Abstract

     Vision plays a peculiar role in intelligence. Visual information, forming a large part of the sensory information, is fed into the human brain to formulate various types of cognition and behaviours that make humans become intelligent agents. Recent advances have led to the development of brain-inspired algorithms and models for machine vision. One of the key components of these methods is the utilization of the computational principles underlying biological neurons. Additionally, advanced experimental neuroscience techniques have generated different types of neural signals that carry essential visual information. Thus, there is a high demand for mapping out functional models for reading out visual information from neural signals. Here, we briefly review recent progress on this issue with a focus on how machine learning techniques can help in the development of models for contending various types of neural signals, from fine-scale neural spikes and single-cell calcium imaging to coarse-scale electroencephalography (EEG) and functional magnetic resonance imaging recordings of brain signals.

Introduction

     Every day, various types of sensory information from the external environment are transferred to the brain through different modalities and then processed to generate a series of coping behaviours. Among these perceptual modalities, vision is arguably the dominant contributor to the interactions between the external environment and the brain. Approximately 70 percent of human perception information is derived from vision[1] , far more than the auditory system, tactile system, and other sensory systems combined. The visual system is the part of the central nervous system that is required for visual perception, processing, and interpreting visual information to build a representation of the visual environment. It consists of the eye, retina, fibers that conduct visual information to the thalamus, the superior colliculus, and parts of the cerebral cortex. Today, researchers can collect neural signals using different recording modalities, e.g., spikes, electroencephalography (EEG), and functional magnetic resonance imaging (fMRI), from brain activity in different parts of the visual system, such as the retina, lateral geniculate nucleus (LGN), and primary visual cortex (V1) cortex, etc. Depending on the corresponding collecting devices, different recording modalities differ in their invasiveness, scale, and precision.

Conclusions

     In this paper, we first briefly analyzed the evolution of decoding tasks, i.e., classification, identification, and reconstruction, as this research field has developed. And we introduced the main neural recording modalities used in visual neural decoding and analyzed the characteristics of the data they acquire. Then we reviewed the main types of decoding approaches that researchers have proposed in recent decades in this field. Open data resources of data and toolkits, as well as open challenges and potential future directions of visual neural decoding, are suggested as well. The ultimate purpose of visual decoding is to decode the content of our experience in the absence of visual input. However, the scarcity of pairwise neurophysiological stimulus datasets and accurate, large-scale recording neural modalities continue to hinder the development of this discipline. Nevertheless, the importance of visual neural decoding cannot be understated. The development of neural decoding technology will promote the development of neural prostheses and brain-computer interface devices. We hope that our brief review will inspire ideas for future work in the cross-disciplinary field of brain science and neural computing.

Abstract

     Traditional MIMO decoding schemes are complex, impractical, and perform poorly for massive multiple-input multiple-output (M-MIMO) systems. Deep learning (DL) has recently emerged to perform many complex operations more efficiently within a shorter time. This paper proposes a learning-based network (DLNet) to design an M-MIMO decoder. The DLNet network architecture is designed by iteratively unfolding the gradient descent algorithm. The proposed DLNet decoder consists of 15 neural networks (NN) layers with some trainable parameters. This work considered uplink Rayleigh and correlated M-MIMO channels, which are perfectly known to the receiver. With the knowledge of the received signals and the M-MIMO channels, the proposed DLNet decoder decodes the messages of all the users. In the M-MIMO perspective, the proposed DLNet has been evaluated for symbol-error-rate (SER) performance, algorithm complexity, and run-time requirement. The simulations show that the proposed DLNet converges faster than other available decoders and performs better than other M-MIMO decoding schemes, by at least 2 dB in SER and at least 11 times faster than the baseline (OAMP-Net) and nine times less complex.

Introduction

     Massive multiple-input multiple-output (M-MIMO) is one of the primary transmission techniques for fifth-generation (5G) wireless communication systems. M-MIMO shows many advantages over classical MIMO schemes and can achieve all of its merits on a grander scale [1]. It mainly uses a large antenna array at a base station (BS) and a few antennas at user equipment (UE) to increase the data rate, link reliability, and coverage and reduce outage in the wireless systems. Additionally, using a sufficiently large number of antennas at BS and UE, the noise and intracell interference can be averaged out [2]. Conventional MIMO decoders are mainly developed using mathematical and information theory concepts that only capture the approximate behavior of the system. This makes it more challenging to perform end-to-end optimization of the communication system in practice and produces sub-optimal performance. These limitations on conventional MIMO decoders motivate researchers to investigate new M-MIMO decoding techniques that give near-optimal solutions, if not optimal, with less complex hardware implementation while faster processing speed. This paper proposes a Massive MIMO decoder using a deep neural network (DNN) that can satisfy the above criteria.

Conclusion

     This paper proposed a DL-based M-MIMO signal decoder DLNet. We have simulated its SER performance, implementation complexity, and decoding time requirement over frequency flat Rayleigh fading and correlated M-MIMO channels. The proposed DLNet is a 15 layers DNN based on the projected gradient descent-based solution of the ML decoder. The proposed DLNet provides near-optimal SER performance without knowing the SNR level and is computationally inexpensive. The training of DLNet was done on the entire channel distribution, which makes it robust and implementable in a system with changing channel values where the receiver perfectly knows the channel state. After doing single-time training, the proposed DLNet decoder can decode signals accurately over various channels. The data obtained from real-world channels and real hardware could be used to train the DLNet, and thus it can be optimized for specific practical M-MIMO environments. Its iterative layering structure enables a flexible complexity-accuracy trade-off required for many modern communication systems.

Abstract

     Modern Machine Learning (ML) techniques offer numerous opportunities to enable intelligent communication designs while addressing a wide range of problems in communication systems. A wide majority of communication systems ubiquitously employ the Maximum Likelihood (MLH) decoder in the symbol decoding process with QPSK modulation, thereby providing a non-reconfigurable solution. This work addresses the application of an ML-based reconfigurable solution for such systems. The proposed decoder can be considered a strong candidate for future communication systems, owing to its upgradable functionality, lower complexity, faster response, and reconfigurability. First, a novel low-complexity dataset for model training/testing is generated, that uses only the received symbols. Subsequently, three predictors are extracted from each of the received noisy symbols for model training/testing. The model is then trained/tested using nineteen standard ML-based classifiers, and the computations of various performance metrics indicate the suitability of Naïve Bayes (NB), and Ensemble Bagged Decision Tree (EBDT) classifiers for the model. The simulation results show that the model respectively delivers significant decoding accuracies and error rates of about 93% and 7% during testing, even for a low SNR of 5 dB. Moreover, the statistical analysis of simulation results shows the marginal superiority of the Gaussian Naïve Bayes (GNB) classifier. Further, the model reconfiguration is validated using a BPSK modulated dataset. Finally, a user-separation scheme that eliminates Successive Interference Cancellation (SIC) in the next-generation Power-Domain (PD) Non-Orthogonal Multiple Access (NOMA) networks is suggested by employing the proposed decoder.

Introduction

     Recently, Artificial Intelligence (AI)/ML techniques are being utilized for various detection-based real-world problems. Applications such as Quadrature Amplitude Modulation (QAM), Spatial Modulation (SM), Generalized Spatial Modulation (GSM), modulation classification, Signal to Noise Power Ratio (SNR) estimation, pulse shaping, Convolutional Neural Network (CNN), and applicability in Long Term Evolution (LTE), Wireless Local Area Network (WLAN), and the next-generation Visible Light Communication (VLC) networks represent their relevancy. AI/ML techniques are significantly helpful in determining the unknown patterns and their influence on the optimizable objective function, so such applications are highly researched in various real-life scenarios. The application of AI in the existing communication systems is still an open area for research, specifically for decoding the received symbols among various modulation schemes. Some ML algorithms are employed for clustering analysis and classification purposes in such AI applications but have not been applied for symbol decoding in the existing communication systems.

     Quadrature Phase-Shift Keying (QPSK) is regarded as a prominent modulation scheme of modern communication systems, that is also being utilized for next-generation communication systems (Tan et al., 2022, Moon et al., 2022), owing to its good trade-off between higher bandwidth utilization and lower error rate. The Fifth-Generation (5G) standards organization, European Telecommunication Standards Institute (ETSI), also mentions the application of the QPSK modulation mapper in the technical specifications of 5G-New-Radio (NR) (Tg, 2018). The QPSK modulation mapper maps a pair of bits  to a modulation symbol in the complex 2-dimensional signal space,

Conclusions

     In this work, the application of an ML-based symbol decoder is proposed as a replacement to the traditional MLH decoder in a QPSK system, where both the decoders have comparable performance, but the former is reconfigurable. Since the model is based on the ML approach rather than the DL approach, it has lower complexity indicating a faster response. The model utilizes only the received symbols to extract all the required predictors. Appropriate low-complexity datasets are also generated utilizing the received symbols. After investigating the performance of nineteen standard ML classifiers, three well-known classifiers, viz: the KNB, the GNB, and the EBDT are found to be appropriate for the proposed system, for both QPSK and BPSK modulations. Additionally, the model shows a high decoding accuracy and low decoding error even for small SNR values. Overall, the test results show the appropriateness of the GNB classifier for the proposed model. The learning property, and the dataset generation mechanism together make the proposed model invariant of channel fading, thereby eliminating the complex channel estimation strategies. Further, the model supports the MIMO configuration and can simultaneously decode PD-NOMA users reducing network latency in next-generation systems where it also solves the problem of SIC.

Abstract

     In this paper, novel hard-decision iterative decoding algorithms for binary Reed-Muller (RM) codes are presented. First, two algorithms are devised based on the majority-logic decoding algorithm with reliability measures of the received sequence. The bit-flipping (BF) and the normalized bit-flipping (NBF) decoding algorithms are hard-decision decoding algorithms. According to the updated hard reliability measures, the BF and NBF algorithms flip one bit of the received hard-decision sequence at a time in each iteration. The NBF decoding algorithm performs better than the BF decoding algorithm by normalizing the reliability measures of the information bits. Moreover, the BF and NBF algorithms are modified to flip multiple bits in one iteration to reduce the average number of iterations. The modified decoding algorithms are called the multiple-bits-flipping (MBF) algorithm and the normalized multiple-bits-flipping (NMBF) algorithm, respectively. The proposed algorithms have low computational complexities and can converge rapidly after a small number of iterations. The simulation results show that the proposed hard-decision decoding algorithms outperform the conventional decoding algorithm.

Introduction

     The Reed-Muller (RM) code is a class of multiple-error-correction codes. In the past, RM codes were used in wireless communications, especially in deep-space communications. RM codes were first discovered by Muller [1] and the conventional decoding scheme of RM code, which is the majority-logic decoding, was proposed by Reed in 1954 [2]. Ever since their discovery, a number of efficient decoding schemes have been constructed. In 1995, Schnabl and Bossert proposed a generation of Reed-Muller codes by multiple concatenations and provided a new decoding procedure using soft-decision information [3]. In 1999, a maximum-likelihood (ML) decoder which uses a distance-preserving map and multiple fast Hadamard transforms (FHTs) was presented by Jones and Wilkinson [4] whereas a maximum a posterior (MAP) decoding algorithm for the first-order RM codes was proposed in [5]. In 2000, a new soft-decision majority-logic decoding algorithm was presented by revising the conventional majority-logic decoding [6]. Besides, the recursive decoding algorithms were provided in [7]–[11]. In 2006, the recursive list decoding was modified by Dumer and Shabunov to approach the performance of ML decoding [9]. Recently, Ye and Abbe proposed the recursive projection-aggregation (RPA) decoding algorithm with lists to have comparable performance with the recursive list decoding [10]. In the same year, the recursive puncturing-aggregation (RXA) algorithm was proposed via replacing the projection by puncturing in RPA [11].

     In recent years, the breakthrough of polar codes [12]–[15] has brought attention back to RM codes due to the similarity of these two codes. The performance comparison between RM codes and polar codes was demonstrated in [10], [15]–[17]. It has been shown that the RM codes with RPA decoding [10] can significantly outperform the polar codes under successive-cancellation list (SCL) decoding [18]–[20]. In addition, by exploiting the idea of decoding polar codes, [21], [22] presented permutation-based decoding methods for RM codes.

Conclusion

     In this paper, we have proposed several hard-decision decoding algorithms for binary RM codes. They are iterative decoding algorithms that have not been proposed in the literature. The performance can be improved by updating the reliability measures and flipping codeword bits. These algorithms do not need large computational complexity since they can converge very rapidly in a small number of iterations. For hard-decision decoding, our proposed NBF decoding algorithm outperforms the conventional majority-logic decoding algorithm with 0.55 dB to 0.8 dB gain. These proposed algorithms have the same complexity orders. Specifically, the BF and MBF decoding algorithms only require integer additions.

     Decoding the RM codes with our iterative decoding algorithms converges very fast with a small number of iterations. Moreover, the proposed MBF/NMBF algorithms can decrease the number of iterations such that the overall complexity can be reduced. The average number of iterations can be reduced by 40% to 80% compared to the BF/NBF algorithms.

Abstract

     Demand for transmission using short block length messages has been increased recently in applications including satellite communication, mobile communication, wireless sensor networks, and machine type communications. Unacceptable performance degradation associated with the short block length Turbo codes restricted its use for applications requiring communication with short block length codewords. A novel performance improved reliability-based decoding algorithm for short block length Turbo codes has been formulated and proposed by the authors. The proposed algorithm has a coding gain of 2.45 dB at a BER of 10−3 over AWGN channel with BPSK modulation for a code rate of 14

. The algorithm has a channel adaptive complexity and has shown nearly 82% reduction in the decoding time complexity for the rate 14

 Turbo code at 3 dB SNR. As an extension of this earlier work, a detailed performance analysis of the algorithm on different Turbo codes has been carried out. A four-state Turbo encoder has been used to bring out the key aspects of the level based algorithm which is driven by reliability as the key parameter. The formulated algorithm has been applied to different Turbo encoder structures namely 3GPP LTE and CCSDS Turbo codes and a detailed analysis has been carried out in this paper. Simulation results show a significant improvement in the error correction performance of short block length Turbo codes. The algorithm also leads to a marked improvement in time complexity at high SNRs. The algorithm is an attractive solution for applications requiring communication with short block lengths.

Introduction

     Achieving optimal error correction capability and computational complexity is one of the major challenges in wireless communication. Turbo codes have shown near Shannon capacity approaching performance for longer codeword lengths [1,2]. Iterative Turbo decoder which uses MAP or its variants like Log-MAP or Max-LogMAP as the constituent decoder performs a fixed number of iterations irrespective of the channel conditions and information block size [3]. The BER performance of Turbo codes flattens in moderate to high SNR regions and the same does not improve even with a large number of iterations. This phenomenon is called as “error floor” [4]. Applications like satellite uplink, real-time communication, machine to machine communication, and mobile communication require transmission with short block length Turbo codes [5,6]. The capacity approaching Turbo codes fail to offer acceptable performance when dealing with short block length codewords due to the high error floor and unacceptable coding gain degradation [7,8]. Dynamic channel conditions introduce varying levels of errors during the transmission. The number of errors introduced also varies according to the channel conditions and hence it is necessary to vary the error correction level accordingly, rather than providing a constant level of error correction at all channel conditions.

Conclusion

     The demand for communication with short data blocks is increasing in recent years. Real-time communication and low latency applications require communication with short block length codewords. Strong channel codes are required to ensure reliable transmission over dynamic channel conditions. The demand for communication with short block Turbo codes is increasing in applications like mobile communication, wireless sensor networks, and satellite communication. In this paper, the performance of the novel reliability-based algorithm has been analyzed for 3GPP LTE, and CCSDS Turbo codes. Simulation results show that the algorithm outperforms the conventional iterative Turbo decoder in terms of BER performance. The time complexity of the performanceenhanced reliability-based Turbo decoder shows a clear advantage as SNR increases. The performance flattening at high SNR region is completely eliminated with the proposed decoding algorithm. This is a clear advantage for applications requiring communications with short block length Turbo codes. The algorithm is an attractive solution to achieve reliable and timely transmission of short block length Turbo codes in mobile and satellite communication applications. The proposed algorithm has a coding gain of 2.45 dB at a BER of 10−3 over AWGN channel with BPSK modulation for a code rate of 1 4 . The algorithm has a channel adaptive complexity and has shown nearly 82% reduction in the decoding time complexity for the rate 1 4 Turbo code at 3 dB SNR. The performance analysis of the level based Turbo decoding algorithm gives an insight into an alternate decoding approach for Turbo codes.

Abstract

     DNA storage is a new digital data storage technology based on specific encoding and decoding methods between 0 and 1 binary codes of digital data and A-T-C-G quaternary codes of DNAs, which and is expected to develop into a major data storage form in the future due to its advantages (such as high data density, long storage time, low energy consumption, convenience for carrying, concealed transportation and multiple encryptions). In this review, we mainly summarize the recent research advances of four main encoding and decoding methods of DNA storage technology: direct mapping method between 0 and 1 binary and A-T-C-G quaternary codes in early-stage, fountain code for higher logical storage density, inner and outer codes for random access DNA storage data, and CRISPR mediated in vivo DNA storage method. The first three encoding/decoding methods belong to in vitro DNA storage, representing the mainstream research and application in DNA storage. Their advantages and disadvantages are also reviewed: direct mapping method is easy and efficient, but has high error rate and low logical density; fountain code can achieve higher storage density without random access; inner and outer code has error-correction design to realize random access at the expense of logic density. This review provides important references and improved understanding of DNA storage methods. Development of efficient and accurate DNA storage encoding and decoding methods will play a very important and even decisive role in the transition of DNA storage from the laboratory to practical application, which may fundamentally change the information industry in the future.

Introduction

     DNA storage technology is a new data storage technology through DNA storage medium, which can achieve digital data storage (text, image, audio, video, etc.) by encoding and decoding for the synthesized DNAs with specific sequences based on certain encoding/decoding methods. Specially, according to certain encoding methods/rules of DNA storage, the 0–1 binary codes encoding for various digital data (text, image, audio, video, etc.) can be converted to corresponding DNA quaternary codes (i.e., combinations of A, T, C, and G), and the corresponding DNAs were then synthesized to store the digital data information into the DNAs with specific sequences. Conversely, based on corresponding decoding methods/rules, the stored DNAs can be sequenced to obtain DNA quaternary codes, further restoring to the digital data with 0–1 binary codes. Here the encoding and decoding methods follow the same “codebook”, and the encoding is the reverse process of the decoding (Fig. 1).

Conclusion

     This paper reviews the research advances of encoding and decoding methods in the field of DNA storage, covering several primary encoding and decoding methods (Table 1): direct mapping between 0–1 binary digital data and A-T-C-G quaternary DNA storage data in the early stages (Church, Blawat, Goldman and Bornholt labs), fountain code (Erlich & Zielinski and Anavy labs), inner and outer codes for random access DNA storage data (Grass and Organick labs), and CRISPR mediated in vivo DNA storage technology (developed by Church et al. 2012).

     Each encoding and decoding method has its advantages and disadvantages. Here, the direct mapping method is easy and efficient but has a high error rate and low logical density. Fountain code made a breakthrough for logical density, reaching up to 80% of the upper limit of theoretical estimation of DNA storage, but it could not achieve random access. Grass’s inner and outer code has an error-correction design (at the chain and data block levels) to realize random access at the expense of logic density. In all, the above three encoding/decoding methods belong to in vitro DNA storage, with the advantage of high-throughput storage and lower cost. CRISPR mediated DNA storage technology belongs to in vivo DNA storage, with the advantage of long-term stable storage and cheaper/random amplification of DNA storage data copies, but it is nowadays in the early exploration stage only for a small amount of data storage due to some insurmountable technical bottlenecks (such as biochemical restrictions in vivo).

1- Introduction

2- Methods

3- Datasets

4- Results

5- Discussion

6- Conclusions

References

Abstract

We introduce two Convolutional Neural Network (CNN) classifiers optimized for inferring brain states from magnetoencephalographic (MEG) measurements. Network design follows a generative model of the electromagnetic (EEG and MEG) brain signals allowing explorative analysis of neural sources informing classification. The proposed networks outperform traditional classifiers as well as more complex neural networks when decoding evoked and induced responses to different stimuli across subjects. Importantly, these models can successfully generalize to new subjects in real-time classification enabling more efficient brain–computer interfaces (BCI).

Introduction

Deep Neural Networks have revolutionized many domains such as image recognition and natural language processing. To date, their application in the analysis of electro- and magnetoencephalographic (EEG and MEG) data has been limited by several domain-specific factors. First of all, electromagnetic brain signals are characterized by very low signal-to-noise ratio (SNR). Here, the term “noise” is understood widely and includes external interference, physiological (e.g. cardiac or oculomotor) artifacts as well as background brain activity unrelated to the studied phenomena. SNR in single-trial EEG and MEG measurements is typically assumed to be < 1 for evoked responses and
1 for oscillatory activity, which puts these data to stark contrast with those in traditional applications of deep learning. Typical EEG/MEG analysis employs a wide range of techniques to increase the SNR, e.g. spatial and temporal filtering, averaging a large number of observations, sourceseparation algorithms, and other complex feature extraction methods (e.g. wavelet transform). Thus, efficient noise suppression is required for high-accuracy classification of EEG/MEG signals. Second, these data have a complex, high-dimensional spatiotemporal structure. Modern EEG and MEG systems comprise several hundreds of sensors capable of sampling brain activity with sub-millisecond temporal resolution. In the case of MEG, these sensors may also measure different components of the neuromagnetic field. On one hand, this multitude of data points enables sophisticated analysis methods to extract finer details of brain function. On the other hand, manual analysis and interpretation of these data become increasingly complex and time-consuming. Machine-learning algorithms can be of great help in such tasks but the mere classification result is often not sufficient; ideally, the experimenter should understand why the algorithm is able to classify the data, i.e., the learned model should be interpretable in neurophysiological terms. A model able to reliably identify those neural sources that contribute to the discrimination between given experimental conditions could enable efficient exploitative analysis of these complex data sets and ultimately allow more complex experimental designs. Finally, deep-learning models require large numbers of training samples to perform optimally. In a typical EEG/MEG or BCI experiment, however, time constraints and data acquisition costs limit the sample sizes severely. Open datasets usually comprise data from a large number of individuals, providing a promising strategy to overcome this limitation, but in this case, the classifier needs to be robust to high interindividual variability stemming from differences in cortical anatomy, mappings of function to structure and physiological state. Taken together, these factors may easily lead to over-fitting (especially in more complex models) and poor interpretability of the findings. To address these challenges, we propose a Convolutional Neural Network (CNN) whose architecture is based on a generative model of non-invasive electromagnetic measurements of the brain activity (Daunizeau and Friston, 2007).

Arikan in his paper [1], proposed a new channel coding scheme by “polarizing” channels w.r.t. their capacities. The process of channel polarization helps to classify every bit channel w.r.t. channel capacity which is used to create a scheme of encoding information bits into a codeword. This form of classification provides a new family of linear block codes called Polar Codes. BICM-ID is a state-of-the-art error correcting scheme. The coded-modulation scheme was proposed in [2] for improving error correction capabilities by using channel coding and modulation schemes as a combined unit instead of independent modules. Adding diversity to the codes by interleaving, should improve the error correction performance as proposed in [3], to hence provide the Bit Interleaved Coded Modulation (BICM) design described in [4]. BICM’s demerits can be overcome by exchanging extrinsic information between multiple modules of the Iterative Decoding (ID) chain iteratively, to improve error correcting capability over every iteration [5]. Such a BICM-ID scheme is helpful for error correction of codes received over AWGN and Fading channels. The idea is to encode the input data bits into codewords generated by polar encoding, interleaving and then modulating them at the transmitter end. Similarly, at the receiver end polar decoder, demodulator, interleaver and de-interleaver iteratively perform their tasks and exchange extrinsic information to produce codeword estimates. The aim in this paper is to develop such a novel BIPCM-ID system and analyze its error correcting capability. Although Arikan’s original idea of channel polarization is limited only to Binary Erasure Channels (BEC) the BIPCM-ID needs to be analyzed over AWGN channels. Thus, a modified approach of channel polarization for AWGN channels is used. The polar decoder which is to be integrated in an ID chain should be a Soft-Input Soft-Output (SISO) decoder so that it can produce extrinsic information to be exchanged with, as well as process the inputs from, the other modules in the ID chain. Modifications can also be made to remove the error floor altogether. These issues have been addressed in this paper. The rest of the paper is organized as follows. In Section II, an overview of Polar Codes and BICM-ID is provided for the reader to get a basic understanding of these concepts. Section III describes the novel approach of integrating Polar Codes in a BICM-ID design by generating the extrinsic information from the decoder module to be used for ID and how the channels are polarized for a AWGN channel. Section IV, provides the simulation results of the BIPCM-ID system, with detailed discussions about the parameters used and the corresponding performance results obtained. Section V provides the key points which merit further research and the existing limitations which can be improved upon. The concluding remarks are mentioned in Section VI. Notations: Letters in bold fonts denote vectors. X and Y denote the Random Variables (RV) corresponding to the input and output of a channel respectively. W denotes a channel as well as the Probability Density Functions (PDF) of the RVs across the channel. N denotes the length of a codeword. Z denotes the Bhattacharyya parameter. L denotes the LogLikelihood Ratio (LLR) values.

A. Related Work: BMI

It has been reported clinically that, diseases like stroke and traumatic brain injury do cause long-term, unilateral loss of motor control. Neurological disabilities and related diseases are causing the permanent loss of motoring of limbs, in addition to sensory malfunction. In particular, even in specific and related cases, limbs disability is very severe that it is not likely to feed oneself or even communicate. With the advances on technology, and in specific – BMI – Brain Machine Interface, there is a new research direction that aims to support disabled patients by translating neural signals from the brain into useful control signals for guiding prosthetic limbs. The prime objective in developing a neural prosthesis is to substitute neural circuitry in the brain, that no longer functions correctly or efficiently, Fig.1. While achieving such goal, this requires artificial reconstruction of neuron-to neuron connections in a way that can be recognized by the remaining normal circuitry, and that promotes appropriate interaction. It is estimated that approximately (9 million) people worldwide suffer from stroke every year and that almost (30%) of stroke survivors suffering from irreversible motor impairments, Teo et al. [2]. According to Andrew et al. [3], brain-controlled interfaces are devices that capture brain transmissions involved in a subject’s intention to act. Neural activated prosthetic devices is becoming an important domain, and progressively relevant to a number of clinical and various neurological related diseases treatments. Fig. 1. Electroencephalogram (EEG) brain waves have been used extensively for people with disabilities, [1]. In particular, we refer to Fayad and Elmiyeh, [4], where it was mentioned about such input devices for stimulating zones within the nervous system, in particular, have been especially successful in achieving therapeutic effects. Charles et al. [5] also reviewed the challenges to clinical translation and discusses potential solutions. They made a focuses on hardware reliability, state-of-the-art decoding algorithms, and surgical considerations during implantation.