Mutual Information Function Research Articles

Increase of Complexity from Classical Greek to Latin Poetry

In this paper a method is developed to analyze the increase of complexity from classical Greek poetry to classical Latin poetry by mapping large samples of poems onto a symbolic time series. This mapping setup intends to characterize the regular succession of rhythms, that is, the patterns of stressed and unstressed syllables in a verse. Using techniques from information theory; more precisely, the mutual information function, it is shown how the rhythmical patterns in Greek poetry evolve to more complex behavior in Latin poetry. Some interesting results are reported.

Interhemispheric connectivity dynamics of brain activity indused by cortical spreading depolarization in rats

Growing experimental and clinical evidence indicates the crucial role of network dysfunction in neurological disorders’ pathogenesis, including migraine, one of the most prevalent chronic brain diseases. Episodic headache attacks, frequently unilateral, accompanied by an aura, are associated with migraine. Migraine aura is a neurological condition characterized by the temporary development of unilateral sensory, motor, and/or speech disturbances. The symptoms are thought to indicate transient cerebral dysfunction in the cerebral cortex resulting from cortical spreading depolarization (SD), a wave of strong cellular depolarization that gradually spreads through the cortex at a rate of 3–5 mm/min. Electrophysiologically, the cortical SD wave is revealed by a high-amplitude slow negative shift in the extracellular potential and temporary suppression of the electrical activity of the cortex (EEG depression). The change in extracellular potential is associated with strong neuroglial depolarization and disruption of local ion homeostasis, which lasts for 1–2 min in healthy neuronal tissue. The SD results in a momentary suppression of the spontaneous electrical activity within the cortex, which is preceded by a brief excitation of the neurons. The neurological symptoms of the aura suggest a unilateral impairment of interhemispheric interactions during the early phase of a migraine attack. Our study investigated the effect of unilateral SD (a probable pathophysiological mechanism of migraine aura) on interhemispheric functional communication in freely behaving rats using local field potentials of the visual and motor cortex. Two methods were used to examine connectivity: mutual information function, computed using the method proposed in [1], and phase synchronization, calculated through the method [2], for four frequency bands: delta (1–4 Hz), theta (4–10 Hz), beta (10–25 Hz), and gamma (25–50 Hz). This was done by performing calculations on non-overlapping twenty-second intervals. Functional connectivity evolution was analyzed using local field potential records collected from homotopic points of the motor and visual cortex of two hemispheres in freely moving rats after inducing a single unilateral cortical SD in the somatosensory cortex. Cortical SD caused a significant wide-band decline (3–4 times) in interhemispheric functional connectivity in both the visual and motor cortex areas. Following the depolarization wave, the functional decoupling of the hemispheres began and progressively intensified, concluding by 5 min after the induction of the cortical SD wave. The network impairment displayed region- and frequency-specific features, with greater prominence observed in the visual cortex than in the motor cortex. The decline in functional connectivity was concurrent with abnormal animal behavior and aberrant activity in the ipsilateral cortex that appeared after the SD wave had ended. The study indicated that unilateral SD leads to a reversible decline in the functional interhemispheric connectivity in the awake animal cortex. Given the crucial role of synchronizing cortical oscillations for processing sensory information and integrating sensorimotor functions, the intracortical functional interactions disruption resulting from a unilateral SD wave, which we discovered in our present study, could contribute to the neuropathological mechanisms of migraine aura and sensory processing dysfunction during a migraine attack.

Intelligent phenotype-detection and gene expression profile generation with generative adversarial networks

Gene expression analysis is valuable for cancer type classification and identifying diverse cancer phenotypes. The latest high-throughput RNA sequencing devices have enabled access to large volumes of gene expression data. However, we face several challenges, such as data security and privacy, when we develop machine learning-based classifiers for categorizing cancer types with these datasets. To address these issues, we propose IP3G (Intelligent Phenotype-detection and Gene expression profile Generation with Generative adversarial network), a model based on Generative Adversarial Networks. IP3G tackles two major problems: augmenting gene expression data and unsupervised phenotype discovery. By converting gene expression profiles into 2-Dimensional images and leveraging IP3G, we generate new profiles for specific phenotypes. IP3G learns disentangled representations of gene expression patterns and identifies phenotypes without labeled data. We improve the objective function of the GAN used in IP3G by employing the earth mover distance and a novel mutual information function. IP3G outperforms clustering methods like k-Means, DBSCAN, and GMM in unsupervised phenotype discovery, while also surpassing SVM and CNN classification accuracy by up to 6% through gene expression profile augmentation. The source code for the developed IP3G is accessible to the public on GitHub.

Distributed photovoltaic short‐term power forecasting using hybrid competitive particle swarm optimization support vector machines based on spatial correlation analysis

AbstractIn order to further improve the accuracy of distributed photovoltaic (DPV) power prediction, this paper proposes a support vector machine (SVM) model based on hybrid competitive particle swarm optimization (HCPSO) with consideration of spatial correlation (SC), for realizing short‐term PV power prediction tasks. Firstly, the spatial correlation analysis is conducted on the distributed PV stations. The k‐means clustering method based on morphological similarity distance improvement and mutual information function is used to select the best reference station and the best delay, which generates strongly correlated PV sequences. Then, a hybrid algorithm of particle swarm optimization (PSO) and sine cosine algorithm (SCA) in a competitive framework (HCPSO) is proposed, aiming to fuse the fast convergence capability of PSO algorithm with the global search capability of SCA algorithm, while enabling the algorithm to effectively handle high‐dimensional optimization problems based on a competitive mechanism. Finally, the HCPSO algorithm is combined with SVM algorithm, which expands the applicable scenarios of the SVM model and effectively improves the accuracy of PV short‐term prediction.

Information-Theoretic Approaches to Differential Privacy

This tutorial studies relations between differential privacy and various information-theoretic measures by using several selective articles. In particular, we present how these connections can provide new interpretations for the privacy guarantee in systems that deploy differential privacy in an information-theoretic framework. Accordingly, the tutorial delivers an extensive summary on the existing literature that makes use of information-theoretic measures and tools such as mutual information, min-entropy, Kullback-Leibler divergence, and rate-distortion function for quantification and characterization of differential privacy in various settings.

Intracortical functional connectivity dynamics induced by reflex seizures

Functional connectivity analysis is gaining more interest due to its promising clinical applications. To study network mechanisms underlying seizure termination and postictal depression, we explore dynamics of interhemispheric functional connectivity near the offset of focal and bilateral seizures in the experimental model of reflex audiogenic epilepsy. In the model, seizures and spreading depression are induced by sound stimulation of genetically predisposed rodents. We characterize temporal evolution of seizure-associated coupling dynamics in the frontoparietal cortex during late ictal, immediate postictal and interictal resting states, using two measures applied to local field potentials recorded in awake epileptic rats. Signals were analyzed with mean phase coherence index in delta (1–4 Hz), theta (4–10 Hz) beta (10–25 Hz) and gamma (25–50 Hz) frequency bands and mutual information function. The study shows that reflex seizures elicit highly dynamic changes in interhemispheric functional coupling with seizure-, region- and frequency-specific patterns of increased and decreased connectivity during late ictal and immediate postictal periods. Also, secondary generalization of recurrent seizures (kindling) is associated with pronounced alterations in resting-state functional connectivity – an early wideband decrease and a subsequent beta-gamma increase. The findings show that intracortical functional connectivity is dynamically modified in response to seizures on short and long timescales, suggesting the existence of activity-dependent plastic network alterations that may promote or prevent seizure propagation within the cortex and underlie postictal behavioral impairments.

Joint Code Rate Compatible Design of DP-LDPC Code Pairs for Joint Source Channel Coding Over Implant-to-External Channel

A CM2-S3 transmission link in wireless body area networks (WBAN) is implemented with a joint source channel coding (JSCC) system based on double protograph low-density parity-check (DP-LDPC) code pairs with high reliability and low power consumption. For the practicality and suitability considerations, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary differential chaos shift keying scheme is introduced to modulate the CM2-S3 channel with better performance than the standard modulations in WBAN. Due to the non-Gaussian-like distribution of the CM2-S3 channel model, the initial joint protograph extrinsic information transfer (JPEXIT) algorithm does not work as a coding analysis tool. To solve this problem, a numerical Gaussian approximation is employed to modify the iterative mutual information function of the JPEXIT for achieving more precise output. Then, a joint code rate compatible (JCRC) method, designed with compatibility in resisting variable channel variances and adapting different source statistics, is proposed for optimizing the DP-LDPC code pairs. Based on the JCRC method, the code searching algorithm is simplified with lower complexity because of the reduced cycle-index. The simulation results show that optimized code pairs have better bit-error ratio performances compared to existing codes, which provides a strong technical support to promote high-quality data transmission in eHealthcare on the physical layer.

Using Chaos Theory to Determine Average Prediction Times of Different Meteorological Variables: A Case Study in Sivas

Processes in the atmosphere can be described by nonlinear approaches since they depend on a large number of independent variables. Even a slight change in initial conditions can cause unpredictable results. Therefore, long-term prediction is not possible to obtain. This is usually called “sensitive dependence on initial conditions”. In this study, average prediction times were determined for different meteorological variables by using a nonlinear approach. Daily values of relative humidity, air temperature, and wind speed in Sivas for the period 2006-2010 were used. To implement the method, the first step is to reconstruct the phase space. Phase space has two embedding parameters, namely time delay and embedding dimension. Mutual Information Function (MIF) can be used to determine the optimal value of the time delay. It considers both linear and nonlinear dependencies in a time series. To define phase space, embedding dimension, which is the number of state variables that define the dynamics of a system, must be identified correctly. The algorithm to describe the dimension is called False Nearest Neighbors (FNN). In the study, average prediction times of variables were calculated by using maximum Lyapunov exponents. Average prediction times for relative humidity, temperature, and wind speed were determined as 6.2, 5.8, and 2.5 days, respectively. In addition, it is found that the sensitivity of measurements increases the prediction time. For relative humidity, the average prediction time can have a 50% increase with 10 times increase of sensitivity.

An Efficient Feature Selection Method for Video-Based Activity Recognition Systems

Human activity recognition (HAR) is the examination of gestures and actions of humans from various resources such as depth or RGB cameras. In this work, we have designed a dynamic and robust feature selection algorithm for a HAR system, through which the system accurately recognizes various kinds of activities. In the proposed approach, we employed mutual information algorithm, which selects the prominent features from the extracted features. The proposed algorithm is the expansion of two methods like max-relevance and min-redundancy, respectively. This method has the capability to gather the assets of various extraction algorithms. But the procedure of selection may be unfair due to the dissimilarity between the classification power and redundancy of the features. To resolve this type of unfair selection, we stabilize both parts through the proposed algorithm that has autonomous upper limit of the mutual information function. Likewise, for the feature extraction and recognition, we used the symlet wavelet transform and hidden Markov model, respectively, for action classification. The proposed algorithm has been justified on depth-based database which has thirteen kinds of activities under comprehensive set of experiments. We showed that the proposed feature selection method achieved best classification accuracy against existing works.

Using mutual information to measure time lags from nonlinear processes in astronomy

Measuring time lags between time series or light curves at different wavelengths from a variable or transient source in astronomy is an essential probe of physical mechanisms causing multiwavelength variability. Time lags are typically quantified using discrete correlation functions (DCFs), which are appropriate for linear relationships. However, in variable sources such as x-ray binaries, active galactic nuclei (AGNs), and other accreting systems, the radiative processes and the resulting multiwavelength light curves often have nonlinear relationships. For such systems it is more appropriate to use nonlinear information-theoretic measures of causation such as mutual information, routinely used in other disciplines. We demonstrate with toy models the limitations of using the standard DCF and show improvements when using a discrete mutual information function (DMIF). For nonlinear correlations, the latter accurately and sharply identifies the lag components as opposed to the DCF, which can be erroneous. Following that, we apply the DMIF to the multiwavelength light curves of AGN NGC 4593. We find that x-ray fluxes are leading UVW2 fluxes by $\ensuremath{\sim}0.2$ days, closer to model predictions from reprocessing by the accretion disk than the DCF estimate. The uncertainties with the current light curves are too large, though, to rule out negative lags. Additionally, we find another delay component at approximately $\ensuremath{-}1$ day, i.e., UVW2 leading x rays, consistent with inward propagating fluctuations in the accretion disk scenario. This is not detected by the DCF. Keeping in mind the nonlinear relation between x ray and UVW2, this is worthy of further theoretical investigation. From both the toy models and real observations, it is clear that the mutual-information-based estimator is highly sensitive to complex nonlinear relations. With sufficiently high temporal resolution and signal-to-noise ratio, we will precisely detect each of the lag features corresponding to these relations.

The Resolved Mutual Information Function as a Structural Fingerprint of Biomolecular Sequences for Interpretable Machine Learning Classifiers.

In the present article we propose the application of variants of the mutual information function as characteristic fingerprints of biomolecular sequences for classification analysis. In particular, we consider the resolved mutual information functions based on Shannon-, Rényi-, and Tsallis-entropy. In combination with interpretable machine learning classifier models based on generalized learning vector quantization, a powerful methodology for sequence classification is achieved which allows substantial knowledge extraction in addition to the high classification ability due to the model-inherent robustness. Any potential (slightly) inferior performance of the used classifier is compensated by the additional knowledge provided by interpretable models. This knowledge may assist the user in the analysis and understanding of the used data and considered task. After theoretical justification of the concepts, we demonstrate the approach for various example data sets covering different areas in biomolecular sequence analysis.

Differences and Reliability of Linear and Nonlinear Acoustic Measures as a Function of Vocal Intensity in Individuals With Voice Disorders

Linear acoustic indices are significantly influenced by speaking voice intensity. The main aim of this work was to compare acoustic measures based on linear and nonlinear models in different speaking voice intensity levels and to analyze the reliability of those measures in different intensity levels in subjects with voice disorders. 435 samples from subjects (314 women, 121 men with a mean age of 41.07 ± 13.73) diagnosed with various voice disorders were used. In total, 17 acoustic measures were derived from the vowel /ɛ/ sustained at three intensity levels (soft, comfortable, and loud). Five were linear (standard deviation of the fundamental frequency (f0), jitter, shimmer, harmonics-to-noise ratio (HNR) and smoothed cepstral peak prominence (CPPS)), and twelve were nonlinear measures, namely correlation dimension (D2), correlation entropy (H2), first minimum of the mutual information function (FMMI), relative entropy (ENTR-R), largest Lyapunov exponent (Lyap), determinism (DET), transitivity, mean diagonal line length (Lmed), Shannon entropy (ENTR-S), mean length of vertical structures, also known as trapping time (TT), laminarity (LAM) and recurrence period density entropy (RPDE). Differences between speaking voice intensity levels were assessed by Friedman's test and Nemenyi as posthoc test. Intraclass correlation coefficient was used to investigate if each acoustic measure remains in agreement (reliability) between different voice intensity levels. There were significant differences in all acoustic measures about vocal intensity level (P < 0.001). Intraclass correlation coefficient was very good for HNR (>0.61) and good for Lyap, DET, ENTR-S, Lmed, RPDE, and TT (0.41-0.60). All acoustic measures varied as a function of vocal intensity in voice disordered adults, while this relation was different for linear and nonlinear measures. Only the measures HNR, Lyap, DET, ENTR-S, Lmed, RPDE and TT had an acceptable reliability between different voice intensity levels. Therefore, patient`s voice SPL should be controlled or indicated during acoustic vocal assessment.

Correlation dimension and bifurcation analysis for the planar slider-crank mechanism with multiple clearance joints

Joint clearance serves as a crucial element of nonlinearity in multibody systems. The quantization of the system chaos is conducive to not only the understanding of the nonlinear nature but the rationalization of system controlled parameters. In the present work, the system dynamics for the planar slider-crank mechanism with multiple clearance joints is depicted by the correlation dimension and bifurcation actions. Considering the obliqueness of the slider, the general configuration of the planar joint is proposed. Generalized coordinates and the Lagrangian approach are adopted to derive the dynamic motion equations. The effects of clearance size and driving speed on the bifurcations of the dynamic response are investigated. Furthermore, the fractal dimension of the strange attractor is identified by the correlation dimension from time series. Based on the Cao method, the Mutual Information (MI) function, and the Grassberger-Procaccia (G-P) algorithm, the controlled factors in the evaluation of correlation dimension are cautiously determined. Ultimately, the compound effect of translational and revolute clearance joints on the mechanism dynamics is featured. The numerical results testify that the correlation dimension of the slider displacement approximately saturates beyond a specific translational clearance value. Moreover, with the parameters used in this work, the complexity of system response seems to be more sensitive to the variation of translational clearance size than with the revolute joint.

Monthly Streamflow Prediction Based on Random Forest Algorithm and Phase Space Reconstruction Theory

In order to find an effective time series forecasting method, a random forest prediction model based on phase space reconstruction theory is proposed in this paper. The Cao method and mutual information function method are used to reconstruct the phase space, and the parameters of the random forest (RF) model are discussed. The feasibility of the model is verified by analyzing the monthly runoff data of Pingshan hydrological station in Jinsha River Basin. Compared with BP neural network (BPnet) model and traditional support vector machine (SVM) model which optimizes parameters by grid algorithm, random forest model has higher prediction accuracy and less calculation in dealing with complex nonlinear hydrological time series as shown by the result.

On the automatic parameter selection for permutation entropy.

Permutation Entropy (PE) is a cost effective tool for summarizing the complexity of a time series. It has been used in many applications including damage detection, disease forecasting, detection of dynamical changes, and financial volatility analysis. However, to successfully use PE, an accurate selection of two parameters is needed: the permutation dimension n and embedding delay τ. These parameters are often suggested by experts based on a heuristic or by a trial and error approach. Both of these methods can be time-consuming and lead to inaccurate results. In this work, we investigate multiple schemes for automatically selecting these parameters with only the corresponding time series as the input. Specifically, we develop a frequency-domain approach based on the least median of squares and the Fourier spectrum, as well as extend two existing methods: Permutation Auto-Mutual Information Function and Multi-scale Permutation Entropy (MPE) for determining τ. We then compare our methods as well as current methods in the literature for obtaining both τ and n against expert-suggested values in published works. We show that the success of any method in automatically generating the correct PE parameters depends on the category of the studied system. Specifically, for the delay parameter τ, we show that our frequency approach provides accurate suggestions for periodic systems, nonlinear difference equations, and electrocardiogram/electroencephalogram data, while the mutual information function computed using adaptive partitions provides the most accurate results for chaotic differential equations. For the permutation dimension n, both False Nearest Neighbors and MPE provide accurate values for n for most of the systems with a value of n=5 being suitable in most cases.

A Modified Algorithm for the Logistic Sequence Based on PCA

In order to deal with the dynamical degradation of logistic chaotic sequence caused by the structures and finite precision computing, we propose a modified algorithm based on phase space reconstruction and PCA. In the process of phase space reconstruction, it uses Cao theory after determining the delay time by the mutual information function and takes the first principal component as the result. Results of experiments demonstrate that: the algorithm erases the relevance among data points and enhances the randomness and complexity of the sequence.

On Design of Protograph LDPC Codes for Large-Scale MIMO Systems

Protograph low-density parity-check (LDPC) codes and large-scale multi-input multi-output (LS-MIMO) systems have achieved great interest with various practical applications. However, how to effectively evaluate and design protograph LDPC codes for LS-MIMO systems remains a challenging yet critical problem, especially for low-latency applications. To solve that design challenge, the protograph extrinsic information transfer chart (PEXIT) algorithm for LS-MIMO systems, so-called LS-MIMO-PEXIT algorithm, is first derived based on the mutual information functions of messages that are passed on the joint MIMO detection and LDPC decoding graph. The proposed LS-MIMO-PEXIT algorithm plays a vital role in the optimization process of designing new protograph LDPC codes, tailored for LS-MIMO communications systems. Experiment results demonstrate that the analytical results based on the LS-MIMO-PEXIT algorithm are in good agreement with the simulation results under various input constraints, including the coding rate, the number of decoding iterations, and the LS-MIMO configuration. On top of that, the new protograph LDPC codes designed using our LS-MIMO-PEXIT algorithm achieve a coding gain from 0.2 dB at a low coding rate to 0.4 dB at a high coding rate in comparison with the state-of-the-art protograph codes in the literature. Additionally, we incorporate the practical design experience and the theoretical analysis of mutual functions into a two-step procedure to search for protograph LDPC codes that do not have error-floor behavior at frame error rate (FER) or bit error rate (BER) as low as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> or 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> , respectively. Together with the coding gain, the error-floor-free feature of the proposed protograph LDPC codes is vitally important for future wireless networks where the ultra-reliability is one of the critical requirements.

Damage quantification in moment resisting frame using phase space reconstructed from independent component sources

In the present study, a damage detection algorithm is proposed based on the amalgamation of independent component analysis (ICA) and phase space topology (PST) reconstruction. An experimental investigation is conducted by inducing damage in steel moment resisting frame (SMRF) and exciting it with ambient white noise base excitation. The experimental study is conducted for a healthy state and multiple progressive damage states. The damage in SMRF is manifested progressively by loosening the bolts of the beam-to-column and column-to-column bolted connections. The algorithm consists of two segments: In the first segment, the modal responses are obtained from the acquired response with the help of ICA. The optimal embedding parameters for modal responses are evaluated with the help of average mutual information function and singular system analysis. The second segment deals with the reconstruction of PST with the help of modal responses and embedding parameters. Lastly, the damage sensitive features (DSFs) are evaluated to identify and quantify the induced damage. The DSFs evaluated in the present study are, namely, (a) change in phase space topology (CPST), (b) Mahalanobis distance between phase space topology (MDPST), and (c) Itakura distance (ID). The CPST and MDPST measure the dissimilarity between the PSTs of healthy and damage states, whereas ID measures the dissimilarity between the set of auto-regressive coefficients of healthy and damage states of SMRF. The DSFs are able to detect and quantify the commencement and evolution of the damage in the SMRF subjected to ambient base excitation.

Alterations in EEG connectivity in healthy young adults provide an indicator of sleep depth.

Current sleep analyses have used electroencephalography (EEG) to establish sleep intensity through linear and nonlinear measures. Slow wave activity (SWA) and entropy are the most commonly used markers of sleep depth. The purpose of this study is to evaluate changes in brain EEG connectivity during sleep in healthy subjects and compare them with SWA and entropy. Four different connectivity metrics: coherence (MSC), synchronization likelihood (SL), cross mutual information function (CMIF), and phase locking value (PLV), were computed focusing on their correlation with sleep depth. These measures provide different information and perspectives about functional connectivity. All connectivity measures revealed to have functional changes between the different sleep stages. The averaged CMIF seemed to be a more robust connectivity metric to measure sleep depth (correlations of 0.78 and 0.84 with SWA and entropy, respectively), translating greater linear and nonlinear interdependences between brain regions especially during slow wave sleep. Potential changes of brain connectivity were also assessed throughout the night. Connectivity measures indicated a reduction of functional connectivity in N2 as sleep progresses. The validation of connectivity indexes is necessary because they can reveal the interaction between different brain regions in physiological and pathological conditions and help understand the different functions of deep sleep in humans.

Performance Analysis of Protograph LDPC Codes Over Large-Scale MIMO Channels With Low-Resolution ADCs

Protograph LDPC (P-LDPC) codes and large-scale multiple-input multiple-output (LS-MIMO) are cornerstones of 5G and future wireless systems, thanks to their powerful error-correcting capability and high spectral efficiency. To alleviate the high complexity in signal detection/decoding that dramatically grows with the number of antennas (in the order of tens or even hundreds), low-resolution analog-to-digital converters (ADCs) and joint detection and decoding using factor graph have recently attracted paramount interest. Unlike high-resolution ADCs, by using a small number of bits to quantize the received signal, low-resolution ADCs help reduce the hardware cost and power consumption of the RF circuit of practical LS-MIMO transceivers. Such a very much desirable reduction comes at the cost of additional quantization noise, introduced by low-resolution ADCs. This work aims to provide a unified framework to analyze the impact of the low-resolution ADCs on the performance of P-LDPC codes in practical LS-MIMO systems. It is worth noting that the previous analytical tools that have been used to evaluate the performance of P-LDPC codes do not account for the quantization noise effect of the low-resolution ADCs and the fact that the covariance of quantization noise depends on the fading channels. This article addresses this shortcoming by first leveraging the additive quantization noise model. We then derive the expression of extrinsic information for the belief-propagation LS-MIMO detector. The mutual information functions, which are the core elements of our proposed protograph extrinsic information transfer (PEXIT) algorithm, are analyzed for LS-MIMO communication systems. Our proposed PEXIT algorithm allows us to analyze and predict the impact of the low-resolution ADCs on the performance of P-LDPC codes, considering various input parameters, including the LS-MIMO configuration, the code rate, and the maximum number of decoding iterations, and the code structure. Based on our extensive analytical and simulation results, we found that the performance of 3-bit and 4-bit ADC systems only have a small gap to that of the unquantized systems. Especially when the 5-bit ADC scheme is applied, the performance loss is negligible. This finding sheds light on the practical design of LS-MIMO systems using P-LDPC codes.