical and simulated error-rate performance of the reduced-state trellis decoding is presented. It is shown that the reduced-state trellis decoding of FRCPM with small modulation index can provide almost the same error-rate performance as the original-state trellis decoding at high signal-to-noise ratio.

Soft decision decoding of Reed-Solomon codes has been implemented by using trellis decoding methods. Trellis decoding schemes make it possible to incorporate both hard and soft decision methods easily. To establish maximum likelihood performance, the Viterbi decoding algorithm has been used. To reduce the decoder complexity caused by full search Viterbi decoding, reduced search methods have been tried, and a computationally efficient reduced search algorithm is suggested. Importance sampling simulation techniques have been used to reduce simulation time. The simulation results for the (15, 13) and the (15, 11) Reed-Solomon code showed that soft decision trellis decoding could give 2 dB and 2.5 dB coding gains relative to hard decision, respectively, and that the performance of reduced search decoding could approximate that of the Viterbi method with reductions in computation of one to two orders of magnitude.

A new simple algorithm which allows the design of a trellis diagram for array codes is introduced. Based on this algorithm, the trellis decoding of array codes with maximum likelihood decoding (MLD) performance and relatively low complexity is proposed. It is shown that the trellis structure of array codes allows the application of combined coding and modulation (CCM) with higher information digit per channel symbol rate than for conventional CCM methods, based on convolutional codes. The bounds on the transmission rates for different types of CCM signals, based on convolutional and array codes, have been obtained and presented in the paper.