Fast performance estimation of block codes

Importance sampling is used in this paper to address the classical yet important problem of performance estimation of block codes. Simulation distributions that comprise discreteand continuous-mixture probability densities are motivated and used for this application. These mixtures are employed in concert with the so-called g-method, which is a conditional importance sampling technique that more effectively exploits knowledge of underlying input distributions. For performance estimation, the emphasis is on bit by bit maximum a-posteriori probability decoding, but message passing algorithms for certain codes have also been investigated. Considered here are single parity check codes, multidimensional product codes, and briefly, low-density parity-check codes. Several error rate results are presented for these various codes, together with performances of the simulation techniques

Joint Channel Estimation and Decoding with Low-Complexity Iterative Structures in Time-Varying Fading Channels

A low-complexity iterative channel estimation (ICE) algorithm is proposed with the promise of improved error performance. The new algorithm operates the LMS filter both in the forward and the backward directions along a block. The feedback from the decoder to the estimator is in the form of soft decisions. The pilot symbol assisted modulation (PSAM) is used as the transmission technique. The effect of code choice on various ICE algorithms is also explored by considering the blockwise concatenated codes initially offered for block-fading channels. The performance of the new estimation algorithm with the proposed coding is shown to outperform the conventional estimation algorithms over a fast time-varying Rayleigh fading channel beside its low complexity structure

Space-Time Codes Concatenated with Turbo Codes over Fading Channels

The uses of space-time code (STC) and iterative processing have enabled robust communications over fading channels at previously unachievable signal-to-noise ratios. Maintaining desired transmission rate while improving the diversity from STC is challenging, and the performance of the STC suffers considerably due to lack of channel state information (CSI). This dissertation research addresses issues of considerable importance in the design of STC with emphasis on efficient concatenation of channel coding and STC with theoretical bound derivation of the proposed schemes, iterative space-time trellis coding (STTC), and differential space-time codes. First, we concatenate space-time block code (STBC) with turbo code for improving diversity gain as well as coding gain. Proper soft-information sharing is indispensable to the iterative decoding process. We derive the required soft outputs from STBC decoders for passing to outer turbo code. Traditionally, the performance of STBC schemes has been evaluated under perfect channel estimation. For fast time-varying channel, obtaining the CSI is tedious if not impossible. We introduce a scheme of calculating the CSI at the receiver from the received signal without the explicit channel estimation. The encoder of STTC, which is generally decoded using Viterbi like algorithm, is based on a trellis structure. This trellis structure provides an inherent advantage for the STTC scheme that an iterative decoding is feasible with the minimal addition computational complexity. An iteratively decoded space-time trellis coding (ISTTC) is proposed in this dissertation, where the STTC schemes are used as constituent codes of turbo code. Then, the performance upper bound of the proposed ISTTC is derived. Finally, for implementing STBC without channel estimation and maintaining trans- mission rate, we concatenate differential space-time block codes (DSTBC) with ISTTC. The serial concatenation of DSTBC or STBC with ISTTC offers improving performance, even without an outer channel code. These schemes reduce the system complexity com- pared to the standalone ISTTC and increase the transmission rate under the same SNR condition. Detailed design procedures of these proposed schemes are analyzed

Minimum-Variance Importance-Sampling Bernoulli Estimator for Fast Simulation of Linear Block Codes over Binary Symmetric Channels

In this paper the choice of the Bernoulli distribution as biased distribution for importance sampling (IS) Monte-Carlo (MC) simulation of linear block codes over binary symmetric channels (BSCs) is studied. Based on the analytical derivation of the optimal IS Bernoulli distribution, with explicit calculation of the variance of the corresponding IS estimator, two novel algorithms for fast-simulation of linear block codes are proposed. For sufficiently high signal-to-noise ratios (SNRs) one of the proposed algorithm is SNR-invariant, i.e. the IS estimator does not depend on the cross-over probability of the channel. Also, the proposed algorithms are shown to be suitable for the estimation of the error-correcting capability of the code and the decoder. Finally, the effectiveness of the algorithms is confirmed through simulation results in comparison to standard Monte Carlo method

On the rate-distortion performance and computational efficiency of the Karhunen-Loeve transform for lossy data compression

We examine the rate-distortion performance and computational complexity of linear transforms for lossy data compression. The goal is to better understand the performance/complexity tradeoffs associated with using the Karhunen-Loeve transform (KLT) and its fast approximations. Since the optimal transform for transform coding is unknown in general, we investigate the performance penalties associated with using the KLT by examining cases where the KLT fails, developing a new transform that corrects the KLT's failures in those examples, and then empirically testing the performance difference between this new transform and the KLT. Experiments demonstrate that while the worst KLT can yield transform coding performance at least 3 dB worse than that of alternative block transforms, the performance penalty associated with using the KLT on real data sets seems to be significantly smaller, giving at most 0.5 dB difference in our experiments. The KLT and its fast variations studied here range in complexity requirements from O(n^2) to O(n log n) in coding vectors of dimension n. We empirically investigate the rate-distortion performance tradeoffs associated with traversing this range of options. For example, an algorithm with complexity O(n^3/2) and memory O(n) gives 0.4 dB performance loss relative to the full KLT in our image compression experiment

Successive interference cancellation schemes for time-reversal space-time block codes

In this paper, we propose two simple signal detectors that are based on successive interference cancellation (SIC) for time-reversal space-time block codes to combat intersymbol interference in frequency-selective fading environments. The main idea is to treat undetected symbols and noise together as Gaussian noise with matching mean and variance and use the already-detected symbols to help current signal recovery. The first scheme is a simple SIC signal detector whose ordering is based on the channel powers. The second proposed SIC scheme, which is denoted parallel arbitrated SIC (PA-SIC), is a structure that concatenates in parallel a certain number of SIC detectors with different ordering sequences and then combines the soft output of each individual SIC to achieve performance gains. For the proposed PA-SIC, we describe the optimal ordering algorithm as a combinatorial problem and present a low-complexity ordering technique for signal decoding. Simulations show that the new schemes can provide a performance that is very close to maximum-likelihood sequence estimation (MLSE) decoding under time-invariant conditions. Results for frequency-selective and doubly selective fading channels show that the proposed schemes significantly outperform the conventional minimum mean square error-(MMSE) like receiver and that the new PA-SIC performs much better than the proposed conventional SIC and is not far in performance from the MLSE. The computational complexity of the SIC algorithms is only linear with the number of transmit antennas and transmission rates, which is very close to the MMSE and much lower than the MLSE. The PA-SIC also has a complexity that is linear with the number of SIC components that are in parallel, and the optimum tradeoff between performance and complexity can be easily determined according to the number of SIC detectors