Takakazu Sakai

Simulation Probability Density Function Design for Turbo Codes

We research on an importance sampling (IS) simulation to estimate a low error probability of turbo codes. The simulation time reduction in IS depends on another probability density function (p.d.f.) called simulation p.d.f. The previous IS simulation method can not evaluate the error probability on the low SNR and waterfall region. We derive the optimal simulation p.d.f. which gives the perfect estimator. A new simulation p.d.f. design, which is related to the optimal one, is proposed to overcome the problem of the previous IS method. The proposed IS simulation can evaluate all possible error patterns. Finally, some computer simulations show that the proposed method can evaluate the error probability on the low SNR, waterfall, and error floor regions. At the evaluation of the BER of 10-7, the simulation time of the proposed method is about 1/350 times as short as that of the Monte-Carlo simulation. When the BER is less than 7 × 10-8, the proposed method requires shorter simulation time than the conventional IS method.

A Blind Adaptive Decorrelating Detector Using Spatial Signature Estimation

The decorrelating detector is one of the detecting methods in a direct sequence code division multiple access systems. We investigate the blind adaptive decorrelating detector (BADD) using only the signature of the desired user (DU) according to the assumption that the algorithm is used in downlink. When the BADD is constructed with an antenna array, both the spatial and temporal signature must be taken into consideration for signal detection. We propose the BADD incorporated with the blind estimation of spatial signature (SS) of the DU only from the received signals. As the estimation procedure of SS, the orthogonal projection approximation and subspace tracking algorithm is adopted. The proposed BADD presented the BER improvement with using antenna array. The BER performance has a lower limit with increasing the number of antenna array elements.

A study on quick simulation for estimation of low FER of LDPC codes

This study shows a new design method of a simulation probability density function (PDF) for a fast frame error rate (FER) evaluation of low-density parity-check (LDPC) codes. It is difficult to evaluate a very low FER of LDPC codes by Monte Carlo simulation methods since it has excellent performance under iterative decoding. Cole et al. proposed a three-step estimation method of the low FER of LDPC codes of moderate block length. By applying the importance sampling method, which is one of the fast simulation methods, the simulation time of the error performance of LDPC codes can be reduced. Another simulation PDF, which can treat more dominant trapping sets (TS) than Cole et al.s method, is proposed. The selection of the dominant TS as proportional to its probability reduces the number of simulation runs without deteriorating the accuracy of the estimator. Unbiased estimator is given as well as that that of the Cole et al.s method. Some numerical examples are shown to demonstrate the effectiveness of the proposed method. The simulation time for an LDPC code of length 504 is reduced to 1/10 when we evaluate FER of around 10−14.

A distance spectrum estimation method of turbo codes

This study shows a new algorithm for distance spectrum (DS) estimation of turbo codes. We propose fundamental error event whose intervals of the consecutive two non zero inputs are less than the fundamental period. The DS is recursively estimated by some consecutive zero inputs with length of the fundamental period and the combination of fundamental error events. The proposed method also reduces the complexity of the calculation of codeword weight by looking up the tables of the number of weights and state transition instead of traversing over the trellis diagram.

Precoder for Chip-Interleaved CDMA Using Space-Time Block-Coding

We study the performances of a synchronous chip-interleaved, block spread (CIBS) code division multiple access (CDMA) with space-time block-coding (STBC) in the presence of frequency-selective fading. For providing the space diversity gain due to STBC, we introduce the optimum precoding for the STBC. Zero-forcing and minimum mean square error equalizers for CIBS-CDMA are derived. Simulation results confirm that the proposed precoder is valid under the frequency selective fading.

Blind Multiuser Detector over a Mobile Communication Channel with ISI

Blind adaptive linear receivers for direct sequence code-division multiple access (DS-CDMA) system are promising techniques for interference suppression and can be used in the situation where a training sequence is not available. This paper describes a method on blind estimation for the DS-CDMA signal whose temporal signature waveform has intersymbol interference due to multipath. The spatial signature due to using an antenna array is also taken into consideration. The proposed method provides the estimation of the composite channel consisting of the unknown transmission channel and spatial signature. It is also shown that the performance of signal to interference and noise ratio can be improved with using an antenna array

A study on simulation probability density function design for fast simulation of turbo codes over slow Rayleigh fading channels

This paper proposes a fast simulation method of turbo codes over slow Rayleigh fading channels. The proposed method reduces the simulation runtime by applying importance sampling (IS). The performance of IS is affected by the design of the simulation probability density function (PDF), which is different from the true PDF of the noise. While the conventional IS method for turbo codes over Rayleigh fading channels focuses only on the modification of the noise sequence of the additive white Gaussian noise channel, the proposed simulation PDF biases channel gains of the Rayleigh fading channel in addition to the channel noises. Moreover, the effectiveness of the proposed method is confirmed by some numerical examples. On the evaluation of a frame error rate of 10 6, the computer runtime of the proposed method is about 1/5 of that of the conventional IS method. When we compare with the Monte Carlo simulation method, the proposed method needs only 1/100 simulation runtime under the condition of the same accuracy of the estimator.

Fast simulation of LDPC codes over additive non-Gaussian noise channel

This paper shows a fast simulation method of low-density parity-check (LDPC) codes over an additive non-Gaussian noise channel. The evaluation of an error performance of LDPC codes is usually executed by using a Monte-Carlo simulation since the theoretical calculation method has not been reported. It is very difficult to evaluate an error performance of LDPC codes with finite block length when the error probability is very low. To solve this problem, some fast simulation methods by using importance sampling (IS) are proposed. However, the conventional methods can not reduce the simulation time of LDPC codes over an additive non-Gaussian noise channel because the simulation probability density function (PDF) used in IS is designed for an additive white Gaussian noise. We propose a new simulation PDF design related to the Chernoff bound to estimate an error performance of LDPC codes over an additive non-Gaussian noise channel. In addition, we show some numerical examples to demonstrate the effectiveness of the proposed simulation method. The simulation time of the proposed method is reduced to about 1/2000 of that of the conventional method when we estimate the frame error rate of 10−10.

Importance sampling for LDPC codes based on optimal simulation probability density function

This paper shows a fast simulation method of low-density parity-check (LDPC) codes by using importance sampling (IS). In IS, the design of the simulation probability density function (PDF) plays a very important role to reduce the simulation time. We derive the optimal simulation PDF, which can reduce the variance of the estimator to zero. Since the optimal simulation PDF includes true error probability, it can not be utilized in the practical simulation. The simulation PDF which approximates the optimal simulation PDF is proposed. In addition, we show some numerical examples to show the effectiveness of the proposed simulation method.

Efficient simulation for turbo codes over additive white class a noise channel

We research on a fast simulation method for turbo codes over an additive white Class A noise (AWAN) channel. The reduction of the estimation time is achieved by applying importance sampling (IS). The design of the simulation probability density function (PDF), which is another PDF used in IS, affects the accuracy of the estimator. Since the previous simulation PDF design based on the optimal simulation PDF for turbo codes is for an additive white Gaussian noise (AWGN) channel, it it hard to estimate an accurate error probability without any modification. In order to adapt the AWAN channel, we propose an an another simulation PDF related to the Bhattacharyya bound. Finally, some numerical examples show the effectiveness of the proposed method.