EXIT charts for turbo trellis-coded modulation

In this letter, we extend the previously proposed extrinsic information transfer charts (EXIT) method to the analysis of the convergence of turbo codes to turbo trellis-coded modulation (TTCM) schemes. The effectiveness of the proposed method is demonstrated through examples. The proposed method provides a convenient way to systematically compare between schemes and thus can be used as a tool in the design of TTCM.     

Symbol-interleaver design for turbo trellis-coded modulation

A design method for a code-matched symbol-interleaver for turbo trellis-coded modulation is proposed. The method constructs an interleaver by code matched criteria to eliminate some input error events of low symbol Hamming weight (SHW) sequences of the code which can produce low SHW codewords. Numerical results confirm that the interleaver can lower the error floor at moderate to high signal-to-noise ratio.     

Bandwidth-efficient turbo trellis-coded modulation using puncturedcomponent codes

We present a bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes. The combination of turbo codes with powerful bandwidth-efficient component codes leads to a straightforward encoder structure, and allows iterative decoding in analogy to the binary turbo decoder. However, certain special conditions may need to be met at the encoder, and the iterative decoder needs to be adapted to the decoding of the component TCM codes. The scheme has been investigated for 8-PSK, 16-QAM, and 64-QAM modulation schemes with varying overall bandwidth efficiencies. A simple code choice based on the minimal distance of the punctured component code has also been performed. The interset distances of the partitioning tree can be used to fix the number of coded and uncoded bits. We derive the symbol-by-symbol MAP component decoder operating in the log domain, and apply methods of reducing decoder complexity. Simulation results are presented and compare the scheme with traditional TCM as well as turbo codes with Gray mapping. The results show that the novel scheme is very powerful, yet of modest complexity since simple component codes are used     

Blind equalization of turbo trellis-coded partial-response continuous-phase modulation signaling over narrow-band Rician fading channels

In this paper, a blind maximum-likelihood channel estimation algorithm is developed for turbo trellis-coded/continuous-phase modulation (TTC/CPM) signals propagating through additive white Gaussian noise (AWGN) and Rician fading environments. We present CPM for TTC signals, since it provides low spectral occupancy and is suitable for power- and bandwidth-limited channels. Here, the Baum-Welch (BW) algorithm is modified to estimate the channel parameters. We investigate the performance of TTC/CPM for 16-CPFSK over AWGN and Rician channels for different frame sizes, in the case of ideal channel state information (CSI), no CSI, and BW estimated CSI.     

Phase-noise effects on turbo trellis-coded over M-ary coherent channels

The effect of the phase noise on the performance of bandwidth-efficient coded modulation is studied. To this end, the average mutual information (AMI) for specific constellations such as 8-phase-shift keying and 16-quadrature amplitude modulation is calculated in the presence of carrier phase error caused by imperfect carrier tracking over an additive white Gaussian noise channel. The AMI not only quantifies the effect of the phase noise from an information-theoretic viewpoint, but also serves as an estimate for a permissible amount of the phase noise for a given signal-to-noise ratio. The bit-error rate (BER) performance of a near-optimal turbo trellis-coded modulation scheme is then investigated over such a channel. For this purpose, an optimal branch metric which best fits the channel characteristics is derived. Furthermore, simple branch metrics (referred to as suboptimal, simplified, and Gaussian metrics) are derived, which may offer the tradeoff between BER performance and computational complexity. Numerical analysis shows that a near-optimal coded-modulation scheme renders a transmission system more robust against phase noise than is the case with a conventional trellis-coded modulation scheme.     

Joint trellis-coded quantisation/modulation

Joint trellis-coded quantisation (TCQ) and trellis-coded modulation (TCM) can achieve considerable signal-to-quantisation noise ratios with moderate complexity. TCM is replaced with turbo TCM (TTCM) and simulation results given which show that the new scheme can achieve the same performance as that possible using by trellis-coded scalar quantisation at an SNR slightly above the channel capacity bound     

Improved codes for space-time trellis-coded modulation

Space-time coded modulation has been shown to efficiently use transmit diversity to increase spectral efficiency. We propose new trellis codes found through systematic code search. These codes achieve the theoretically maximal diversity gain and improved coding gain compared to known codes     

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 pragmatic approach to trellis-coded modulation

Since the early 1970s, for power-limited applications, the convolutional code constraint length K=7 and rate 1/2, optimum in the sense of maximum free distance and minimum number of bit errors caused by remerging paths at the free distance, has become the de facto standard for coded digital communication. This was reinforced when punctured versions of this code became the standard for rate 3/4 and 7/8 codes for moderately bandlimited channels. Methods are described for using the same K=7, rate 1/2 convolutional code with signal phase constellations of 8-PSK and 160PSK and quadrature amplitude constellations of 16-QASK, 64-QASK, and 256-QASK to achieve, respectively, 2 and 3, and 2, 4, and 6 b/s/Hz bandwidth efficiencies while providing power efficiency that in most cases is virtually equivalent to that of the best Ungerboeck codes for constraint length 7 or 64 states. This pragmatic approach to all coding applications permits the use of a single basic coder and decoder to achieve respectable coding (power) gains for bandwidth efficiencies from 1 b/s/Hz to 6 b/s/Hz     

Space-frequency-time turbo coded modulation

A new bandwidth and power efficient signaling scheme is proposed that achieves high data rates over wideband radio channels exploiting the bandwidth efficient OFDM modulation, multiple transmit and receive antennas and large frequency selectivity offered in typical low mobility indoor environments. Owing to its maximum transmit diversity gain and large coding gain, space-frequency-time turbo coded modulation strongly outperforms other space-frequency-time coding schemes proposed in literature. A simple way of combining space-frequency-time coding with OFDM delay diversity for cost effective exploitation of more than two transmit antennas is also proposed in this paper     

RBF-based decision feedback aided turbo equalisation ofconvolutional and space-time trellis-coded systems

A reduced-complexity Jacobian radial basis function aided turbo equalisation (TEQ) scheme is proposed, 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     

Adaptive trellis-coded modulation for bandlimited meteor burstchannels

The throughput performances of three adaptive information rate techniques on the bandlimited meteor burst channel are investigated. Closed-form expressions for throughput are derived based on the channel model commonly used in the literature. The throughput performance is compared to the conventional fixed information rate modem and upper bounds on throughput improvement over the fixed rate modem are derived. It is shown that an adaptive technique that uses trellis-coded modulation (TCM) with three phase-shift keyed (PSK) signal sets can increase throughput over the conventional fixed rate modem by more than a factor of 3. Data from the US Air Force High Latitude Meteor-Scatter Test Bed confirm the superiority of the adaptive TCM technique. A practical implementation is suggested that uses a single rate 1/2 convolutional code for all three PSK signal sets. The use of this single code, versus the three best Ungerboeck codes, results in a throughput loss of less than 2%. An expression for the theoretical information capacity of the bandlimited meteor burst channel is derived     

Chernoff bound of trellis-coded modulation over correlated fadingchannels

We derive a Chernoff upper bound for the pairwise error probability in the presence of an additive white Gaussian noise and a Rayleigh or Rice correlated fading. The bound is useful for situations where perfect interleaving cannot be achieved. We use it to determine some indications in the design of optimum trellis coded modulation for correlated fading channels     

Turbo coding applied to pragmatic trellis-coded modulation

This letter reports the application of the powerful turbo coding technique combined with the bandwidth efficient method known as trellis-coded modulation (TCM). Implemented as a simple modification of pragmatic TCM, our turbo-coded pragmatic TCM system achieved coding gains of 1-2 dB in simulations relative to pragmatic TCM. These gains were achieved with comparable complexity but greater delay than with pragmatic TCM. A table of delay as a function of interleaver length and data rate is provided as a preliminary analysis of the trade-off between the benefits of large coding gain and the costs of increased delay     

Performance bounds for trellis-coded modulation on time-dispersivechannels

The performance of trellis-coded modulation (TCM) on additive white Gaussian noise channels is well understood, and tight analytical bounds exist on the probability of the Viterbi decoder making a decision error. When a channel is also time-dispersive, the performance of TCM systems has been studied mainly by simulation. However, simulation is limited to symbol error probabilities greater than 10^-6 and is not a particularly useful tool for designing codes. Tight analytical bounds on the error probability of TCM on time-dispersive channels are required for a more thorough study of performance. Moreover, the design of good codes and optimum metrics for time-dispersive channels requires tight analytical bounds. In this paper we derive analytical upper bounds, which, although requiring numerical techniques for tractable evaluation, are tight for a wide range of time-dispersive channel conditions. The bounds are based on a union bound of error events that leads to a summation of pairwise error probabilities, which are themselves upper bounded     

Two-level coding based on trellis-coded modulation and Reed-Solomoncodes

A number of two-level codes based on trellis-coded modulation (TCM) schemes and their matched single or double error-correcting Reed-Solomon codes using QAM constellations are presented and evaluated. Compared to the well-known 4D 16-state TCM scheme with a comparable bandwidth efficiency, these two-level codes provide greater immunity from both Gaussian and impulse noise, at the cost of a reasonably higher complexity and a longer decoding delay, on the order of a few hundred symbols. The authors also show how to cope with phase ambiguities of the constellation in these two-level codes. Both rotationally invariant coding and rotation detecting techniques are considered     

Performance of trellis-coded modulation for equalized multipathfading ISI channels

The performance of TCM on equalized multipath fading ISI channels with different equalization schemes is examined. Trellis codes that are effective for AWGN channels and flat fading channels with interleaving are evaluated for equalized multipath fading channels. For joint MLSE equalization and decoding the equivalent uncoded system outperforms all the trellis-coded systems that are examined. Trellis codes that are designed for flat fading channels with interleaving perform well if interleaving is used and an MLSE equalizer is used before deinterleaving. An effective interleaver-deinterleaver is identified that allows joint DDFSE equalization and decoding to be used without the need for equalization before decoding     

Optimized signal constellations for trellis-coded modulation onAWGN channels

Previously, performance gains over Ungerboeck type trellis-coded modulation schemes were obtained by optimizing (by hand) the signal constellation. Using genetic algorithms and simulated annealing, we have found additional cases with performance gains over the Ungerboeck type schemes