A new design method, which is referred to as the matched design method, for concatenated trellis-coded modulation (TCM) is presented. Most of the conventional concatenated TCM employs TCM designed to maximize the minimum squared Euclidean free distance, d2free. With the matched design method, we maximize d21(t) instead of d2free, where d21(t) is the effective minimum squared Euclidean distance (MSED) when the outer code has a t-error correcting capability. The effective MSED is derived from the Euclidean/Hamming (E/H) joint weight distribution of terminated TCM. We here assume the concatenated TCM whose transmitted symbol corresponds to a symbol of outer code. The new classes of 2-dimensional (2D) and 4-dimensional (4D) codes are found by a computer search. Under the performance measures of the effective MSED or the effective multiplicity, these codes are superior to the conventional codes such as the Ungerboeck's 2D-codes when those are used as an inner code. We disclose an interesting fact that the new class of codes using rate-1/2 encoder is superior to the class of codes using rate-2/3 encoder. This fact implies that the codes using rate-1/2 encoder have two advantages: 1) better overall decoding performance and 2) less decoding complexity.

In this paper partial response signalling and trellis coded modulation are considered together to improve bandwidth efficiency and error performance for M-QAM and denoted as Modified/Quadrature Partial Response-Trellis Coded Modulation (M/QPR-TCM) and two new non-catastrophic schemes M/6QPR-TCM and M/9QPR-TCM are introduced for 4QAM. In colored noise with correlation coefficient less than zero, the proposed schemes perform better than in AWGN case. Another interesting result is that when the combined system is used on a Rician fading channel, the bit error probability upper bounds of the proposed systems are better than their counterparts the 4QAM-TCM systems with 2 and 4 states, respectively, for SNR values greater than a threshold, which have the best error performance in the literature.

The evaluation of a error probability of a trellis-coded modulation scheme by an ordinary Monte-Carlo simulation method is almost impossible since the excessive simulation time is required to evaluate it. The reduction of the number of simulation runs required is achieved by an importance sampling method, which is one of the variance reduction simulation methods. The reduction of it is attained by the modification of the probability density function, which makes errors more frequent. The error event simulation method, which evaluates the error probability of finite important error events, cannot avoid a truncation error. It is the fatal problem to evaluate the precision of the simulation result. The reason of it is how to design the simulation probability density function. We propose a evaluation method and the design methods of the simulation conditional probability density function. The proposed method simulates any error event starting at the fixed time, and the estimator of it has not the truncation error. The proposed design method approximate the optimum simulation conditional probability density function. By using the proposed method for an additive non-Gaussian noise case, the simulation time of the most effective case of the proposed method is less than 1/5600 of the ordinary Monte-Carlo method at the bit error rate of 10-6 under the condition of the same accuracy if the overhead of the selection of the error events is excluded. The simulation time of the same bit error rate is about 1/96 even if we take the overhead for the importance sampling method into account.

A channel coding which combines convolutional coding and M-ary PSK/orthogonal multi-carrier (MPSK/OMC) transmission is proposed. A coding gain is achieved without sacrificing the data rate or occupying extra bandwidth. The proposed coding formula is that the imformation data bits of bit interval Ts are serial to parallel converted to P parallel branches where each branch has a bit interval Tp = PTs. The data bits of the parallel branches are encoded through a rate nP/(n + 1)(2P - 1) convolutional encoding process and the total (n+1)(2P-1) symbol of the encoder output is transmitted by 2P - 1 OMCs where each carrier is modulated by MPSK/OMC (M = 2n + 1). Following performance analysis of a coding form using rate P/(2P - 1) convolutional encoder and BPSK/OMC modulation, a general channel coding combining convolutional coding and MPSK/OMC modulation is discussed.

In conventional trellis coded modulation (TCM), higher-ary modulation scheme combining with a convolutional code is employed not to expand the transmitted bandwidth. This forces the system to be attended with signal constellation expansion and increasing the average signal power. As the solutions to avoid signal constellation expansion, TCM systems using totally overlapped signal sets (TO-TCM and RU-TCM) were proposed. These schemes can realize a coded modulation system without signal constellation expansion and achieve more coding gain compared with the conventional TCM. However, a problem that the systems with totally overlapped signal sets might be catastrophic has been remained. In this paper, we propose a novel TCM system using partially overlapped signal sets of non-equiprobable signaling (PO-TCM-NE). This scheme employs the partially overlapped signal constellation to control increasing signal points, and to avoid catastrophic error propagation. The non-equiprobable signaling is employed to reduce average signal power. Coding gain of the proposed PO-TCM-NE is considerably improved in consequence the average signal power is reduced much lower than that of other TCM systems with equiprobable signaling.

Distance properties of trellis codes are of great importance for performance evaluation. In this paper, we use random coding analysis to study the average distance structures of trellis codes. The generating function enumerating the average number of error events of each distances is fully determined in the ensemble of time-varying trellis codes. The results obtained can be used to predict the growth rate of the number of error events at large distance and hence determine the signal-to-noise range in which the transfer function bound for error performance is convergent. Other applications of the average distance structure include a Gilbert-type lower bound on minimum distance.

Co-channel interference is a major factor limiting spectral efficiency of a cellular radio system. The trellis-coded co-channel interference canceller (TCC) leading to the significant increase of traffic capacity of a cellular system has been proposed. In this scheme, a maximum-likelihood sequence estimation implemented with the Viterbi algorithm is extended to estimate both desired signal and co-channel interference, and combined with trellis-coded modulation to enhance the co-channel interference cancelling capability. The complexity of TCC grows exponentially with the channel memory and the constraint length of the trellis encoder. In this paper, two reduced-state sequence estimation algorithms, namely, the delayed decision feedback sequence estimation and the M-algorithm, are applied to TCC and their performance is compared. In addition, effective trellis coded modulation schemes to reduce the computational complexity are proposed. The performance of these schemes is examined through simulations, and compared to that of a conventional interference canceller.

When bit error probability of a trellis-coded modulation (TCM) scheme becomes very small, it is almost impossible to evaluate it by an ordinary Monte-Carlo simulation method. Importance sampling is a technique of reducing the number of simulation samples required. The reduction is attained by modifying the noise to produce more errors. The low error rate can be effectively estimated by applying importance sampling. Each simulation run simulates a single error event, and importance sampling is used to make the error events more frequent. The previous design method of the probability density function in importance sampling is not suitable for the TCM scheme on an additive non-Gaussian noise channel. The main problem is how to design the probability density function of the noise used in the simulation. We propose a new design method of the simulation probability density function related to the Bhattacharyya bound. It is reduced to the same simulation probability density function of the old method when the noise is additive white Gaussian. By using the proposed method for an additive non-Gaussian noise, the reduction of simulation time is about 1/170 at bit error rate of 106 if the overhead of the calculation of the Bhattacharyya bound is ignored. Under the same condition, the reduction of the simulation time by the proposed method is 1/65 of the ordinary Monte-Carlo method even if we take the overhead for importance sampling into account.

This letter is concerned with the evaluation of the average computational complexity of the maximum likelihood decoding of a linear block code using its trellis diagram. Each section of the L-section minimal trellis diagram for a linear block code consists of parallel components which are structurally identical subgraphs without cross connection between them. A parallel component is also known to be decomposed into subgraphs, and a decoding algorithm by using the structure of the subgraphs of parallel components was proposed, and an upper bound on the worst case computational complexity was derived. In this letter, the average computational complexity of the decoding algorithm is evaluated by computer simulation. We evaluated the average numbers of additions and comparisons performed in the decoding algorithm for example codes, (64,45) extended and permuted binary primitive BCH code, the third order Reed-Muller (64,42) code and its (64,40) subcode. It is shown that the average numbers are much smaller than those for the worst case, and hence the decoding algorithm is efficient when the number of sections, L, is small, say 4 or 8, for the example codes. Especially, for the (64,45) extended binary primitive BCH code with L4, the average numbers of additions and comparisons in the decoding algorithm for finding the survivor's metric of each state after finding the smallest metric among parallel branches are about 1/50 and 17/100 of those in the conventional exhaustive search, respectively. The number of additions and comparisons by the conventional search for all the example codes is smallest when L is 4. As a result, the decoding algorithm with L4 gives the smallest number of operations among those decoding methods considered here.

Future digital land mobile communication, for a moving picture, requires more transmission speed and less bit error rate than the existing system does for speech. In the system, the intersymbol interference may not be ignored, because of higher transmission speed. An adaptive equalizer is necessary to cancel intersymbol interference. To achieve low bit error rate performance on the mobile radio channel, trellis-coded modulation with interleaving is necessary. This paper proposes an interleaved trellis-coded modulation scheme combined with a decision feedback type adaptive equalizer of high performance. The reliable symbol reconstructed in the trellis decoder is used as the feedback signal. To make equalizer be free from decoding delay, deinterleaving is effectively utilized. The branch metric, for trellis-coded modulation decoding, is calculated as terms of squared errors between a received signal and an expected signal by taking the reconstructed symbol and the impulse response estimated by the recursive least squares algorithm into account. The metric is constructed to have good discrimination performance to incorrect symbols even in non-minimum phase and to realize path diversity effect in a frequency selective fading channel. Computer simulation results are shown for several channel models. On a frequency selective fading channel, average bit error rate is less than 1/100 of that of the RLS-MLSE equalizer for fdTs=1/1000 at average Eb/N0 beyond 15dB. Performance degradation due to equalization error is less than 1.8dB. Performance is greatly improved by the effect of the reconstructed symbol feedback.

Although Hidden Markov Modeling (HMM) is widely and successfully used in many speech recognition applications, duration control for HMMs is still an important issue in improving recognition accuracy since a HMM places no constraints on duration. For compensating this defect, some duration control algorithms that employ precise duration models have been proposed. However, they suffer from greatly increased computational complexity. This paper proposes a new state duration control algorithm for limiting both the maximum and the minimum state durations. The algorithm is for the HMM trellis likelihood calculation, not for the Viterbi calculation. The amount of computation required by this algorithm is only order one (O(1)) for the maximum state duration n; that is, the computation amount is independent of the maximum state duration while many conventional duration control algorithm require computation in the amount of order n or order n2. Thus, the algorithm can drastically reduce the computation needed for duration control. The algorithm uses the property that the trellis likelihood calculation is a summation of many path likelihoods. At each frame, the path likelihood that exceeds the maximum likelihood is subtracted, and the path likelihood that satisfies the minimum likelihood is added to the forward probability. By iterating this procedure, the algorithm calculates the trellis likelihood efficiently. The algorithm was evaluated using a large-vocabulary speaker-independent spontaneous speech recognition system for telephone directory assistance. The average reduction in error rate for sentence understanding was about 7% when using context-independent HMMs, and 3% when using context-dependent HMMs. We could confirm the improvement by using the proposed state duration control algorithm even though the maximum and the minimum state durations were not optimized for the task (speaker-independent duration settings obtained from a different task were used).

The performance of trellis coded hybrid frequency and phase shift modulation (TC HFPSK) with the expurgated phase code and the asymmetric signal constellation is investigated by using the minimum squared free Euclidean distance d 2free and the bit error rate (BER). It is found that TC hybrid 2FSK/4PSK with the expurgated phase code shows larger d 2free than the corresponding TC hybrid 2FSK/4PSK with the complete phase code for varying the angle φ that determines the asymmetric signal constellation. The maximum value of d 2free of TC hybrid 2FSK/4PSK with the expurgated phase code can be obtained when the signal constellation is symmetric. The performance of BER is analyzed in additive white Gaussian noise (AWGN) and fading channels by using uniform error property and error bound based on transfer function. It is found that the coding gain of TC hybrid 2FSK/4PSK with the expurgated phase code over uncoded hybrid 2FSK/2PSK at BER=10-4 are 2.71dB and 4.74dB in AWGN and fading channels, respectively. The performance improvements of TC hybrid 2FSK/4PSK with the expurgated phase code over TC 8PSK at BER=10-4 are 0.68dB and 4.07dB in AWGN and fading channels, respectively.

In this paper, a design of TCM signals for Middleton's class-A impulsive noise environment is investigated. The error event characteristics under the impulsive noise is investigated, and it is shown that the length of the signal sequence is more important than Euclidean distance between the signal sequences. Following this fact, we introduce the shortest error event path length as a measure of the signal design. In order to make this value large, increasing of states of convolutional codes is employed, and the performance improvement achieved by this method is evaluated. Numerical results show the great improvement of the error performance and conclude that the shortest error event path length is a good measure in the design of TCM signals under impulsive noise environment. Moreover, the capacity of class-A impulsive noise channel is evaluated, and the required signal sets expansion rates to obtain the achievable coding gain is discussed.

A Trellis-Coded 8PSK (TCM) modem has been developed. This modem can transmit HDTV programs at a bit rate of 60Mbps over a satellite channel. In addition to Trellis coding, the (255, 235) Reed-Solomon code is adopted together with an interleaving technique to improve bit error performance. As a result, it has been confirmed that bit error rate of 10-10 is achievable at a carrier to noise ratio of around 8.5dB over a 30MHz Gaussian noise channel. This TCM modem is also designed to double as a DQPSK modem. We examined the performances of these two modulation methods in a nonlinear channel. It was found that TCM is less disturbed than DQPSK by nonlinear distortion due to TWT. In addition, a limiter amplifier cascaded to TWT improves DQPSK performance and disturbs TCM performance. However it was confirmed that TCM still has a coding gain of 3dB over DQPSK.

We analyze the error performance of overlapping multipulse pulse position modulation (OMPPM) in optical direct-detection channel with existing noise. Moreover we analyze the error performance of trellis-coded OMPPM with the small overlap index N=2 in optical direct-detection channel to achieve significant coding gains over uncoded PPM, uncoded MPPM and the trellis coded overlapping PPM (OPPM) with the same pulsewidth. First we analyze the symbol error probability of OMPPM in both the quantum-limited case and the quantum and background noise case by using the distance defined as the number of nonoverlapped pulsed chips between symbols. Second by using this distance, we partition the OMPPM signals and apply the four-state and the eight-state codes described by Unger-boeck to OMPPM. It is shown that the trellis coding over OMPPM is effective in optical direct-detection channel: the eight-state trellis coded (4,2,2) OMPPM can achieve gains of 3.92dB and 3.23dB over uncoded binary PPM in the quantum-limited case and in the quantum and background noise case with noise photons per slot time is one, respectively.

Recently there has been considerable interest in coded modulation schemes that offer multiple levels of error protection. That is, constructions of (block or convolutional) modulation codes in which signal sequences associated with some message symbols are separated by a squared Euclidean distance that is larger than the minimum squared Euclidean distance (MSED) of the code. In this paper, the trellis structure of linear unequal-error-protection (LUEP) codes is analyzed. First, it is shown that LUEP codes have trellises that can be expressed as a direct product of trellises of subcodes or clouds. This particular trellis structure is a result of the cloud structure of LUEP codes in general. A direct consequence of this property of LUEP codes is that searching for trellises with parallel structure for a block modulation code may be useful not only in analyzing its structure and in simplifying its decoding, but also in determining its UEP capabilities. A basic 3-level 8-PSK block modulation code is analyzed under this new perspective, and shown to offer two levels of error protection. To illustrate the trellis structure of an LUEP code, we analyze a trellis diagram for an extended (64,24) BCH code, which is a two-level LUEP code. Furthermore, we introduce a family of LUEP codes based on the |||-construction, using Reed-Muller (RM) codes as component codes. LUEP codes in this family have the advantage of having a well known trellis structure. Their application in constructing LUEP-QPSK modulation codes is presented, and their error performance over an AWGN channel examined.

A method is presented for computing the number of codewords of weight less than or equal to a given integer in a binary block code by using its trellis diagram. The time and space complexities are analyzed. It is also shown that this method is very efficient for the codes which have relatively simple trellis diagram, say some BCH codes. By using this method, the weight distribution of (128,36) extended BCH code is computed efficiently.

An encoder of a trellis coded modulation (TCM) is composed of a linear convolutional encoder followed by a mapper to channel signals. A new condition, under which the performance evaluation of the TCM is possible based on the 2ν state error state transition diagram, is proposed, where ν is the number of delay elements in the convolutional encoder. There have been proposed three similar methods. This paper points out the restriction of the previous methods, and proposes a new method. The condition, under which the previous method is useful, is called nuiformity, such as, the error weight profile is independent from the encoder state. When uniformity does not hold, we discuss to divide an error state into substates based on the coset decomposition of output vectors of the convolutional encoder. The coset is determined by the vector called coset selector. If the condition defined as equal dividing holds, the subdivided states can be merged and the performance can be evaluated based on the 2ν state transition diagram, even for the codes without uniformity. When the row rank of the transformation matrix, from the input vector of the encoder to the coset selector vector, is full, the equal dividing condition holds under the assumption of equally probable i.i.d. (independently identically distributed) input sequence. For TCM schemes without uniformity (in the case, previous methods can not be applied), upper bounds of the bit error rate are evaluated by the proposed method and compared with the simulation results. The difference is less than 10% in the range of bet error rate 10-4.

In an earlier paper, we have shown that each section of the L-section minimal trellis diagram for a linear block code consists of parallel and structurally identical (except branch labels) subgraphs without cross connections. These parallel subgraphs are called parallel components of the section. In this paper, it is shown that if the sets of path label sequences of two parallel components have a common sequence, then the parallel components have the same branch labels, and the number of parallel components with the same branch labels in each section and the detail structure of each parallel component up to its branch labels are analyzed and expressed in terms of the dimensions of specific linear codes related to the given code. As an example, the 2i-section minimal trellis diagram for a Reed-Muller code is analyzed. Complexity measures of soft-decision maximum likelihood decoding for binary linear block codes are also discussed.

In this paper we analize the performance of Trellis Coded Modulation (TCM) schemes with coherent detection operating in a frequency flat, mobile Rayleigh fading environment, and with different knowledge levels on both the amplitude and phase fading processes (the latter is not assumed as usual to be ideally tracked), or Channel State Information (CSI). For example, whereas ideal CSI means that both the amplitude and phase fading characteristics are perfectly known by the receiver, other situations that are treated consider perfect knowledge of the amplitude (or phase) with complete disregard of the phase (or amplitude), as well as non concern on any of them. Since these are extreme cases, intermediate situations can be also defined to get extended bounds based on Chernoff which allow the phase errors, in either form of constant phase shifts or randomly distributed phase jitter, to be included in the upper bounds attainable by transfer function methods, and are applicable to multiphase/level signaling schemes. We found that when both fading characteristics are considered, the availability of CSI enhances significatively the performance. Furthermore, for non constant envelope schemes with non ideal CSI and for constant envelope schemes with phase errors, an asymmetry property of the pairwise error probability is identified. Theoretical and simulation results are shown in support of the analysis.