We study irregular repetition slotted ALOHA (IRSA) with multi-antenna reception over Rayleigh block fading channels. An exact closed-form expression for the average decoding error probability ¯ϵm,L is derived for collision sizes m = 1 and m = 2 by applying the inclusion–exclusion principle, which generalizes known single-antenna results and remains valid for any finite number of antennas. Using this result, we develop a density-evolution-based analysis of multi-antenna IR-SA systems and characterize belief-propagation (BP) thresholds. Numerical results for the corresponding maximum a posteriori (MAP) decoding thresholds and converse bounds are also presented, demonstrating threshold saturation with spatial coupling.

This paper explores the optimization of transmission probability and code rate in multi-device slotted ALOHA systems employing successive interference cancellation (SIC) and feedback over Nakagami- m fading channels. Although previous research has derived the optimal probability and the code rate to maximize the sum rate in a two-device scenario analytically using Markov process, its extension to configurations with more than two devices remains challenging. The complexity of Markov modeling arises from two main challenges: 1) an increase in the number of devices greatly expands the state space, precluding the analytical determination of system throughput; 2) deriving transition probabilities in the Nakagami- m channel model is difficult. In this study, we use computer simulations to evaluate the sum rate and to search for the optimal transmission probability and code rate to maximize the sum rate of the systems. Our simulation findings reveal that at an average SNR the optimal code rate is independent of the number of devices and transmission probability. In a 30-device slotted ALOHA system with an SNR of 15 dB, the maximum sum rate of 2.9235 is almost achieved at a transmission probability of 0.0665 and an optimal code rate of approximately 4.02, regardless of the number of devices.

We examine a neural network-based system designed to identify$K$devices, each with device-specific I/Q imbalances in the RF modulator, as they transmit signals to an access point using time-division multiple access. Traditional methods begin training with randomly chosen initial parameters and need numerous pilot symbols, which can be impractical in scenarios such as when a unmanned aerial vehicle (UAV) serves as the access point, collecting data from massive device sensor networks. In this work, we focus on adaptive learning with minimal pilot symbols to train the neural network to classify devices by their I/Q imbalances. Reptile is an efficient meta-learning algorithm designed to help models rapidly adjust to new tasks with minimal training data. By employing Reptile, we pre-train neural network model parameters offline, facilitating rapid online adaptation and fine-tuning for effective identification of new devices. Simulations indicate that Reptile surpasses conventional methods in device identification with fewer pilot symbols.

In wireless communication systems, the presence of inter-symbol interference (ISI), resulting from multipath propagation and channel memory, poses a significant challenge to reliable symbol detection and message recovery. A blind estimation of the ISI channel with a memory length-$L$is proposed. In the receiver, the iterative$K$-means clustering algorithm is used for this blind channel estimation process and a cyclic redundancy check (CRC) is employed to ultimately validate the recovered message. The algorithm produces$K^{L}$potential sets of channel taps as a consequence of channel phase uncertainties caused by phase rotation. Subsequently, these are reduced to$K$sets using the squared error comparison between the received and the reconstructed symbols. The transmitted message is subsequently obtained using these$K$candidate channel tap sets through Viterbi demodulation, channel decoding, and verification of CRC. The simulation results show that for the ISI channel with a dominant line-of-sight component, the block error rate of the proposed approach is close to that of a perfectly known channel, yet it nearly aligns with the performance of the conventional MMSE estimator utilizing a few pilot symbols.

Throughput analysis for successive interference cancellation-based two-device slotted ALOHA with feedback is studied over Nakagami-m fading channels. Explicit expressions for the state transition probabilities are derived for a Markov process, thus facilitating the computation of the throughput. Through optimization of the transmission probability, it is shown that the maximum throughput is achieved for a given code rate.

In this work, we develop a pair of rate-diverse encoder and decoder for a two-user Gaussian multiple access channel (GMAC). The proposed scheme enables the users to transmit with the same codeword length but different coding rates under diverse user channel conditions. First, we propose the row-combining (RC) method and row-extending (RE) method to design practical low-density parity-check (LDPC) channel codes for rate-diverse GMAC. Second, we develop an iterative rate-diverse joint user messages decoding (RDJD) algorithm for GMAC, where all user messages are decoded with a single parity-check matrix. In contrast to the conventional network-coded multiple access (NCMA) and compute-forward multiple access (CFMA) schemes that first recover a linear combination of the transmitted codewords and then decode both user messages, this work can decode both the user messages simultaneously. Extrinsic information transfer (EXIT) chart analysis and simulation results indicate that RDJD can achieve gains up to 1.0 dB over NCMA and CFMA in the two-user GMAC. In particular, we show that there exists an optimal rate allocation for the two users to achieve the best decoding performance given the channel conditions and sum rate.

Random access systems are potential for Internet of Things in the future wireless communication network for its operational simplicity. Irregular repetition slotted ALOHA (IRSA) system is one of the high-efficiency random access systems. In this paper, performance analysis of the irregular repetition slotted ALOHA systems with short-packet, i.e. finite-blocklength, transmission for the quasi-static Rayleigh fading channel is given. A cumulative distribution function of signal-to-interference power ratio (SIR) is derived and thus a closed-form expression of an average packet error probability (PEP) at the SIR with short packets for the Rayleigh fading channel is given. The closed-form expression makes it possible to optimize the degree distributions at a specific blocklength in the sense that the systems give the maximum system load.

Owing to the effect of data retention noise in multi-level-cell NAND flash memory, the initial threshold-voltage distributions and read voltages can no longer be used to accurately calculate log-likelihood ratios (LLRs) as the retention time increases, thus causing retention errors. To solve this problem, we first utilize the so-called “correction factors” to optimize the LLR accuracy by maximizing the achievable rate of a flash-memory system without introducing extra memory-sensing operations. We further prove that the optimization of the correction factors is a convex optimization problem and can be solved analytically. To obtain the optimal correction factors, we propose two retention-error correction schemes, referred to as offline maximum-achievable-rate correction (MARC) algorithm and online MARC algorithm, which enable the flash-memory controller to utilize the corrected LLRs that are stored in a look-up table and correct the inaccurate LLRs in real time, respectively. Motivated by the variation characteristics of the threshold-voltage distributions, we also propose an enhanced expectation–maximization (EM) algorithm to reestimate their corresponding parameters, and then adjust the read voltages. By combining the enhanced EM algorithm with the MARC algorithms, an enhanced EM-based correction strategy is developed to further boost the retention-error endurance of flash memory while avoiding excessive memory-sensing overhead. Theoretical analyses and simulation results illustrate the superiority of the proposed correction mehtods in terms of the robustness against retention errors.

Resistive random-access memory is one of the most promising candidates for the next generation of non-volatile memory technology. However, its crossbar array structure causes severe “sneak-path” interference, which also leads to strong inter-cell correlation. Recent works have mainly focused on sub-optimal data detection schemes by ignoring inter-cell correlation and assuming sneak-path interference is independent between different array cells. In this paper, we propose a near-optimal data detection scheme that can approach the performance bound of the optimal detection scheme. Our detection scheme leverages a joint data and sneak-path interference recovery and can use all inter-cell correlations. The proposed scheme is suitable for data detection of large memory arrays with only linear operation complexity.

The sneak path (SP) interference problem in resistive random access memory (ReRAM) severely affects the data storage reliability. Recent works showed that the occurrence of the SP is highly related to the selector failures (SFs) in the resistive memory arrays. In this work, we propose a novel scheme to detect the location of the failed selector, based on the signal read back from the memory array. The detected SF location information can be used to assist the data detection to mitigate the SP interference or to construct SP-free constrained codes.

Resistive random-access memory (ReRAM) is a promising candidate for the next generation non-volatile memory technology due to its simple read/write operations and high storage density. However, its crossbar array structure causes a severe interference effect known as the “sneak path.” In this paper, we propose channel coding techniques that can mitigate both the sneak-path interference and the channel noise. The main challenge is that the sneak-path interference is data-dependent, and also correlated within a memory array, and hence the conventional error correction coding scheme will be inadequate. In this work, we propose an across-array coding strategy that assigns a codeword to multiple independent memory arrays, and exploit a real-time channel estimation scheme to estimate the instantaneous status of the ReRAM channel. Since the coded bits from different arrays experience independent channels, a “diversity” gain can be obtained during decoding, and when the codeword is adequately distributed over different memory arrays, the code actually performs as that over an uncorrelated channel. By performing decoding based on the scheme of treating-interference-as-noise (TIN), the ReRAM channel over different memory arrays is equivalent to a block varying channel we defined, for which we propose both the capacity bounds and a coding scheme. The proposed coding scheme consists of a serial concatenation of an optimized error correction code with a data shaper, which enables the ReRAM system to achieve a near capacity limit storage efficiency.

In this paper, we propose channel coding techniques that can mitigate both the sneak-path interference and the channel noise for resistive random-access memory (ReRAM) channels. The main challenge is that the sneak-path interference is data-dependent, and also correlated within a memory array, and hence the conventional error correction coding scheme will be inadequate. We propose an across-array coding scheme, which assigns a code-word to multiple independent memory arrays. Since the coded bits from different arrays experience independent channels, a “diversity” gain can be obtained during decoding, and when the code-word is adequately distributed over different memory arrays, the code actually performs as that over an uncorrelated channel. We also present a real-time channel estimation scheme together with an elementary signal estimator (ESE) to obtain the instant channel status as well as the soft information of the channel coded bits for decoding. By further combining with a data shaping technique to produce an optimized channel input distribution, significant error performance gain is obtained.

The user identification scheme for a multiple-access fading channel based on the binary signature code is considered. In previous works, the signature code was used over a noisy multiple-access adder channel, and only the status of uses was decoded by the signature decoder. In this study, by considering the communication model as a compressed sensing process, it is possible to estimate the channel coefficients while identifying users. To improve the efficiency of the decoding process, we proposed an iterative deep neural network (DNN)-based decoder. Our simulation results show that for the binary signature code, our proposed DNN-based decoder requires less computing time to achieve higher active user detection accuracy and channel estimation accuracy than the classical signal recovery algorithm used in compressed sensing.

The performance of the quasi-cyclic low-density parity-check (QC-LDPC) coded partial-access interleave division multiple access (IDMA) systems is evaluated with the SNR (signal-to-noise ratio) evolution algorithm. The partial access IDMA system is the IDMA system in which the 0s, i.e., non-energy transmission, are inserted into the chip sequence. The SNR evolution algorithm is developed and employed to evaluate the systems. Numerical and simulation results show that the partial access has better BER (bit error rate) performance than that of the conventional full access in a range of low Eb/N0, and the proposed IDMA system with the 3GPP NR QC-LDPC codes has a good error-floor performance.

A very low-complexity on-off division multiple access (ODMA) scheme is proposed for K-user non-orthogonal multiple access (NOMA) systems. At the transmission side, each user employs the same length-m channel code whose coded bits, after modulation, are sent in a random time-hopping manner. Specifically, m coded bits are randomly scheduled and sent using n time slots with n≫m, i.e., only m slots are used for signal transmission and the other n- m slots are idle. The slot selection, referred to as an on-off pattern, is unique to each user, and it is the only means of user separation. Consequently, at each time slot only a very few users (i.e., 2 or 3) may simultaneously access the channel, leading to a super-sparse access system. Due to the sparse access property, a very low-complexity iterative multi-user decoding method can be implemented on an almost tree-like factor graph. Compared with existing iteratively decodable code division multiple access (CDMA) schemes, such as sparse-CDMA and interleave division multiple access (IDMA), ODMA does not rely on repetition (spreading) or user interleaving. In fact, we show that in using extrinsic information transfer (EXIT) analysis and simulation, idling is more effective than repetition in terms of enhancing the multi-user iterative decoding performance. By replacing repetition with idling, a remarkable multi-user decoding performance gain is achieved and, at the same time, the decoding complexity is significantly reduced.

A T -user UD k-ary codes for MAAC is proposed. First, a coding scheme for a Tf+g-user UD k-ary code with code length f + g is proposed that is constructed from a Tf-user UD k-ary code and a Tg-user UD (2k - 1)-ary difference set. In fact, the Tg-user UD (2k - 1)-ary difference set is associated with Tg-user UD (2k - 1)-ary code. Second, originally from the multi-user UD (2i(k - 1) + 1)-ary (i = 0, 1, 2,..., m) codes with unitary code length, by recursively employing the coding scheme, 2m+1-user k-ary code with code length 2mis obtained. Finally, by recursively employing the coding scheme, 2n-user UD k-ary code with arbitrary code length n from the codes with length 2i(i = 0, 1,..., ⌊log2n⌋) is given. Since introducing the high-order multiary difference sets, the total rates of the proposed codes are higher those of conventional codes.

A partial-access scheme is proposed for coded-IDMA (interleave-division multiple-access) systems. Similar to conventional IDMA systems, the transmitter of each user consists of a concatenation of channel encode, spreading, and user-specific interleaving. The only difference is that after spreading, some 0s are inserted into the chip sequence. Among the transmitted symbols of -1, 0, 1, symbol 0, however, implies a non-energy transmission or non-access to the channel. In the IDMA receiver, we use a customary joint iterative decoding based on a single factor graph. In our proposed IDMA systems, partial access not only greatly decreases the complexity of the joint decoding; it also decreases the number of short loops in the factor graph. Our extrinsic information transfer (EXIT) analysis and bit-error-rate (BER) simulations show that the proposed partial-access scheme outperforms conventional full-access-IDMA systems in a low SNR range.

In this paper, we consider a detection method against fake messages in sparse mobile ad-hoc networks, where nodes are temporally isolated. In these networks, messages are delivered to their destination nodes using store-carry-forward routing, where they are relayed by some nodes. Therefore, when a node has messages in its buffer, it can easily rewrite them. When there exist malicious nodes in the network, they can alter messages to fake message and launch fake message attacks, spreading the fake messages over the network. In this paper, we first model system dynamics as a continuous-time absorbing Markov chain, and clarify how fake message attacks affect the system performance using Markov analysis. We then propose a detection method that uses the hash value of messages. Whenever a node that has a message and its hash value encounters another node, it forwards only one of them to that node. By doing so, the message and its hash value are delivered to the destination node via different paths. Through simulation experiments, we show the effectiveness of our proposed method.

Multilevel flash memories enable multiple bits to be stored in a single memory cell and hence a significant increase of the storage capacity. The multiple bits that are used for labeling the threshold voltage level of a memory cell belong to different pages. A multilevel flash memory channel resembles a multi-user channel with asymmetric noise, while the data of different pages, which are encoded independently, resembles data of multiple users. In this paper, performance analyses are proposed for this channel by using the union bound technique. In particular, we investigated two different binary labeling schemes of a cell level, the Gray labeling and non-Gray labeling with three maximum-likelihood (ML)-based decoding schemes, which are the joint multi-page ML decoding, page-separate ML decoding, and default setting ML decoding. Our analysis reveals an asymptotic diminishing rate of decoding errors as the channel noise approaches zero, based on which the code design criteria are proposed. It is shown theoretically that the Gray mapping has no joint (i.e., multi-page) decoding gain. The corresponding diminishing decoding error rate is dominated by the weakest code in each page and hence a separate decoding scheme is adequate. On the other hand, the non-Gray mapping has a joint decoding gain which means the weak code can exploit the decoding of the strong code and the diminishing rate of its decoding errors is not subject to the cask effect. Therefore, for Gray mapping, a symmetric coding scheme using equal-strength code for each page achieves better error performance, while for non-Gray mapping with joint decoding, the symmetric coding is not necessary. Moreover, by using the asymmetric coding scheme through assigning different code rates to different pages, the non-Gray mapping can achieve higher overall sum rate than Gray mapping with a similar decoding error rate performance.

This work introduces a novel coding paradigm for the unsourced multiple access channel model. The envisioned framework builds on a select few key components. First, the transmission period is partitioned into a sequence of sub-blocks, thereby yielding a slotted structure. Second, messages are split into two parts. A portion of the data is encoded using spreading sequences or codewords that are designed to be recovered by a compressed sensing type decoder. In addition to being an integral part of the data, the information bits associated with this first part also determine the parameters of the low-density parity check code employed during the subsequent stages of the communication process. The other portion of the message is encoded using the aforementioned low-density parity check code. The data embedded in this latter stage is decoded using a joint message passing algorithm designed for the T-user binary input real adder channel. Finally, devices repeat their codeword in multiple sub-blocks, with the transmission pattern being a deterministic function of message content independent of the identity of the device. When combined with successive interference cancellation, the ensuing communication infrastructure offers significant performance improvement compared to coding schemes recently published in the literature for unsourced random access.

A recursive construction of k-ary uniquely decodable multiuser codes is proposed for use in a noiseless multiple-access adder channel. The code rates of the proposed codes are higher than those of previous uniquely decodable multiuser codes. A recursive decoding algorithm is also proposed.

In this paper, we introduce the extended mean king's problem and its solutions. Also, we show a quantum key distribution (QKD) using the extended mean king's problem. By using the quantum key distribution, a sender can share a secret key with each of receivers. Besides, we consider the tolerance to an eavesdropper who makes intercept-resend attacks. As a result, in the case of two receivers, we indicate that the quantum key distribution is robust against the intercept-resend attacks by showing that the error occurs between the secret keys of a sender and receivers.

For the problem of multiple users simultaneously communicating with a single receiver, a sparse multiple access scheme is proposed. Each user employs a low-density parity-check (LDPC) code. To mitigate multi-user interference, the codeword of each user is randomly punctured and the punctured bits are replaced by idle slots. That is, only a small random set of users are active at each time. The restriction of number of concurrent users significantly reduces the multi-user decoding complexity. Moreover, this puncture facilitates an efficient message-passing decoding over a sparse graph. With a joint optimization of the degree distribution of the LDPC code and the column weight distribution of the puncture matrix, capacity-approaching performance is achieved.

The frame error rate (FER) of spatially-coupled irregular low-density parity-check (SC-iLDPC) code ensemble in error floor region is estimated. First, the number of codewords of each weight is calculated by the permutations of all the sub-codewords at their coupling positions. Second, the FER is estimated by these numbers of the codewords of each weight. Numerical results show that the FER performances in the error floor regions of the SC-iLDPC code ensembles are superior to the conventional irregular LDPC code ensembles at almost identical belief-propagation (BP) thresholds.

In this paper, spatial coupling technique is used to improve the error-correcting performance of finite length polar codes. Polar codes are considered as base codes of coupling. Two types of spatial-coupling methods are investigated. For the first coupling method, some message bits of a polar base code at each coupling position are used as frozen bits of one-side adjacent polar base code. For the second spatial-coupling method, multiple polar codes are associated by combining message bit blocks of adjacent coupling positions with modular-two addition. Simulation results show that, with a little extra iteration complexity, the two types of spatially coupled polar codes can provide better error-correcting performance than original polar codes. When setting the coupling ratio at 0.33 and coupling pattern as Uncertain-Certain, the first spatial-coupling method provides the best performance output. The second spatial-coupling method with coupling width 3 provides better performance than that with coupling width 2. Furthermore, the first spatial-coupling method with short message block length provides better decoding performance, and the second method with large message block length performs better.

A kind of multiuser k-ary codes for the multiple-access adder channel is proposed. Given any Tf-user and Tg-user k-ary uniquely decodable (UD) codes with code lengths f and g, respectively, a (Tf+ Tg+ 1)-user k-ary UD code with code length f + g is obtained. The proposed scheme has no restriction on the code structure, e.g., affine, and can be constructed from any arbitrary two UD codes. Moreover, a recursive construction of a kind of k-ary UD codes with arbitrary code length is given. The proposed codes have the higher code rate and the shorter code length than those of the previous codes for a fixed number of users.

A union bound analysis is given for codes over binary asymmetric channels. By considering a random mapping that modulates each coded bit equiprobably to the signal constellation point, an average union bound is derived explicitly as a function of the code's weight spectrum. The bound can be used for estimating the error floor performance of maximum-likelihood decoding or near optimal decodings.

Recent years have seen increasing efforts to improve the input/output performance of multilevel flash memory. In this regard, we propose a coding scheme for two-page unrestricted-rate parallel random input-output (P-RIO) code, which enables different code rates to be used for each page of multilevel memory. On the second page, the set of cell-state vectors for each message consists of two complementary vectors with length n. There are a total of 2n-1sets that are disjoint to guarantee that they are uniquely decodable for 2n-1messages. On the first page, the set of cell-state vectors for each message consists of all weight-u vectors with their non-zero elements restricted to the same (2u-1) positions, where the non-negative integer u is less than or equal to half of the code length. Finding cell-state vector sets such that they are disjoint on the first page is equivalent to the construction of constant-weight codes, and the number of disjoint sets is the best-known number of code words in the constant-weight codes. Our coding scheme is constructive, and the code length is arbitrary. The sum rates of our proposed codes are higher than those of previous work.

An asymmetric multiple access channel (AMAC) is a multiple-access channel where a portion of the users can observe the messages of other users. We first propose three 2-user uniquely decodable (UD) codes for two-user AMAC, which are shown to achieve higher sum-rate than the previous 2-user codes. Then, we consider multiuser error correcting codes for T-user noisy AMAC. A theorem shows that given a Ta-user δa-decodable k-ary code A and a Td-subset δa-decodable difference set D a priori, a larger error-correcting T-user code C is obtained by Hadamard matrices. For practical construction, we give 2-user difference sets based on the 2-user UD codes, and obtain multiuser correcting codes for multiuser AMAC. The proposed correcting codes have increasing sum-rate and error-correcting capability with an increasing code length.

A union bound and its asymptotic analysis are presented for multilevel flash memory channels. The bound reveals an asymptotic decoding error behaviour under the maximum-likelihood decoding, based on which code design criteria are proposed.

We propose a novel coding scheme for the unsourced multiple access channel model introduced by Polyanskiy [1]. This new paradigm is composed of four main ingredients: (i) the transmission period is partitioned into sub-blocks, thereby instituting a slotted framework; (ii) The message (data) is split into two parts and one part chooses an interleaver for a low density parity check (LDPC) type code. This part of the message is encoded using spreading sequences or codewords that are designed to be decoded by a compressed sensing type decoder; (iii) The other part of the message is encoded using a low density parity check (LDPC) type code and decoded using a joint message passing decoding algorithm designed for the T-user binary input real adder channel; (iv) users repeat their codeword in multiple sub-blocks, with the transmission pattern being a deterministic function of message content and independent of the identity of the user. When this coding scheme is combined with serial interference cancellation, the ensuing communication infrastructure can offer significant performance improvements compared to the recently proposed coding scheme in [2] and results in the best performing coding scheme to date.

A K ‐user multi‐rate code is proposed for a Gaussian multiple access channel with binary inputs, equal‐power, and symbol synchronisation. In this multi‐rate transmission, K users are equally divided into M groups. For each user in the m th group, a rate‐ regular repeat‐accumulate code serially concatenated with a length‐ spreading is employed. The transmitted rate of each user in the m th group is . At the receiver, iterative joint decoding (IJD) and hybrid interference cancellation (HIC) schemes are considered. For each decoding scheme, a bivariate fixed‐point analysis is applied to explicitly represent as a function of mutual information outputs. On the basis of these basic explicit representations, a united unreliable region is given, where users in at least one group are undecodable. The complementary set of the united unreliable region gives an optimal rate profile that achieves the maximum sum rate. Numerical results show that, for the IJD scheme with M increments, the maximum sum rate increases, approaches the Shannon limit, and exceeds that in conventional equal rate transmission. The maximum sum rate of the HIC scheme, which provides much lower decoding complexity than the IJD scheme, is superior to the conventional successive interference cancellation scheme.

A family of rate‐compatible capacity‐approaching codes is obtained by spatially coupling multiple identical copies of rate‐compatible base codes. The base code consists of a given regular low‐density parity‐check (LDPC) code and a parameter‐adjustable repeat‐accumulate (RA) extension. The RA‐extension repeatedly accumulates all of the variable nodes of the given LDPC code by q + 1 times to generate q + 1 blocks of accumulated nodes, in which all of the accumulated variable nodes in the first q blocks and the α ‐fractional accumulated variable nodes in the last block are transmitted. The spatially coupled versions of the base codes, called RA‐extended spatially coupled LDPC (SC‐LDPC) codes, achieve arbitrary rates by simply adjusting parameters q and α , and thus they are rate‐compatible. The potential thresholds of the base code ensembles are calculated to predict the iterative decoding performance of the proposed RA‐extended SC‐LDPC codes. Numerical results and simulations show that the authors’ proposed rate‐compatible codes are capacity‐approaching over binary erasure channels.

Consider an interleave-division multi-user coding model for a Gaussian multiple-access channel (MAC). Each user's message is encoded by a separate channel encoder followed by a user-interleaver, which is employed for user separation. All the users' codewords are jointly regarded as one multi-user codeword, and the distance between two multi-user codewords is defined as the Euclidean distance after the inter-user superposition caused by the MAC. A distance enumerator analysis estimates the multi-user maximum likelihood decoding performance. By introducing user-scramblers, a multi-user code ensemble is defined, and its distance enumerator is calculated as concatenated multiple single-user codes and a superposition code. Both finite-length and asymptotic analyses are given and it is shown that interleave-division multi-user codes have much better distance properties than conventional random direct-sequence code-division multiple-access. In fact, the codes achieve almost the same asymptotic uniquely decodable performance as a multi-user random code.

A very simple coding scheme, called multi-user repetition-aided irregular repeat-accumulate (IRA) code, is proposed to approach the multiple-access channel (MAC) capacity. The main idea is that not only parity checks, which are generated by an IRA encoder, but also repetitions are used in each user's codeword to reduce the coding and decoding complexities. Repetition is a simple way to construct a low-rate code and is shown to be beneficial for multi-user decoding iteration. It is shown that there is a maximum allowable fraction of repetitions in codewords, below which channel capacity can always be approached by optimizing the degree distribution of the IRA encoder. As users increase, the maximum allowable fraction of repetitions increases, and therefore, very low encoding and decoding complexities are required.

A coding scheme of (k+1) -ary error-correcting signature codes for a noisy multiple-access adder channel is proposed. Given a signature matrix A and a difference matrix D=D+- D-a priori, a larger signature matrix is obtained by replacing each element in the Hadamard matrix with A , or D+, or D-depending on the values of the elements and their locations in the Hadamard matrix. The set of rows in the proposed matrix gives an error-correcting signature code. Introducing a difference matrix makes it possible to construct an error-correcting signature code whose sum rate is increased with an increase in the order of the Hadamard matrix. Either binary or non-binary signature codes are constructed when the pairs of matrices A and D are given.

A K-user nonbinary parallel concatenated code (PCC) is proposed for a Gaussian MAC with symbol synchronization, equal-power, and equal-rate users. In a K-user q-ary PCC over finite field GF(q), each user employs a parallel concatenated code, with a rate-(1/r) q-ary repetition component code and M rate-1 q-ary accumulation component codes. Employing q-ary repetition code is to overcome the multi-user interference and also provide coding gain. The K-user q-ary PCC is not only rate compatible, but also with very low encoding and decoding complexities due to employing such simple component codes. An EXIT chart analysis is given to estimate the decoding threshold of the K-user q-ary PCC. Numerical results show that the decoding threshold of K-user q-ary PCC improves as the field order q increases. The 10-user 64-ary PCC improves the decoding threshold by 1.88 dB over the binary case. The decoding threshold of 15-user 64-ary PCC at sum rate 3/4 is only 0.75 dB away from the Shannon bound. Bit-error-rate simulations are provided to verify the analysis.

A K-user repeat-accumulate interleave-division (RAID) system is considered for a Gaussian multiple access channel (GMAC) with binary inputs, equal-power, and symbol synchronization. In this system, a regular repeat accumulate (RA) code serially concatenated with spreading, where the rate of RA code and spreading length both can be changed, is employed for each user. K users are divided into M groups equally. The mth group contains K/M users with rate Rm(1 ≤ m ≤ M). At the receiver, multiuser message-passing decoding is performed on a single factor graph. A fixed point analysis is developed to obtain all achievable rate profiles for an arbitrary small decoding error rate over the GMAC. It shows that the sum rate of our optimal rate profile is superior to that of conventional multiuser RAID scheme with equal rate.

A distance enumerator analysis is given for multiuser codes over a Gaussian multiple-access channel (MAC). A multi-user code distance is defined as the Euclidean distance between two multi-user codewords after their inter-user super-position caused by MAC. By employing a user-interleaving and a user-scrambling, a multi-user code ensemble is defined, and its distance enumerator is calculated as a concatenated multiple single-user codes and a superposition code.

As a generalization of the binary spreading scheme in conventional direct-sequence code-division multiple-access (DS-CDMA) and interleave-division multiple-access (IDMA), a finite field spreading scheme is proposed for a synchronous multiple-access channel (MAC) with Gaussian noise and equal-power users. For each user, each information symbol over a finite field is spread into a length-L field vector by L-field multiplications. At the receiver, an iterative multi-user decoding algorithm on a factor graph is developed to recover each user's information symbol. To estimate the bit error rate performance of an uncoded finite field spreading system, an extrinsic information transfer analysis of the finite field despreading is given. This analysis shows that in addition to overcoming multi-user interference, the finite field spreading scheme can also provide an additional coding gain to overcome Gaussian noise compared with the conventional spreading scheme. This coding gain increases with the field order. The finite field spreading serially concatenated with a nonbinary low-density parity-check (LDPC) code, with field order 64, approaches the MAC capacity within 0.26 dB at a sum rate of 0.25.

A k-user parallel concatenated code (PCC) is proposed for a Gaussian multiple-access channel with symbol synchronization and equal power users. In this code, each user employs a PCC with M + 1 component codes, where the first component code is a rate 1/q repetition code and the other M component codes are the same rate-1 convolutional code 1/1+D. The K-user PCC achieves a larger maximum sum rate, at the high rate region, than the conventional scheme of an error correction code serially concatenated with a spreading.

We propose a generalized construction scheme of error-correcting signature code. We form a signature matrix whose rows become the non-zero codewords of the signature code. In the coding scheme, a signature matrix is obtained from a Hadamard matrix by replacing every element by an initial signature matrix or its associated matrix depending on the element's binary value. The proposed code has longer length, higher decodability, and larger cardinality. In this coding scheme, the initial signature matrix is in a general form and can be a signature matrix of any initial signature code. Different initial matrices provide different error-correcting signature codes, including conventional codes. This general form makes it possible to obtain error-correcting signature codes with a higher sum rate than conventional codes.

As a generalization of the binary coding-spreading scheme, nonbinary coding-spreading scheme is proposed for a synchronous binary-input multiple-access channel (MAC) with Gaussian noise, equal-power, and equal-rate users. In this scheme, each user employs the same nonbinary low-density parity-check code serially concatenated with a nonbinary low-rate mapping, referred to as nonbinary spreading. A user-specific interleaving is employed to make the transmitted data of each user random-like. It is shown that the iterative multi-user decoding threshold of nonbinary coding-spreading scheme is less than 0.5 dB away from the MAC capacity at many sum rates.

A multi-user repeat-accumulate interleave-division (RAID) system is considered for a multiple-access channel (MAC) with binary inputs, equal-power, and symbol synchronization. In the system, a regular repeat-accumulate (RA) code serially concatenated with block spreading is employed for each user. At the receiver, multi-user message-passing decoding is performed on a single factor graph. Over the MAC with additive white Gaussian noise (AWGN), a fixed point analysis is developed to obtain the optimal code rate and the spreading length that give the maximum sum rate for an arbitrary small decoding error rate.

A method for full-azimuth DoA estimation of multiple signals with a hexagonal array is proposed. The DoA estimation is performed in two steps. In the first, a set of estimate candidates is constructed by gathering the estimates that are obtained from applying the Unitary-ESPRIT algorithm to several translational invariances designed into a hexagonal array. In the second step, the DoA estimates are successively selected from the estimate candidate set by using a selection function. The proposed method removes the north-or-south signal membership ambiguity and the limitation on the number of estimable sources, problems common to any ESPRIT-based algorithm used with one translational invariance. Therefore, up to M - 1 signal DoA estimations can be expected with an M-element hexagonal array in the full azimuth. The successive-selection approach is based on a selection function that uses an estimate of the signal's spatial correlation matrix to successively select the DoA estimates. For each DoA estimate selection, the already estimated signal components are removed from the correlation matrix. The method's DoA estimation and resolution capabilities are demonstrated by computer simulation.

Error-correcting non-binary signature code is proposed. A 2j-1-decodable (k + 1)-ary signature code with code length 2j- 1 is recursively constructed. The code is used to identify users through a multiple-access adder channel, even in the presence of channel noise.

The performance of a multi-phase cooperative communication is studied in a wireless network. Each node is a mobile module having multiple antennas (MA) or a group of sensors forming a virtual antenna array (VAA). The scenario comprises a number of multiple-input multiple-output (MIMO) channels with mutually independent Rayleigh fading processes. A data frame from a signal source node is split into portions. Each portion is transmitted from a distinct node in a sequential manner to the destination node. First, we give the criterion on how to select wireless nodes for achieving the lowest outage probability of information capacity. Second, the analytical expressions of the optimal frame splitting (FS) ratios are derived for arbitrary signal-to-noise (SNR) situations. This is fulfilled by employing Gaussian approximations of those random MIMO channel capacities. Finally, we examine the optimal FS ratios in high-SNR regime. The theoretical results are useful to designing cooperative communication protocols.

User identification by signature code is considered for noisy multiple-access adder channel. An n/2-decodable signature code is developed from a Hadamard matrix of order n. The code is used to identify users through the multiple-access adder channel even in the presence of channel noise. A decoding rule is provided to correct lfloor(n/2 - 1)/2rfloor errors and then to identify users

The necessary and sufficient condition for constructing a spreading set with decodability is investigated. It is proved that for a given ${\delta}$ -decodable spreading set and a $q \times q$ square matrix $H$ with components $1$ or $-1$ , a ${q\delta}$ -decodable spreading set $S^\ast$ is obtained if and only if $H$ is a Hadamard matrix. In addition, a decoding rule with error correction and message data detection is provided.

Error-correcting signature code is proposed. An n/2-decodable signature code with code length n - 1 and cardinality n - 1 is developed from an Hadamard matrix of order n. The code is used to identify users through the multiple-access adder channel, even in the presence of channel noise

The electronically steerable parasitic array radiator (ESPAR) antenna offers low cost and low complexity relative to conventional array antennas. Because of the low complexity of the antenna there is only a single-port output for processing the signals impinging on the antenna elements. Since a reactance-domain MUSIC algorithm for ESPAR antennas has been proposed, the practical problem of estimating the direction of arrival of signals impinging toward an ESPAR antenna can be tackled. In this paper, two experimental methods of estimating the arrival signal angles are proposed. A method of solving the practical problem of calibrating the ESPAR antenna output signal model is also shown. The experimental results show that for one impinging signal the direction of arrival can be estimated with precision of 3 degrees.

Multiuser k-ary coding is proposed for a noisy multiple-access adder channel. It is shown that when a T-user /spl delta/-decodable k-ary code C is given a priori, a qT-user /spl lambda//spl delta/-decodable k-ary code C/sup */ is obtained by using a matrix, such as a Hadamard matrix or a conference matrix of order q, where /spl lambda/ is a positive integer depending on the matrix. More noteworthy is that the code C is an arbitrary /spl delta/-decodable k-ary code, and that the coding scheme preserves the total rate, i.e., the total rate of C/sup */ is equal to that of C.