A function approximation based on an orthonormal wave function expansion in a complex space is derived. Although a probability density function (PDF) cannot always be expanded in an orthogonal series in a real space because a PDF is a positive real function, the function approximation can approximate an arbitrary PDF with high accuracy. It is applied to an actor-critic method of reinforcement learning to derive an optimal policy expressed by an arbitrary PDF in a continuous-action continuous-state environment. A chaos control problem and a PDF approximation problem are solved using the actor-critic method with the function approximation, and it is shown that the function approximation can approximate a PDF well and that the actor-critic method with the function approximation exhibits high performance.

In this letter we present steady-state analyses of a gradient algorithm (GA) for second-order adaptive infinite impulse response (IIR) notch filters. A method for deriving more accurate estimation mean square error (MSE) expressions than the recently proposed method is presented. The method is based on the estimation error power spectral density (PSD). Moreover, an expression for the estimation bias for the adaptive IIR notch filter with constrained poles and zeros is shown to be obtained from the estimation MSE expression. Simulations are presented to confirm the validity of the analyses.

This paper deals with a secret key agreement problem from correlated random numbers. It is proved that there is a pair of linear matrices that yields a secret key agreement in the situation wherein a sender, a legitimate receiver, and an eavesdropper have access to correlated random numbers. A relation between the coding problem of correlated sources and a secret key agreement problem from correlated random numbers are also discussed.

The most powerful channel coding schemes, namely those based on turbo codes and low-density parity-check (LDPC) Gallager codes, have in common the principle of iterative decoding. However, the relative coding structures and decoding algorithms are substantially different. This paper presents a 2048-bit, rate-1/2 soft decision decoder for a new class of codes known as Turbo Gallager Codes. These codes are turbo codes with properly chosen component convolutional codes such that they can be successfully decoded by means of the decoding algorithm used for LDPC codes, i.e., the belief propagation algorithm working on the code Tanner graph. These coding schemes are important in practical terms for two reasons: (i) they can be encoded as classical turbo codes, giving a solution to the encoding problem of LDPC codes; (ii) they can also be decoded in a fully parallel manner, partially overcoming the routing congestion bottleneck of parallel decoder VLSI implementations thanks to the locality of the interconnections. The implemented decoder can support up to 1 Gbit/s data rate and performs up to 48 decoding iterations ensuring both high throughput and good coding gain. In order to evaluate the performance and the gate complexity of the decoder VLSI architecture, it has been synthesized in a 0.18 µm standard-cell CMOS technology.

In this paper, the performance of Tree-LDPC code [1] is presented based on the min-sum algorithm with scaling and the asymptotic performance in the water fall region is shown by density evolution. We presents that the Tree-LDPC code show a significant performance gain by scaling with the optimal scaling factor [3] which is obtained by density evolution methods. We also show that the performance of min-sum with scaling is as good as the performance of sum-product while the decoding complexity of min-sum algorithm is much lower than that of sum-product algorithm.

This paper presents a performance and thresholds for Irregular Tree-LDPC codes. We obtain optimal irregular degree distributions and threshold by the density evolution technique. It is presented that Irregular Tree-LDPC code has performance gain at low SNR.

We propose transformation of a parity-check matrix of any low-density parity-check code. A code with transformed parity-check matrix is an equivalent of a code with the original parity-check matrix. For the binary erasure channel, performance of a message-passing algorithm with a transformed parity-check matrix is better than that with the original matrix.

The Reliability-Based Hybrid ARQ (RB-HARQ) scheme, which can be used with error correcting codes using soft-input soft-output (SISO) decoders such as convolutional codes and turbo codes has been proposed. In the RB-HARQ scheme, the error rate performance is improved by selecting the retransmission bits based on Log Likelihood Ratio (LLR) of each bit in the receiver. However, the receiver has to send the bit positions of retransmission bits to the transmitter. Therefore, the RB-HARQ scheme requires a great number of feedback bits. On the other hand, Low Density Parity Check (LDPC) codes are attracting a lot of interest, recently. Because LDPC codes can achieve near Shannon limit performance and be decoded easily compared to turbo code. In this paper, we evaluate the RB-HARQ scheme using LDPC code. Moreover, we propose a RB-HARQ scheme that requires a fewer feedback bits by utilizing a code structure of LDPC code. We refer to the scheme as the RB-HARQ (row base) scheme. We show that the RB-HARQ and RB-HARQ (row base) schemes using LDPC code have better error rate performance than the scheme without ARQ. We also show that the RB-HARQ (row base) scheme has a good trade-off between error rate performance and the number of feedback bits compared to the RB-HARQ scheme.

Recently, various decoding algorithms with Low Density Parity Check (LDPC) codes have been proposed. Most algorithms can be divided into a hard decision algorithm and a soft decision algorithm. The Weighted Bit Flipping (WBF) algorithm that is between a hard decision and a soft decision algorithms has been proposed. The Bootstrapped WBF and Modified WBF algorithms have been proposed to improve the error rate performance and decoding complexity of the WBF algorithm. In this letter, we apply the Bootstrap step to the Modified WBF algorithm. We show that the Bootstrapped modified WBF algorithm outperforms the WBF, Bootstrapped WBF, and Modified WBF algorithms. Moreover, we show that the Bootstrapped modified WBF algorithm has the lowest decoding complexity.

In this paper, we propose a partially-parallel LDPC decoder which achieves a high-efficiency message-passing schedule. The proposed LDPC decoder is characterized as follows: (i) The column operations follow the row operations in a pipelined architecture to ensure that the row and column operations are performed concurrently. (ii) The proposed parallel pipelined bit functional unit enables the column operation module to compute every message in each bit node which is updated by the row operations. These column operations can be performed without extending the single iterative decoding delay when the row and column operations are performed concurrently. Therefore, the proposed decoder performs the column operations more frequently in a single iterative decoding, and achieves a high-efficiency message-passing schedule within the limited decoding delay time. Hardware implementation on an FPGA and simulation results show that the proposed partially-parallel LDPC decoder improves the decoding throughput and bit error performance with a small hardware overhead.

Double-sided YBa2Cu3O7 (YBCO) films were successfully prepared on 50-mm-diameter CeO2-buffered sapphire substrates by metalorganic deposition (MOD) process using an acetylacetonate coating solution. Mapping analysis of superconducting current densities (Jc) at 77.3 K revealed that Jc values of the double-sided films indicated in excess of 2 MA/cm2 in the center parts with a small decrease of Jc at the outer side of the specimens. The Jc values of one side (A) are higher than those of the other side (B). Microwave surface resistance (Rs) of sides A and B of the film exhibited 0.57 and 0.60 mΩ, respectively, at 70 K (12 GHz). The difference in the Rs values should be attributed to the slight difference in the Jc values, which arose from the surface morphology of the CeO2 buffer layer and heat treatment conditions during the firing process in MOD.

In this paper by using an exactly analytic approach the clock jitter in the feedback path of the continuous time Delta Sigma modulators (CT DSM) is modeled as an additive jitter noise, providing a time invariant model for a jittery CT DSM. Then for various DAC waveforms the power spectral density (psd) of the clock jitter at the output of DAC is derived and by using an approximation the in-band power of the clock jitter at the output of the modulator is extracted. The simplicity and generality of the proposed approach are the main advantages of this paper. The MATALB and HSPICE simulation results confirm the validity of the proposed formulas.

Irregular Low-Density Parity-Check (LDPC) codes generally achieve better performance than regular LDPC codes at low Eb/N0 values. They have, however, higher error floors than regular LDPC codes. With respect to the construction of the irregular LDPC code, it can achieve the trade-off between the performance degradation of low Eb/N0 region and lowering error floor. It is known that a decoding algorithm can achieve very good performance if it combines the Ordered Statistic Decoding (OSD) algorithm and the Log Likelihood Ratio-Belief Propagation (LLR-BP) decoding algorithm. Unfortunately, all the codewords obtained by the OSD algorithm satisfy the parity check equation of the LDPC code. While we can not use the parity check equation of the LDPC code to stop the decoding process, the wrong codeword that satisfies the parity check equation raises the error floor. Once a codeword that satisfies the parity check equation is generated by the LLR-BP decoding algorithm, we regard that codeword as the final estimate and halt decoding; the OSD algorithm is not performed. In this paper, we propose a new encoding/decoding scheme to lower the error floor created by irregular LDPC codes. The proposed encoding scheme encodes information bits by Cyclic Redundancy Check (CRC) and LDPC code. The proposed decoding scheme, which consists of the LLR-BP decoding, CRC check, and OSD decoding, detects errors in the codewords obtained by the LLR-BP decoding algorithm and the OSD decoding algorithm using the parity check equations of LDPC codes and CRC. Computer simulations show that the proposed encoding/decoding scheme can lower the error floor of irregular LDPC codes.

Conventional video compression methods generally require a large amount of computation in the encoding process because they perform motion estimations. In order to reduce the encoding complexity for video compression, this paper proposes a new video compression method based on low-density parity check codes. The proposed method is suitable for resource-constrained devices such as mobile phones and satellite cameras.

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach in case the signal is Gaussian. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. This paper presents a recursive form of PSD to reduce the complexity. If the signal is not Gaussian, the PSD approach is insufficient and we estimate the higher order spectra of the signal. Estimation of higher order spectra is even more time consuming. In this paper, recursive versions for computation of bispectrum has been presented as well. The computational complexity of PSD and bispectrum for a window size of N, are O(N) and O(N2) respectively.

In [1], an algorithm based on phase variations of received pilot symbols was proposed to estimate one of the most important channel parameters, maximum Doppler shift, fd. However, AWGN (Additive white gauss noise) will cause large estimation error in some cases. In order to analyze the influence of noise, we extended the phase probability density function (pdf) in [1] to the scenario with both fading and AWGN, then the estimation error is characterized in closed-form expression. By this error expression, we found that power control will affect the estimator of [1] and we proposed a modification method based on SNR estimation to obtain accurate Doppler shift estimation in moderate low SNRs (signal-to-noise ratio). Simulation results show high accuracy in wide range of velocities and SNRs.

As an enhancement of the state-of-the-art solutions, a high-throughput architecture of a decoder for structured LDPC codes is presented in this paper. Thanks to the peculiar code definition and to the envisaged architecture featuring memory paging, the decoder is very flexible, and the support of different code rates is achieved with no significant hardware overhead. A top-down design flow of a real decoder is reported, starting from the analysis of the system performance in finite-precision arithmetic, up to the VLSI implementation details of the elementary modules. The synthesis of the whole decoder on 0.18µm standard cells CMOS technology showed remarkable performances: small implementation loss (0.2dB down to BER = 10-8), low latency (less than 6.0µs), high useful throughput (up to 940Mbps) and low complexity (about 375 Kgates).

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 710-8, the proposed method requires shorter simulation time than the conventional IS method.

This paper studies power spectrum density (PSD) of multi-user aggregate time hopping (TH) ultra wideband (UWB) signal with asynchronous transmission and synchronous transmission. TH codes under consideration are deterministic periodic code and random integer code. Based on the PSD, the in-band interference power for TD SCDMA is investigated as function of UWB system parameters. Two UWB modulations, TH pulse position modulation (PPM) and TH BPSK, are considered for calculating the in-band interference power. The numerical results indicate that asynchronous transmission is an effective way to decrease the peak in-band interference caused by multi-user aggregate TH-PPM UWB signal. Although increasing the maximum of time hopping code elements can smooth the PSD of TH UWB signal, it is not a good idea for reducing the peak in-band interference for TD SCDMA. For the random integer TH code, while only TH UWB continuous spectral exists in TD SCDMA band or multi-user signals of TH UWB are transmitted asynchronously, the in-band interference for TD SCDMA is in proportion to the number of the UWB users. For TD SCDMA in which band discrete spectral line exists the in-band interference caused by TH UWB with synchronous transmission is in proportion to the square of the number of the UWB users.

In this paper we focus on the decoding error of the Log-Likelihood Ratio Belief Propagation (LLR-BP) decoding algorithm caused by oscillation. The decoding error caused by the oscillation is dominant in high Eb/N0 region. Oscillation of the LLR of the extrinsic value in the bit node process (ex-LLR) is propagated to the other bits and affects the whole decoding. The Ordered Statistic Decoding (OSD) algorithm is known to improve the error rate performance of the LLR-BP decoding algorithm. The OSD algorithm is performed by deciding the reliability of each bit based on a posteriori probability. In this paper we propose two decoding algorithms based on two types of oscillations of LLR for LDPC codes. One is the oscillation-based OSD algorithm with deciding the reliability of each bit based on oscillation. The other is the oscillation-based LLR-BP decoding algorithm that modifies ex-LLR based on oscillation. In the oscillation-based LLR-BP decoding algorithm, when ex-LLR oscillates, then we reduce the magnitude of this ex-LLR to reduce the effects on the other bits. Both algorithms improve the decoding errors caused by oscillation. From the computer simulations, we show that paying attention to the oscillation, we can improve the error rate performance of the LLR-BP decoding algorithm.