In this paper, we develop a new approach for rank analysis of parity-check matrices for quasi-cyclic low-density parity-check codes based on the associated polynomials of circulant matrices, applicable to general finite fields and arbitrary circulant sizes. Some formulas on the rank for parity-check matrices with one, two, and three row-blocks are first derived. For the general case with arbitrary numbers of row-blocks, lower and upper bounds on the rank are presented, and these bounds can be combined to give the exact rank result under certain conditions. We also investigate the effect on the rank by changing the circulant size. Furthermore, we study the relations between the rank of the masked matrix and that of the masking matrix, which can be used to predict the rank of the parity-check matrix after masking. The obtained rank analysis results are then applied to several classes of existing algebraically constructed parity-check matrices, along with their masked matrices. Finally, we demonstrate how rank analysis can be used in the code design procedure.

Small fiber neuropathy analysis in the epidermis of the skin is critical to the diagnosis of various diseases such as diabetes mellitus and familial amyloid polyneuropathy. Intraepidermal nerve fiber examination plays an important role to serve as a highly sensitive indicator of sensory nerve fiber damage. Segmentation of the epidermis region is a prior image processing task for subsequent image analysis. Due to the lack of suitable and available tools for this specific task, this paper investigates an automatic epidermis segmentation framework in skin fluorescence images. To maintain the high resolution and increase the image amount, the original image is decomposed into a series of sub-images for model input. A U-shaped network structure consisting of five block layers with different depths is proposed for epidermis segmentation. Each model block is designed in a multi-scale manner, which is composed of two different convolution kernel pipelines. By combining and sharing the information from these model blocks with skip connections between them, we can effectively increase the diversity of the feature maps for more accurate segmentation. Experiments on in-house epidermis images demonstrated the advantages of the proposed epidermis segmentation network, which outperformed many state-of-the-art deep learning-based segmentation models. The proposed network architecture is potential in facilitating the epidermis segmentation task for further small fiber neuropathy research.

Belief propagation (BP) decoding of polar codes, which can be executed in parallel, is suitable for low-latency applications. In this paper, we first give a sparse parity-check matrix representation for polar codes, based on which several strategies for performance improvement are proposed. We then devise a scheme of which the performance can approach the maximum-likelihood lower bound and that of successive cancellation list (SCL) decoding. For cyclic redundancy check (CRC)-concatenated polar codes, a parity-check matrix representation is also presented so that joint decoding between the CRC code and polar code is possible. An improved CRC-aided BP decoder is hence proposed with performance close to that of the state-of-the-art CRC-aided SCL decoder.

In this paper, the hybrid beamforming design for multiple-input multiple-output orthogonal frequency-division multiplexing systems is studied over the indoor millimeter wave (mm-wave) channels. Under practical hybrid beamforming constraints for multi-carrier systems and the study of sub-systems, we propose the sub-system SVD (SS) hybrid beamforming design. To alleviate the complexity problem of channel estimation, reduction of the amount of the required channel state information (CSI) is also studied based on the statistical properties of indoor mm-wave channels. The SS hybrid beamforming algorithm is then extended to the limited feedback SS (LSS) scheme in which the transmit beamformers are designed based on limited information fed back from the receiver. A fast codeword selection algorithm is also developed to reduce the search complexity of the LSS algorithm. The simulation results show that our SS algorithm achieves the performance level of traditional full-digital beamforming with low complexity and the LSS algorithm has better performance and lower complexity than the previous algorithm, even if the amount of CSI is greatly reduced.

Quasi-cyclic low-density parity-check (QC-LDPC) codes are an important class of LDPC codes which can be encoded and decoded with low complexity and suitable for many applications. As the code dimension, which describes the number of protected information bits, is equal to the code length minus the rank of the parity-check matrix and the parity-check matrix for QC-LDPC codes is usually not full-rank, determining the rank of the parity-check matrix is of essential importance. In this paper, we study the rank of the parity-check matrix for QC-LDPC codes based on the associated polynomials for circulant matrices. A formula for the rank of the parity-check matrix with only one row-block is first derived. We then extend the result to matrices with two, three, or more row-blocks. Some bounds are also presented for matrices with arbitrary numbers of row-blocks. Furthermore, the exact rank is determined for a class of algebraically constructed parity-check matrices.

In this paper, hybrid beamforming design for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems is studied over the indoor millimeter wave (mmWave) channels. Under practical hybrid beamforming constraints for multicarrier systems, we propose the sub-system SVD hybrid beamforming design which provides good performance with low complexity. Moreover, we reduce the amount of the required channel state information (CSI) in our design based on the statistical properties of indoor mmWave channels. Simulation results show that our design achieves the performance of traditional full-digital beamforming even if the amount of CSI is greatly reduced.

In this paper, the algebraic constructions of quasi-cyclic low-density parity-check (QC-LDPC) codes with the unequal error protection (UEP) property are considered. A criterion for constructing such codes via the masking technique is proposed, based on which explicit conditions on the base parity-check matrices and masking matrices to achieve UEP are provided. We also give three specific constructions of UEP QC-LDPC codes. Furthermore, a sufficient condition to ensure strict UEP is presented. Simulation results demonstrate the superiority of our constructed codes over time-sharing schemes. The constructed codes also have competitive error performance against randomly constructed equal-error-protection LDPC codes and irregular UEP LDPC codes designed based on the degree distribution.

In this paper, the signal-to-interference-plus-noise ratio (SINR) analysis of orthogonal frequency-division multiplexing (OFDM) systems over the IEEE 802.15.3c 60 GHz channel models is investigated. The derivation precisely captures the distinctive path clustering phenomenon in the spatial-temporal domain and provides the exact SINR. Based on the analytical results, a universal rule for adapting the near-optimal half-power beamwidth is identified. Moreover, numerical results are provided to verify the analytical findings.

The advantage of using channel feedback information to determine the optimal pilot placement is examined for amplify-and-forward OFDM relay links. This work extends upon the previously proposed feedback-aided pilot placement scheme to systems that employ subcarrier pairing at the relay. With channel feedback, the pilot subcarriers can be properly chosen to reduce the channel estimation error and increase the effective signal-to-noise ratio (SNR) of data subcarriers. When subcarrier pairing is employed, the relay reselects the subcarriers used to forward the source's data based on the effective SNR of each subcarrier, which in order is affected by the pilot placement policy. Here, the minimum effective SNR observed by all subcarriers' data is utilized as the performance measure since it is what dominates the symbol-error-rate (SER) at high SNR. For a given pilot placement, the best subcarrier pairing scheme is found to be the inverse mapping of the source-to-relay (SR) and relay-to-destination (RD) channels based on the quality of their effective SNR. A lower bound is derived for the gain achievable with any feedback-aided pilot placement scheme. Due to the complexity of finding the optimal pilot placement, a more efficient iterative pilot relocation (IPR) scheme is then proposed. In this scheme, the subcarrier with the worst equivalent channel is used to replace one of the originally selected pilot locations in each iteration. The efficacy of the proposed policy is demonstrated through numerical simulations.

In this paper, a new construction of quasi-cyclic low-density parity-check (QC-LDPC) codes for unequal error protection (UEP) is proposed. We first give a new class of UEP block codes. QC-LDPC codes with binomial-term parity-check matrices which can avoid girths less than 8 and achieve an enlarged upper bound on the minimum distance are also introduced. An effective UEP scheme based on the proposed UEP block codes and QC-LDPC codes which can provide flexible choice of protection levels is then presented. Simulation results show that the new QC-LDPC codes can achieve good performance and low error floors. The bits with different designed protection levels can indeed have unequal bit-error-rate performance.

This paper presents a novel low-complexity iterative reliability-based decoding algorithm for LDPC codes over q-ary finite fields. This proposed algorithm has low complexity and hence provides an effective trade-off between error performance and decoding complexity compared to q-ary sum product algorithm. This decoding algorithm is devised based on simple orthogonal concept of one-step majority-logic decoding for q-ary linear block codes. It requires only integer and finite field operations and converges very fast in decoding. It is particularly effective for decoding LDPC codes constructed based on finite geometries and finite fields.

Subcarrier allocation, power allocation, and partner selection algorithms are examined for amplify-and-forward cooperative multicarrier systems. Consider a network that consists of multiple cooperative pairs employing a two-phase cooperation scheme where the users first transmit their own messages on each of their subcarriers in Phase I and either retransmit their own messages or relay the messages of their partners in Phase II, i.e., the cooperative phase. In general, subcarrier allocation and partner selection problems are known to be intractable for systems with large number of users and subcarriers. In this work, we propose a mathematically tractable approach to address these issues and show its effectiveness compared to existing algorithms. Specifically, we consider a relaxed problem formulation, where each subcarrier is able to retransmit or relay for all other subcarriers in Phase II over orthogonal channels, and derive the optimal power allocation for this scenario. Efficient subcarrier allocation policies can then be derived based on the power allocation result and a sufficient condition is obtained to determine when cooperation is helpful among two users. A partner selection algorithm is then devised based on the sufficient condition. Given the subcarrier allocation scheme, the optimal power allocation among subcarriers in the cooperative phase can be shown to be a convex optimization problem and, thus, can be solved efficiently using standard convex optimization tools. The efficacy of the proposed algorithms is demonstrated through numerical simulations.

In this paper, a new construction of irregular low-density parity-check convolutional codes (LDPC-CCs) is presented. Both upper and lower bounds on the free distance are derived as well. Compared with previously constructed irregular LDPC-CCs, our design can not only avoid a girth less than 8 but also provide an enlarged free distance. Since some undesired cycles occur due to the binomial terms in the parity-check matrices of general LDPC-CCs, we provide a specific procedure to remove this kind of length-8 cycles. It can also be applied to our irregular construction. Simulation results show that the codes based on the new construction and the cycle-removal procedure can achieve better bit-error-rate performance and a lower error-floor.

Due to the large signal bandwidth of an ultra-wideband (UWB) transmitted reference (TR) system, the clustering channel statistics, as defined in the IEEE 802.15.3a channel models, should be taken into account in performance characterization. In this paper, we address the optimal mean channel energy capture for the maximal signal-to-interference-plus-noise ratio (SINR) regarding the special UWB channel statistics. It is analytically shown that a simple receiver that captures a fixed ratio of the mean channel energy can perform quite well, which is valid universally for non-line-of-sight channels and a generic class of TR systems. For line-of-sight channels, it is noticed that optimal SINR may be achieved at an integration time approaching zero, revealing a new interesting phenomenon. The channel conditions under which the phenomenon tends to happen are also provided. Furthermore, we characterize the channel conditions suitable for different TR systems.

This paper presents two low-complexity reliability-based message-passing algorithms for decoding LDPC codes over non-binary finite fields. These two decoding algorithms require only finite field and integer operations and they provide effective trade-off between error performance and decoding complexity compared to the non-binary sum product algorithm. They are particularly effective for decoding LDPC codes constructed based on finite geometries and finite fields.

In this paper, convolutional codes are studied for unequal error protection (UEP) from an algebraic theoretical viewpoint. We first show that for every convolutional code there exists at least one optimal generator matrix with respect to UEP. The UEP optimality of convolutional encoders is then combined with several algebraic properties, e.g., systematic, basic, canonical, and minimal, to establish the fundamentals of convolutional codes for UEP. In addition, a generic lower bound on the length of a UEP convolutional code is proposed. Good UEP codes with their lengths equal to the derived lower bound are obtained by computer search.

Establishing a radio link in cell-based mobile communication systems involves searching and synchronizing the downlink known pattern of sequences associated with the base stations. The performance of the searching process, often referred to as cell search, depends greatly on the employed preamble sequences. In this paper, we propose a construction of quasi complete complementary codes (QCCCs) from Reed-Muller codes and, due to their good auto-correlation and cross-correlation properties, a preamble structure based on QCCCs. Furthermore, the constructed QCCCs have low peak-to-average power ratios (PAPRs) and hence are suitable for use in orthogonal frequency division multiplexing (OFDM) systems. Simulation results show that the QCCC-based preambles outperform the preambles employed in the WiMAX system, both in terms of PAPR and cell search performance. Moreover, the rich algebraic structures of QCCCs potentially admit low-complexity encoding and decoding.

Ultra-wideband (UWB) communications exhibit many unique characteristics, one of which is the random clustering phenomenon in the resolved channel multipaths. The randomness in path arrivals will, however, make exact performance analysis quite challenging. In this paper, an analytical framework for precise performance characterization of communications over the generic IEEE 802.15.4a channel structure is developed. The key idea is to capture the average effect of the cluster and ray arrival processes through the extended density functions, which can then be shown to be useful in deriving various channel statistical quantities of interests, e.g., the channel second-order and fourth-order cross moments. Applications of obtaining the average tap energy as well as the amount of fading for IEEE 802.15.4a channel models are demonstrated. Agreements between the analytical and simulation results hence verify the value of the established framework.

In this paper, canonical convolutional encoders are studied for unequal error protection (UEP) from an algebraic theoretical viewpoint. We show that for any convolutional code there exists at least a canonical generator matrix which has the greatest separation vector, and hence the optimal UEP capability, among all canonical ones. A procedure for obtaining such desirable generator matrices is also proposed.

In this paper, we propose a new construction of (3, t)-regular low-density parity-check convolutional codes by properly including binomial entries in the parity-check matrices. Both of the upper and lower bounds on free distance are derived for the new codes. Compared with previous constructions, our design can not only avoid codes of girth less than 8 but also provide enlarged free distances for some code rates. Simulation results show that the codes based on the new construction can achieve better bit-error-rate performance and lower error floor.

One of the unique characteristics of ultra-wideband channels is the clustering phenomenon resolved by the ultra-wide signal bandwidth. Channel structures extended from the Saleh-Valenzuela model, e.g., the IEEE 802.15.3a and IEEE 802.15.4a models, have been proposed to describe such phenomenon. It is, however, noticed that a clear and systematic procedure to estimate the model parameters is still missing. Based on the recently developed analytical results, a new estimation approach is proposed in the paper to resolve the inconvenience and ambiguity in previous methods. The key step is to match the statistical profiles of interests by formulating an optimization problem with an explicit analytical objective function that can be systematically solved. Numerical tests have also been conducted to demonstrate the effectiveness of the proposed method.

In this paper, exact signal-to-interference-plus-noise ratio (SINR) analysis of direct-sequence ultra-wideband (UWB) systems with rake receiving in the presence of inter-symbol interference and multiple-access interference over realistic UWB channel models is conducted. The SINR expression, considering the code correlation functions and a generic rake receiver with variable number of combining fingers, is first derived. The statistics of the UWB channel models, defined by the IEEE 802.15.3a Task Group, are then taken into account. Because of the high multipath resolution offered by UWB signals, the UWB channel exhibits a unique path-arriving phenomenon, which can, however, complicate the analysis. Nevertheless, by exploiting the property of Poisson path arrivals, the exact average SINR is obtained in this paper. The analytical results well match computer simulations and can readily be applied to the performance evaluation or system optimization over realistic channel and interference models.

In this paper, we investigate a novel coding idea proposed previously to enable under-sampled receivers. An under-sampled receiver can sample the received baseband signals at only a fraction of the Nyquist rate and turns out to be an effective solution to the bottleneck of high-rate sampling and processing in ultra-wideband (UWB) communications. The spectrum aliasing problem can be solved by an analogy between an under-sampled system and a multiple-antenna one. However, underlying differences between the two systems exist and motivate the study of the fundamental limits of a coded under-sampled system. The study is carried out by characterizing the optimal coding structures with and without channel state information at transmitter (CSIT). A practical selective coding structure is also developed to provide satisfactory performance with reduced CSIT requirement. Finally, simulations are conducted to verify the theoretical characterization. Our results indicate that an under-sampled UWB system can benefit from power-saving, cost reduction, and full multipath diversity at the expanse of little or confined performance degradation

Orthogonal frequency division multiplexing (OFDM) has been proposed for use as the physical layer of ultra-wideband (UWB) systems for high-rate, short-range personal area networking (PAN). For ultra-wideband systems, there is a constraint on the maximum power spectral density for the transmitted signal. Therefore, the bandwidth of the transmitted spectrum must be spread widely by a bandwidth expansion scheme so that the transmitted power spectral density can be kept as low as possible. In this paper, frequency expansion of the UWB system is achieved by using a simple frequency-diversity coding scheme. A major issue for the frequency-diversity coding scheme is that the receiver must sample the baseband received signal using high-sampling-rate analog-to-digital converters (ADCs) for discrete signal processing (DSP). However, such high-sampling-rate ADCs and DSP are expensive and have high power consumption. One advantage of the proposed frequency-diversity coding scheme is that the sampling rate of the baseband ADCs and DSP can be less then the Nyquist rate. The aliasing phenomenon occurs due to the reduced sampling rate, yet it, however, appears as transmission diversity to the receiver. The performance of the frequency-diversity coded OFDM system with an under-sampling-rate receiver is analyzed by evaluating the pairwise error probability. From the analysis of the pairwise error probability, design criteria for the frequency-diversity coded OFDM are obtained. A practical construction of frequency-diversity codes is proposed based on linear block codes. Simulation and analytical results for frequency-diversity coded OFDM systems are presented. The results show that a significant diversity/coding gain can be achieved with the under-sampling-rate receiver.

In this paper, a general reliability-updating formula is proposed for trellis-based soft-output decoding algorithms to optimize the tradeoff between performance and complexity. Based on the general formula, new algorithms are presented, and a concise interpretation is provided to relate new proposed algorithms and those reported previously. In addition, we devise a unified decoding structure with respect to the general formula. All trellis-based algorithms are mapped into a single decoding process under the unified structure, and different algorithms can be easily switched between one another. Owing to the modularity and flexibility, this unified structure is especially suitable for turbo decoders with programmable implementation.

Path pruning, a new coding concept to achieve free distance enlargement for convolutional codes, is proposed. Through path pruning, every convolutional code can be used for unequal error protection (UEP), no matter whether it is originally a UEP code. To avoid undesired path discontinuity and reduce possible path distance loss, a cascaded implementation together with a path-compatible criterion is proposed, under which path-compatible pruned convolutional (PCPC) codes are constructed. Necessary and sufficient conditions are also derived for a subclass of PCPC codes whose decoding can be done by a single decoder for the parent code. Finally, some PCPC codes with good UEP capabilities found by computer search are given.

This paper proposes new multiuser detectors for frequency-hopped spread spectrum multiple-access (FH-SSMA) based on binary frequency shift keying (BFSK) modulation and channelized frequency hopping. With knowledge of hopping sequences and envelopes of active users, the proposed scheme is a sub-optimal detector under maximum likelihood test. Diversity combining is employed as an anti-multiple-access interference technique which improves the performance significantly. In slow frequency-hopped systems, we demonstrate that the proposed multiuser detector combined with diversity is robust to multiple-access interference. In fast frequency-hopped systems with heavy load of multiple-access, the detector can afford more simultaneous users than the multiuser detector with M-ary frequency shift keying (MFSK) modulation.

We investigate the connection admission control problem in mobile personal communications networks. In contrast to other studies on this aspect which either focused on only single-class call connections or ignored user mobility, our study directly addresses the connection admission control for multiple-class calls with user mobility. A generic class of coordinate-convex admission control policies is considered. An efficient numerical method is proposed to derive the connection-level quality of service (QoS) and is verified with computer simulation results. The proposed analysis may be employed in a network design tool for studying the admission control policy and selecting system parameters to satisfy the required connection-level QoS.

In this paper, we investigate the connection admission control problem in mobile personal communications networks. Since user mobility and multimedia traffic are important factors in personal communications networks, in contrast to other studies on this aspect which either focused on only single-class call connections or ignored user mobility, our study directly addresses the connection admission control for multiple-class calls with user mobility. A generic class of coordinate-convex admission control policies is considered. An efficient numerical method is proposed to derive the connection-level quality of service (QoS), and is verified with computer simulation results. The results obtained show that, besides offered load, user mobility can have a great impact on the connection-level QoS. The proposed analysis may be employed in a network design tool for studying the admission control policy and for selecting system parameters to satisfy the required connection-level QoS.

The performance of synchronous spread-spectrum multiple-access (SSMA) communications based on direct-sequence (DS), slow frequency-hopped (SFH), and fast frequency-hopped (FFH) systems for wireless local communications of micro-cellular personal communications is analyzed. Using an indoor multipath fading channel model with clusters of arriving rays, we investigate multiuser DS systems with RAKE and diversity reception by selection combining (SC), multiuser SFH systems with equal-gain (EG) diversity reception, and multiuser FFH systems with correlated EG and self-normalization (SN) combining techniques. Reed-Solomon codes are considered to further improve the system performance. Given a fixed available bandwidth with narrow band interference (NBI), capacities and packet error rates are determined under various system configurations. Total capacities of hybrid frequency-division multiple-access (FDMA)/SSMA (DS and SFH) systems are compared with those of wide-band SSMA systems. For high data rate communications, wide-band DS-SSMA systems have larger capacities than hybrid FDMA/DS-SSMA systems. For low data rate communications, a capacity comparison between wide-band DS-SSMA and hybrid FDMA/DS-SSMA systems depends on fading statistics. Hybrid FDMA/SFH-SSMA systems have larger capacities than wide-band DS-SSMA systems, FFH-SSMA systems could not provide satisfactory performance due to correlation among hopping bands.

The generalized Hamming weights introduced by Wei (1991) have been shown to be fundamental descriptive parameters of a linear block code. They have been found to be useful in certain cryptographic applications and in the studies of minimal trellis diagrams of linear block codes. In this correspondence, we determine the first few and the last few generalized Hamming weights of binary primitive BCH codes with minimum distance one less than a power of two, of their extensions, and of the duals of both.

Coexisting analog frequency modulation (FM) based on frequency division multiple access (FDMA) and narrow-band code division multiple access (N-CDMA) in adjacent spectrum is studied. The allocation on different spectrum can avoid the serious performance degradation as transitioning from fully loaded analog FM/FDMA to N-CDMA. The guard-band needed between the adjacent spectrum to maintain acceptable performance degradation is derived and evaluated. Numerical results indicate that at least a 255 kHz bandwidth to separate the two systems is necessary. The worst case of the interference from FDMA degrades the performance of N-CDMA, even under appropriate guard-band separation. This study demonstrates the capacity reduction of N-CDMA as coexisting analog FM/FDMA in adjacent spectrum.

The method of the hidden Markov model (HMM) is used to develop a faithful model for the burst error statistics of Viterbi decoding of convolutional codes. One of the advantages of building such a model is that it can be used to generate the output sequence with little cost and can provide a basis for studying other system parameters. The HMM developed generally performs better than the geometric model and, in most cases, better than the previously proposed Markov model, and it requires much fewer parameters than those of the Markov model for convolutional codes of large constraint length.

We consider a practical maximum-likelihood sequence estimation (MLSE) equalizer on multipath fading channels in conjunction with an adaptive channel estimator consisting of a least mean square (LMS) estimator and a linear channel predictor, instead of assuming perfect channel estimates. A new LMS estimator model is proposed which can accurately characterize the statistical behavior of the LMS estimator over multipath fading channels. Based on this model, a new upper-bound on block error rate is derived under the consideration of imperfect channel estimates. Computer simulations verify that our analytical results can correctly predict the real system performance and are applicable over a wide range of the step size parameter of the LMS estimator.

In the literature the performance of joint maximum-likelihood sequence estimation for trellis-coded modulation systems was analyzed under the assumption that fading is so slow that the channel does not change during all error events. In this paper we extend the performance analysis to general fading processes by considering the correlation function of the time-variant channel impulse response instead of assuming constant fading. An easily evaluated closed-form upper bound is derived for the pairwise error probability. The bit error rate is then estimated by using a truncated union bound. Computer simulations show that our analytical results are good for all cases considered especially when diversity reception is used.>

Commentson a paper by Rouanne and Costello Jr. (IEEE Trans. Inform. Theory, vol.34, p.1011-20, 1988). It is shown that the derivation in the above paper is incorrect and hence the lower bound obtained is not valid for general trellis-coded modulation schemes. A corrected bound is presented to remedy this flaw. Also shown is a similar lower bound derived from the average distance structure. Both bounds have similar asymptotic behavior and are linear in the constraint length. Unfortunately, they are bad and not very useful for short and medium constraint lengths. The present author points out that there is still much room for further research in finding a good lower bound on the maximal minimum distance for trellis-coded modulation schemes.>

The performance of general binary block codes on an unquantized additive white Gaussian noise (AWGN) channel at low signal-to-noise ratios is considered. Expressions are derived for both the block error and the bit error probabilities near the point where the bit signal-to-noise ratio is zero. These expressions depend on the global geometric structure of the code, although the minimum distance still seems to play a crucial role. Examples of codes such as orthogonal codes, biorthogonal codes, the (24,12) extended Golay code, and the (15,6) expurgated BCH code are discussed. The asymptotic coding gain at low signal-to-noise ratios is also studied.>