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.

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.

For an additive white Gaussian noise (AWGN) channel, a performance evaluation of parallel concatenated turbo trellis-coded modulation (turbo TCM) using bit-interleavers is reported. By obtaining weight distribution, the performance is evaluated by using a union bound method. Comparison between the result of evaluated performance and simulation results is shown, and the usefulness of the evaluated performance is shown. An optimum code and an optimum mapping are sought. The result of the optimum code with the optimum mapping is a new interleaver size N dependency which is proportional to N-3. It is better than the interleaver size dependency for Benedetto code with the natural mapping which is proportional to N-1. The reasons why these dependencies can happen are also discussed.

Simple computation method of soft value, that is used in iterative soft decision decoding, is proposed. For the product code composed of BCH(63, 57) and that composed of BCH(63, 45), computation time with the proposed method is 1/15-1/6 as that with a method based on the Chase algorithm. Bit error rate (BER) performance with the proposed method is within 0.8 [dB] inferior to that with the method based on the Chase algorithm at BER=10-5.

Bit-interleaving can enhance performance of a trellis coded modulation system over a fading channel. A combined system with decision feedback equalization is proposed. In the system, TCM decoded symbols are fed back for equalization. To avoid a bad effect of decoding delay, a deinterleaver is utilized effectively. Information sequence is divided into three subsequences and encoded by three encoders. Among the 3 code vectors from the encoders, bits are interleaved and decoding proceeds in parallel. Simulation results show that the proposed system realizes 0.6 dB more coding gain than a symbol interleaved system. A calculation method of a branch metric for decoding is proposed. Performance with the branch metric is shown to be nearly independent from the desired/undesired power ratio of a intersymbol interference channel. An approximate upper bound is analyzed for the proposed system, and the optimum code is searched.

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.

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.

Performance of turbo codes over an impulsive noise channel is analyzed by extending an evaluation method over AWGN channels. Burst noise generation is considered with respect to the noise model by applying a hidden Markov model (HMM). A bound calculation method is derived by using a combined trellis which consists of code trellis and HMM trellis. In the simulation, an iterative decoder using the combined trellis into each component decoder is proposed. By using this method, the simulation results show the expectation of the coincidence with the calculated bounds at larger Eb/N0 for various conditions. Search results of optimum component code using proposed bound are shown.

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.

In high-speed digital land mobile radio communication, communication quality is degraded by frequency selective fading that has intersymbol interference. It causes increase of bit error rate (BER). To decrease BER in the channel, this paper proposes a system with combined multilevel coding and adaptive equalization using interleaving. By using interleaving, the proposed system obtains time diversity effect. Furthermore the system realizes a type of decision feedback adaptive equalizer where signal after multilevel decoder is fed back. These features of the system cause decrease of BER. The proposed system is compared with a similar system with a feedback signal before multilevel decoder. The average bit error rate of the proposed system is less than 1/100 with that of the compared system at average Eb/No = 22 [dB] in a case of fading channel with one intersymbol interference.

A performance evaluation method of turbo codes is proposed. For turbo codes with code-matched interleaver, performance is approximately evaluated by using conditional weight enumerating function with input weight greater than two. Performance of turbo codes over an inter-symbol interference (ISI) channel is evaluated by using a combined trellis diagram, into which the trellis diagram of the component code and the trellis diagram of the inter-symbol interference channel are combined. Optimum codes are searched for an ISI channel and for an ISI-free channel with the code matched-interleaver. Simulation results show the evaluated performance is valid.

This paper describes a least complex, high speed decoding method named multi-stage threshold decoding (MTD-DR). Each stage of MTD-DR is formed by the traditional threshold decoder with a special shift register, called difference register (DR). After flipping each information bit, DR helps to shorten the Hamming and the Euclidian distance between a received word and the decoded codeword for hard and soft decoding, respectively. However, the MTD-DR with self-orthogonal convolutional codes (SOCCs), type 1 in this paper, makes an unavoidable error group, which depends on the tap connection patterns in the encoder, and limits the error performance. This paper introduces a class of SOCCs type 2 which can breakdown that error group, as a result, MTD-DR gives better error performance. For a shorter code (code length = 4200), hard and soft decoding MTD-DR achieves 4.7 dB and 6.5 dB coding gain over the additive white Gaussian noise (AWGN) channel at the bit error rate (BER) 10-5, respectively. In addition, hard and soft decoding MTD-DR for a longer code (code length = 80000) give 5.3 dB and 7.1 dB coding gain under the same condition, respectively. The hard and the soft decoding MTD-DR experiences error flooring at high Eb/N0 region. For improving overall error performance of MTD-DR, this paper proposes parity check codes concatenation with soft decoding MTD-DR as well.

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.

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.

This paper presents a way to quantitatively characterize switching processing features by information theoretical analysis. The analysis concept is based on understanding that a switching processor is an information processing machine for obtaining input information from subscribers and for sending output information to a speehpath network. In order to convert the input information to the output information, the switching system must choose a suitable internal action out of many possibilities, namely, the system has some entropy in making a decision on its response to the input information. The internal processing is considered, therefore, to contribute to decreasing the entropy. Based on the above comprehension on the switching system, an information processing evaluation principle and some parameters for control structure design are proposed. Using those parameters, partition and assignment way of processing amount to control stages or to switching functions such as input, internal and output processing are decided. Those parameters can be used also as measures of system flexibility or service variety and speechpath network control ease. Example figures of those parameters are given by analysis of a 7 digit rotary dialing intra-office call processing in a large scale stored program controlled model switching system. The values obtained can be considered to indicate the information processing level in the present switching system and may be also used to design quantitatively call processing capacity of a switching system and simultaneously to show an objective to be surpassed in future switching system development.

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.

An iterative decoder of turbo code over an inter-symbol interference channel is proposed. A component decoder realizes decoding and equalization simultaneously with the soft-output Viterbi algorithm (SOVA). A decoding algorithm and simulation results are shown.

This paper proposes methods to improve soft-input and soft-output decoding performance of BCH codes by sum-product algorithm (SPA). A method to remove cycles of length four (RmFC) in the Tanner graph has been proposed. However, the RmFC can not realize good decoding performance for BCH codes which have more than one error correcting capability. To overcome this problem, this paper proposes two methods. One is to use a parity check matrix of the echelon canonical form as the starting check matrix of RmFC. The other is to use a parity check matrix that is concatenation (ConC) of multiple parity check matrices. For BCH(31,11,11) code, SPA with ConC realizes Eb/No 3.7 dB better at bit error rate 10-5 than the original SPA, and 3.1 dB better than the SPA with only RmFC.

To evaluate the coding performance of a multilevel coding scheme for Rayleigh fading channel, a virtual automatic gain control and interleaving are applied to the scheme. The automatic gain control is assumed only for the theoretical evaluation of the performance. It is noted that the bit error-rate performance of the scheme for phase shift keying does not change whether the control is assumed or not. By the effect of the virtual automatic gain control and the interleaving, a fading channel with Gaussian noise is theoretically converted into an equivalent time-invariant channel with non-Gaussian noise. The probability density function of the converted non-Gaussian noise is derived. Then, the function is applied to a formula of the bit error-rate of the scheme for non-Gaussian noise. The formula is derived for phase shift keying by modifying that for pulse amplitude modulation. The coding performance for the non-Gaussian noise channel is evaluated by the formula, and the suitable coding with ideal interleaving is searched. As a result, the coding gain of 28 dB is obtained at the bit error-rate of 10-6 by using BCH code of length 31. This result is confirmed by a simulation for the fading channel. Then, the effectiveness of the formula for finite interleaving is evaluated. Finally, the usefulness of the formula, where the noise power is doubled, is shown for a case of a differential detection.