A-posterior Probability Research Articles

Performance of Iterative Coded CDMA Receivers with APP Feedback: A Use of a Weighted Delay Filter

The prohibitive computational complexity of optimal coded multiuser detection necessitates using suboptimal detectors in practical implementations. The filter is very computationally simple and is also demonstrated to provide faster convergence and superior bit error rate (BER) performance. Further investigation of the weighted delay filter concept produces a second filter—derived via the joint likelihood function. It is analytically demonstrated that extrinsic feedback systems will not benefit from weighted delay filtering. A system model is provided that introduces the notion of feedback ‘residue’, which is shown to be the key difference between a-posterior probability (APP) and extrinsic systems when determining the parallel interference cancellation (PIC) output statistics. It is analytically shown that the weighted delay filter derived via a maximum signal-to-noise ratio (SNR) approach is identical to a weighted delay filter derived via the joint likelihood function. It is analytically shown that when extrinsic feedback is used in a coded-code division multiple access (C-CDMA) system, no benefit will be realised by weighted delay filtering, as soft outputs from previous cycles are a merely scaled, noisy version of the most recent data. The notion of a ‘feedback residue’ for systems with APP feedback is introduced, and it is empirically shown that this residue term is a key consideration when determining the PIC output statistics. Using the ‘residual feedback’ model, it is shown that when APP feedback is utilised, data from previous cycles is not simply “a scaled, noisy version” of the current data. For this reason, benefits may be realised by APP feedback use. The simulation results shows that the residue may be trivial at small loads, the residue builds to the substantial value of nearly 0.4 at a reasonably modest load of K/N=15/10, and continues to grow as the load increases.

Concatenated Permutation Codes under Chebyshev Distance

Permutation codes are error-correcting codes over symmetric groups. We focus on permutation codes under Chebyshev (ℓ∞) distance. A permutation code invented by Kløve et al. is of length n, size 2n-d and, minimum distance d. We denote the code by φn,d. This code is the largest known code of length n and minimum Chebyshev distance d > n/2 so far, to the best of the authors knowledge. They also devised efficient encoding and hard-decision decoding (HDD) algorithms that outperform the bounded distance decoding. In this paper, we derive a tight upper bound of decoding error probability of HDD. By factor graph formalization, we derive an efficient maximum a-posterior probability decoding algorithm for φn,d. We explore concatenating permutation codes of φn,d=0 with binary outer codes for more robust error correction. A naturally induced pseudo distance over binary outer codes successfully characterizes Chebyshev distance of concatenated permutation codes. Using this distance, we upper-bound the minimum Chebyshev distance of concatenated codes. We discover how to concatenate binary linear codes to achieve the upper bound. We derive the distance distribution of concatenated permutation codes with random outer codes. We demonstrate that the sum-product decoding performance of concatenated codes with outer low-density parity-check codes outperforms conventional schemes.

Novel memory efficient LDPC decoders for beyond 5G

Beyond-5G wireless networks are expected to gain a excellent trade-off among computational accuracy, latency, and efficient use of available resources. This poses a significant challenge to the channel decoder. In this paper, a novel memory efficient algorithm for decoding Low-Density Parity-Check (LDPC) codes is proposed with a view to reduce the implementation complexity and hardware resources. The algorithm, called Check Node Self-Update (CNSU) algorithm, is based on layered normalized min-sum (LNMS) decoding algorithm while utilizing iteration parallel techniques to integrate both Variable Nodes (VNs) message and A-Posterior Probability(APP) message into the Check Nodes (CNs) message, which eliminates memories of both the VNs message and the APP message as well as updating module of APP message in CNs unit. Based on the proposed CNSU algorithm, design of partially parallel decoder architecture and serial simulations followed by implementation on the Stratix II EP2S180 FPGA are presented. The results show that the proposed algorithm and implementation bring a significant gain in efficient using of available resources, include reducing hardware memory resources and chip area while keeping the benefit of bit-error-rate (BER) performance and speeding up of convergence with LNMS, which are beneficial to apply in Beyond-5G wireless networks.

Design Analysis of Turbo Decoder Based on One MAP Decoder Using High Level Synthesis Tool

High Level Synthesis (HLS) tool does not only simplify the designing operation and rapid prototyping but also allows the designers to explore large number of design’s techniques such as parallelism, pipeline, memory partitioning and many other techniques. Turbo decoder based on Maximum APosterior Probability (MAP) algorithm is designed in this work using Vivado HLS. The normal turbo decoder with two MAP decoders were implemented with and without parallelism and proposed a new design of turbo decoder with one MAP decoder and it was designed with and without parallelism using different window technique in HLS tool which it is not explored previously. These designs were implemented for different frame size in this work. A comp-arison in latency and resource utilization where done and how a tradeoff done between these two parameters to reach the specific design that we need. The new design produces better results.

Expectation Propagation Aided Frequency Domain Turbo Equalizer for Single-Carrier Spatial Modulation Systems

An efficient frequency-domain equalizer is developed for single-carrier (SC) aided spatial modulation (SM) systems over frequency-selective fading channels, by employing the idea of expectation propagation (EP) algorithms. Specifically, we design an EP-aided frequency domain turbo equalizer (EP-FDTE) for iterative information exchange between the equalizer and the soft decoder, leading to more reliable a posterior probability (APP) estimation for signal detection. Our simulation results demonstrate that the proposed equalizer outperforms conventional frequency-domain turbo equalizer (FDTE) and generalized approximate message passing (GAMP)-aided turbo equalizer for SC-SM transmission.

A DIAGNOSTICS PROBLEM OF A-POSTERIOR PROBABILITY DETERMINATION VIA BAYES’ FORMULA OBTAINED IN THE MULTI-OPTIONAL HYBRID FUNCTIONS ENTROPY CONDITIONAL OPTIMIZATION WAY

The paper theoretically considers the possibility of the multi-optional hybrid functions entropy conditional optimization principle applicability with the purpose of discovering one more substantiated reason for the Mr. Thomas Bayes’ Theorem Formula existence, as well as the reasons for the formula optimality. The Bayes’ formula for a hypothesis’ a-posterior probability is obtained on the basis of multi-optional optimality doctrine with taking into account the degree of uncertainty, in the view of the entropy member, for a certain type hybrid-optional effectiveness functions. With the help of the variational principle it is shown the optimality of the Bayes’ formula. The approach is applicable to the variety of issues since it has a significance of a plausible explanation for phenomena stipulated by multi-optionality.

Automated pattern recognition to support geological mapping and exploration target generation – A case study from southern Namibia

This paper demonstrates a methodology for the automatic joint interpretation of high resolution airborne geophysical and space-borne remote sensing data to support geological mapping in a largely automated, fast and objective manner. At the request of the Geological Survey of Namibia (GSN), part of the Gordonia Subprovince of the Namaqua Metamorphic Belt situated in southern Namibia was selected for this study.All data – covering an area of 120km by 100km in size – were gridded, with a spacing of adjacent data points of only 200m. The data points were coincident for all data sets. Published criteria were used to characterize the airborne magnetic data and to establish a set of attributes suitable for the recognition of linear features and their pattern within the study area. This multi-attribute analysis of the airborne magnetic data provided the magnetic lineament pattern of the study area.To obtain a (pseudo-) lithology map of the area, the high resolution airborne gamma-ray data were integrated with selected Landsat band data using unsupervised fuzzy partitioning clustering. The outcome of this unsupervised clustering is a classified (zonal) map which in terms of the power of spatial resolution is superior to any regional geological mapping. The classified zones are then assigned geological/geophysical parameters and attributes known from the study area, e.g. lithology, physical rock properties, age, chemical composition, geophysical field characteristics, etc. This information is obtained from the examination of archived geological reports, borehole logs, any kind of existing geological/geophysical data and maps as well as ground truth controls where deemed necessary.To obtain a confidence measure validating the unsupervised fuzzy clustering results and receive a quality criterion of the classified zones, stepwise linear discriminant analysis was chosen. Only a small percentage (8%) of the samples was misclassified by discriminant analysis when compared to the result obtained from unsupervised fuzzy clustering. Furthermore, a comparison of the aposterior probability of class assignment with the trustworthiness values provided by fuzzy clustering also indicates only slight differences. These observed differences can be explained by the exponential class probability term which tends to deliver either fairly high or low probability values.The methodology and results presented here demonstrate that automated objective pattern recognition can essentially contribute to geological mapping of large study areas and mineral exploration target generation. This methodology is considered well suited to a number of African countries whose large territories have recently been covered by high resolution airborne geophysical data, but where existing geological mapping is poor, incomplete or outdated.

Construction of quasi-cyclic low-density parity-check codes for simplifying shuffle networks in layered decoder

Offset Shuffle Networks (OSNs) interleave a-posterior probability messages in the Block Row-Layered Decoder (BRLD) of Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes. However, OSNs usually consume a significant amount of computational resources and limit the clock frequency, particularly when the size of the Circulant Permutation Matrix (CPM) is large. To simplify the architecture of the OSN, we propose a Simplified Offset Shuffle Network Block Progressive Edge-Growth (SOSN-BPEG) algorithm to construct a class of QC-LDPC codes. The SOSN-BPEG algorithm constrains the shift values of CPMs and the difference of the shift values in the same column by progressively appending check nodes. Simulation results indicate that the error performance of the SOSN-BPEG codes is the same as that of the codes in WiMAX and DVB-S2. The SOSN-BPEG codes can reduce the complexity of the OSNs by up to 54.3%, and can improve the maximum frequency by up to 21.7% for various code lengths and rates.

Detection of Non-Contiguous OFDM Symbols for Cognitive Radio Systems without Out-of-Band Spectrum Synchronization

For non-contiguous OFDM (NC-OFDM) based cognitive radio systems, one challenge is to establish the spectrum synchronization before the data transmission over an idle channel. In this paper, we propose two novel detection schemes, i.e., hard-decision-based detection (HDD) and soft-decision-based detection (SDD) schemes, to detect NC-OFDM symbols without the information of out-of-band spectrum synchronization. The key idea of the proposed schemes is to employ the received training symbol to calculate a posterior probability (APP) of each subchannel's being active. Specifically, for the proposed HDD scheme, the secondary receiver detects whether a subchannel is active or not based on its APP. When the APP of a subchannel is larger than a preset threshold, it will be employed for the data detection. Moreover, we derive the miss detection and false alarm probabilities of the hard decision based detection of active subchannels, respectively. For the proposed SDD scheme, all subchannels are employed for the data detection, in which as a priori information of the subchannels' being active, all APPs are taken into account in the bit metric calculation. Theoretical analysis and simulation results show that the proposed schemes can provide satisfactory performance.

Turbo decoding for high-rate concatenated parity-check codes on PRML channels

A simple turbo decoding scheme is proposed for partial-response (PR) channels by using high-rate parity-check codes as an outer error-correction code (ECC). The use of the simple parity codes enables a simplified and high-speed implementation of the a posterior probability (APP) decoder. Its key feature is an iterative decoding step for the parallel concatenation of two parity-check outer codes connected via an interleaver. The parity iterative decoding can provide the high-rate parity-check outer codes with superior correction capability for random error-events, so it can help to reduce the decoding latency. The combination of the serial turbo decoding for a modified E/sup 2/PR (ME/sup 2/PR) channel and the parity iterative decoding demonstrated a coding gain of 4-5 dB at a bit error rate of 1.0E-5 for a coding rate of 8/9.

Minimum-Description-Length Criterion for Image Interpretation and Data Analysis in Spatial Informatics

Abstract Spatial Informatics typically involves interpretation of remotely sensed images and analysis of multi-sources of data. Random perturbation in the observations and diversity of hypothesized models give rise to the uncertainty and difficulty of image interpretation and data analysis. The Minimum-Description-Length (MDL) principle is a beet established criterion, which selects the best model with the minimal length of jointly encoding the data and the model. Although in terms of probability, MDL criterion is equivalent to the Maximum Aposterior Probability (MAP) criterion, it is advantageous at Combining different data types and different model structures in a uniform measure – the total number of bits. It is more realistic to computerized information processing, because everything is discrete with limited resolution. This paper clarifies the formulation of the MDL criterion, its relationships to information theory, stochastic complexity, and Bayesian decision strategy. To sufficiently demonstrate t...

Bayesian System Classification

The problem of system classification can be stated (after Zadeh) as determination, on the basis of observation of inputs and outputs, of one among specified classes of systems to which the system under test belongs. If the system is stochastic and the amount of input-output data is finite the system under test cannot be classified with certainty, i.e. even after the experiment the experimenter cannot state with certainty which one of his hypotheses is true. In the present paper the Bayesian statistics, with subjective interpretation of probability as a measure of belief, is employed to extract the relevant information contained in the data. Given the prior probability distribution (a model of the prior uncertainty) the aposterior probability distribution on the set of hypotheses (conditioned on the data observed) is calculated in order to obtain a rational basis for some kind of decision (e.g. the choice of model structure). The unknown order of a linear system is a special case of this kind. Power and limitations of the theory are demonstrated on examples.