Efficient detection schemes for an overloaded multiple-input multiple-output (MIMO) system have been investigated recently. The literature shows that trellis coded modulation (TCM) is able to enhance a system's capability to separate signal streams in the detection process of MIMO systems. However, the computational complexity remains high as a maximum likelihood detection (MLD) algorithm is used in the scheme. Thus, a sphere decoding (SD) algorithm with a pseudo distance (PD) is proposed in this paper. The PD maintains the coding gain advantage of the TCM by keeping some potential paths connected unlike conventional SD which truncates them. It is shown that the proposed scheme can reduce the number of distance calculations by about 98% for the transmission of 3 signal streams. In addition, the proposed scheme improves the performance by about 2dB at the bit error rate of 10-2.

We propose a quasi-linear trellis-coded modulation (TCM) using nonbinary convolutional codes for quadrature amplitude modulation (QAM). First, we study a matched mapping which is able to reduce the computational complexity of the Euclidean distances between signal points of MQAM. As an example, we search for rate R=1/2 convolutional codes for coded 64QAM by this method. The symbol error rates of the proposed codes are estimated by the distance properties theoretically and they are verified by simulation. In addition, we compare the minimum free Euclidean distances of these new codes with their upper bounds. Finally, the bit error probabilitiy of the proposed coded modulation is compared with uncoded signal constellations and a conventional TCM code proposed by Ungerboeck. The result shows the proposed scheme outperform them on the AWGN channels.

An automatic-repeat-request (ARQ) scheme for improving the system throughput efficiency is evaluated in coded multiple-input multiple-output (MIMO) transmissions. Supplementary trellis-coded modulation (TCM) code has been proposed for hybrid ARQ schemes. The free distance of the TCM after code combining can be increased by employing different TCM codes for retransmissions. The MIMO scheme offers additional flexibility in preventing successive frame errors by changing the connections between transmitters and transmit antennas upon retransmission. In this paper, an ARQ strategy employing both TCM reassignment and antenna permutation technique is investigated. It is shown through computer simulations that this ARQ scheme achieves high throughput even in severe conditions of low signal-to-noise ratio and high Rician factor over spatially and temporally correlated Nakagami-Rice fading MIMO channels.

In this paper, the Viterbi decoder containing new branch metrics of the squared Euclidean distance with multiple order phase differences is introduced in order to improve the bit error rate (BER) in the differential detection of the trellis-coded MDPSK-OFDM. The proposed Viterbi decoder is conceptually same as the sliding multiple phase differential detection method that uses the branch metric with multiple phase differences. Also, we describe the Viterbi algorithm in order to use this branch metrics. Our study shows that such a Viterbi decoder improves BER performance without sacrificing bandwidth and power efficiency. Also, the proposed algorithm can be used in the single carrier modulation.

In this letter, we introduce a two-state turbo-TCM scheme based on the concatenated tree codes. The proposed scheme can achieve near capacity performance yet has considerably lower decoding complexity compared with other existing turbo-TCM codes.

Performance of parallel concatenated trellis-coded modulation (turbo TCM) with Ungerboeck type constituent codes with maximum likelihood decoding over the AWGN channel is analyzed by extending the method of performance evaluation proposed by Benedetto et al. for binary turbo codes with uniform interleaving. Although a performance evaluation of turbo TCM has been proposed, the system model discussed in the proposal has some auxiliary interleavers only necessary for the evaluation. This paper removes such auxiliaries. Since the direct extension of Benedetto's method for turbo TCM needs huge memories for computation, an efficient numerical evaluation method is proposed in order to reduce the memory requirement. Based on the analysis, the relation between bit error rate and interleaver size is discussed. The analyzed performance is compared with simulation results of iterative decoding of turbo TCM.

This paper discusses a communication system with a multiple-access channel where two users simultaneously send complex-valued signals in the same frequency-band. In this channel, ambiguity in decoding occurs when receiver trying to estimate each users' signal. In order to solve the ambiguity problem, a family of uniquely decodable code is derived in this paper. The uniquely decodable code is designed by using trellis-coded modulation (TCM) pair where the trellis structure of one TCM is a transformation of the other in the pair. It is theoretically proved that, with the proposed coding scheme, the composite received signal can be uniquely decomposed into the two constituent signals for any power ratio and any phase difference between the received two users' signals. Improvement of BER performance over non-uniquely decodable code is illustrated by computer simulation.

Iterative decoding of serially concatenated code is extended to punctured trellis-coded modulation. A system configuration, a decoding algorithm and a performance evaluation method are proposed. It realizes a total coding rate of m/(m+1) by puncturing parity bits. Simulation results indicate that the proposed system shows no flattening effect which is observed in parallel concatenated system and realizes BER of 10-6 at Eb/N0=4.43 dB even with a small interleaver of size 2047.

Multi-ary Trellis-Coded Modulation (TCM) schemes have been studied for use with digital radio communication systems. Among these TCM schemes, we have already reported the optimum signal constellation of a rate-3/4 trellis-coded (TC) 16-ary Amplitude and Phase Shift Keying (APSK) scheme and computed the minimum Euclidean distance: dfree. In this paper, we evaluate other performance parameters: Nfree and bit error rate (BER) over an additive white Gaussian noise channel, and further investigate the various signal constellations of rate-4/5 TC 32-APSK schemes. It is found that the BER performances of circular-type signal constellations are superior to that of rectangular-type in the TC 16-APSK, and a (24,8) circular type signal constellation is superior to other constellations in the TC 32-APSK.

In this paper, we present a method for evaluating the minimum free Chernov distance of trellis-codes for a discrete memoryless channels (DMC). In order to design an efficient trellis-code for the DMC, we need to evaluate the minimum free Chernov distance of the target code. However, the lack of the additive property of the Chernov distance prevents a conventional branch-and-bound search for evaluating the minimum distance. To overcome the difficulty, we present a lower bound on the Chernov distance with an additive property. The lower bound plays a key role in the minimum distance evaluation algorithm presented here. By using the proposed algorithm, we have derived the minimum free Chernov distance of some binary linear convolutional codes over Z-channel.

A structure and an iterative decoding algorithm of a turbo trellis-coded modulation system, proposed by Robertson and et al. , are improved. For the encoder, removal of the odd-even constraint of an interleaver is discussed and a structure which removes a serial connection of an interleaver and a deinterleaver is proposed. The latter makes encoding delay nearly half. A decoding algorithm which is a natural extension of the standard decoding algorithm to TCM is proposed. In the proposed algorithm, logarithm of an a posteriori probability ratio is divided into three component values: an a priori value, a channel value and an extrinsic information. The extrinsic information is transferred to the next decoding stage as an a priori value. The proposed algorithm is easier to understand than the Robertson's algorithm in which a combination of the channel value and the extrinsic information is transferred to the next stage. Simulation results show the proposed algorithm realizes equivalent or better performance than the Robertson's algorithm. The removal of the odd-even constraint gives a little better performance than that with odd-even constraint in some conditions. By this improvement, bit error rate of 10-5 is obtained at Eb/N0 0. 4 dB from the Shannon limit for 2 bit/symbol transmission with 8-PSK modulation.

A deterministic simulation method is investigated for rate 3/4 trellis-coded (TC) 16PSK, TC-16QAM and TC partially overlapped (PO) 12QAM schemes. The BER performance of these schemes are evaluated on realistic channels with the same transmisson parameters, and are compared with BER values obtained from a distance spectrum expression. The results of this study show that the BER values obtained by the deterministic simulation coincide well with those from the distance spectrum method, and that TC-16PSK is superior to both TC-16QAM and TC-PO-12QAM in terms of BER performance over linear and nonlinear channels. The BER degradation caused by a nonlinear amplifier and the BER difference between two mapping methods ( Gray code and natural binary code mapping) are also clarified.

Co-channel interference is a major deteriorating factor limiting the capacity of mobile communication systems. To mitigate the effect of the interference, a kind of nonlinear interference canceller named trellis-coded co-channel interference canceller (TCC) has been proposed. In TCC the trellis-coded modulation (TCM) is introduced to both the desired signal and the interference signal in order to enhance the cancelling performance. In this paper, the bit error rate (BER) performance of TCC in static channel is theoretically evaluated for the first time. An equivalent TCM (E-TCM) model is firstly established, and a BER asymptotic estimate (AE) and a BER upper bound (UB) of TCC are then evaluated respectively by analyzing E-TCM. In the evaluation of AE, the BER performance is calculated as a function of phase difference between the desired signal and the interference signal (φ), subsequently the average BER performance over φ can be evaluated. The UB of BER is calculated using a transfer function based on the matrix representation. This paper also demonstrates that AE gives higher accuracy and less calculation complexity than UB. Performance comparisons reveal the consistency of these theoretical results with that of computer simulations.

Recently reported multidimensional geometrically uniform signal constellations (L MPSK and Decomposed-Lattice constellations) are joined in the term of Generalized Permutation Alphabets (GPA). Possibility of a binary isometric labeling of GPA's is completely characterized. An algorithm for constructing generating groups of PSK-type GPA is proposed. We show that this concept, when is extended to the lattice, gives rise to a class of new coset codes which perform out best codes listed in [11].

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.

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.

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.

In the maximum-likelihood decoding under a non-Gaussian noise, the decoding region is bounded by complex curves instead of a perpendicular bisector corresponding to the Gaussian noise. Therefore, the error rate is not evaluated by the Euclidean distance. The Bhattacharyya distance is adopted since it can evaluate the error performance for a noise with an arbitrary distribution. Upper bound formulae of a bit error rate and an event error rate are obtained based on the error-weight-profile method proposed by Zehavi and Wolf. The method is modified for a non-Gaussian channel by using the Bhattacharyya distance instead of the Euclidean distance. To determine the optimum code for an impulsive noise channel, the upper bound of the bit error rate is calculated for each code having an encoder with given shift-register lehgth. The best code is selected as that having the minimum upper bound of the bit error rate. This method needs much computation time especially for a code with a long shift-register. To lighten the computation burden, a suboptimum search is also attempted. For an impulsive noise, modeled from an observation in digital subscriber loops, an optimum or suboptimum code is searched for among codes having encoders with a shift-register of up to 4 bits. By using a code with a 4-bit encoder, a coding gain of 20 dB is obtained at the bit error rate 10-5. It is 11 dB more than that obtained by Ungerboeck's code.