In this paper, we propose a novel downlink multiple access system with a multi-antenna transmitter and two single-antenna receivers, inspired by the underlying principles of hierarchical quadrature amplitude modulation (H-QAM) based multiple access (QAMA) and space-division multiple access (SDMA). In the proposed scheme, coded bits from two users are split and assigned to one shared symbol and two private symbols carried by different beams. Based on joint symbol mapping of H-QAM constellations and phase-aligned precoding at the transmitter, each receiver observes a different H-QAM constellation with Gray mapping, a unique parallax feature not shared by existing schemes. In addition to avoiding successive interference cancellation (SIC), each user independently demodulates its own bits on separate I and Q branches with calculations based on closed-form expressions. Hence the receiver complexity is on par with that of orthogonal multiple access (OMA), which is much lower than that in other competing alternatives such as non-orthogonal multiple access (NOMA) and rate-splitting multiple access (RSMA). We carry out system optimization and determine the achievable rate region. Numerical results show that the proposed system achieves superior performance compared with benchmark schemes employing SIC-free receivers, and further demonstrates competitive results across various performance metrics even relative to benchmark schemes relying on SIC-based receivers. The proposed scheme is attractive to 6G and IoT applications where the increased system complexity is at the transmitter while the receivers maintain low complexity.

ABSTRACT Multi‐input multi‐output orthogonal frequency‐division multiplexing (MIMO‐OFDM) has been actively studied for high data rate communications over the bandwidth‐limited underwater acoustic (UWA) channels. Unlike existing receivers that treat the intercarrier interference (ICI) as additive noise, in this paper, the proposed receiver considers ICI explicitly together with the co‐channel interference (CCI) due to parallel transmissions in MIMO‐OFDM. Using a recently developed progressive receiver framework, the proposed receiver starts with low‐complexity ICI‐ignorant processing and then progresses to ICI‐aware processing with increasing ICI levels. The key components of the proposed receiver include the following: (1) compressed sensing‐based sparse channel estimation, (2) soft‐input soft‐output minimum mean square error/Markov chain Monte Carlo detector for interference mitigation, and (3) soft nonbinary low‐density parity check decoding. In addition to simulation, we use real data from the Surface Processes and Acoustic Communications Experiment 2008 (SPACE08) and the Mobile Acoustic Communications Experiment 2010 (MACE10) to verify the system performance, where the transmitter in SPACE08 was stationary and that in MACE10 was slowly moving. Simulation and experimental results show that explicitly addressing ICI and CCI significantly improves the performance of MIMO‐OFDM in UWA systems. Copyright © 2012 John Wiley & Sons, Ltd.

Physical-layer network coding (PLNC) allows two remote terminals to exchange information in two time slots via a half-duplex relay. In this paper, we consider PLNC in underwater acoustic (UWA) two-way relay networks, with particular attention on the recovery of the network-coded codeword at the relay. Considering multiple paths in UWA channels with large delay spreads and temporal variations, orthogonal-frequency division-multiplexing (OFDM) is used as an underlying modulation. Distinct from existing works which mainly focus on the flat-fading channel and the non-iterative PLNC decoding, we investigate three iterative receivers at the relay in doubly-selective UWA channels. To estimate the network-coded codeword, the three receivers respectively adopt i) a conventional decoding scheme to recover the codewords from two terminals independently; ii) a decoding scheme to recover the network-coded codeword directly, and iii) a joint decoding scheme to recover a composite codeword formed by the codewords from the two terminals. In the time-varying channel, the intercarrier interference (ICI) in the received signal has been explicitly addressed in three receivers. Extensive simulations and experimental results reveal that the decoding scheme for direct recovery of the network-coded codeword cannot work well in the multipath channel, and that with a lower complexity the performance of the iterative separate-decoding scheme can catch up with that of the joint decoding scheme.

In this paper, we investigate multi-hop reliable data transfer for underwater acoustic networks. We propose a new protocol, called FOuntain Code based Adaptive multi-hop Reliable data transfer (FOCAR). FOCAR is essentially a hybrid ARQ scheme which integrates Fountain codes with hop-by-hop retransmission-upon-failure. It considers the half duplex nature of the underwater acoustic modems and adapts the block size of each hop to optimize the end-to-end delay for the multi-hop network scenario. Extensive simulation results show that FOCAR can achieve high reliability with low end-to-end delay and high energy efficiency.

Finding the minimum distance of low-density-parity-check (LDPC) codes is an NP-hard problem. Different from all existing works that focus on binary LDPC codes, we in this paper aim to compute the minimum distance of nonbinary LDPC codes, motivated by the fact that operating in a large Galois field provides one important degree of freedom to achieve both good waterfall and error-floor performance. Our method is based on the existing nearest nonzero codeword search (NNCS) method, but several modifications are incorporated for nonbinary LDPC codes, including the modified error impulse pattern, the dithering method, and the nonbinary decoder. Numerical results on the estimated minimum distances show that a code's minimum distance can be increased by careful selection of nonzero elements of the parity check matrix, or by increasing the mean column weight, or by increasing the size of the Galois field. These results support observations that have been made based on simulated performance in the literature. Finally, we provide an upper bound on the minimum distance for nonbinary quasi-cyclic LDPC codes.

A new decoder architecture for nonbinary low-density paritycheck (LDPC) codes is presented in this paper to reduce the hardware operational complexity in VLSI implementations. The low decoding complexity is achieved by employing adaptive message control (AMC) that dynamically trims the message length of belief information to reduce the amount of memory accesses and arithmetic operations. To implement the proposed AMC, we develop the architecture of a horizontal sequential nonbinary LDPC decoder. Key components in the architecture have been designed with the consideration of variable message lengths to leverage the benefit of the proposed AMC. Simulation results demonstrate that the proposed nonbinary LDPC decoder architecture can significantly reduce hardware operations and power consumption as compared with existing work with negligible performance degradation.

In this paper, we propose a practical scheme, Non-Binary Joint Network-Channel Coding (NB-JNCC), for reliable multi-path multi-hop communication in arbitrary large-scale wireless networks. NB-JNCC seamlessly couples channel coding and network coding to effectively combat the detrimental effect of fading of wireless channels. Specifically, NB-JNCC combines non-binary irregular low-density parity-check (LDPC) channel coding and random linear network coding through iterative joint decoding, which helps to fully exploit the spatial diversity and redundancy residing in both channel codes and network codes. In addition, since it operates over a high order Galois field, NB-JNCC can be directly combined with high order modulation without the need of any bit-to-symbol conversion nor its inverse. Through both analysis and simulation, we demonstrate the significant performance improvement of NB-JNCC over other schemes.

A new decoding algorithm, referred to as Min-Sum with Adaptive Message Control (AMC-MS), is proposed to reduce the decoding complexity of nonbinary LDPC codes. The proposed algorithm adaptively trims the message length of belief information to reduce the amount of arithmetic operations. Exploiting the fact that during the decoding iteration, the distribution of belief information will become more concentrated around the correct element in the case of convergence, the messages can be truncated accordingly by considering only a few entries with large likelihood. Simulation results with a GF(16) nonbinary LDPC code indicate that the proposed approach can reduce arithmetic operations by up to 65% compared with non-truncated cases. Compared with the state-of-the-art extended MS (EMS) decoding, the proposed AMC-MS algorithm can reduce the computation by up to 50%, thereby enabling low-complexity decoding of nonbinary LDPC codes.

Although time-domain oversampling of the received baseband signal is common for single-carrier transmissions, the counterpart of frequency-domain oversampling is rarely used for multicarrier transmissions. In this paper, we explore frequency-domain oversampling to improve the system performance of zero-padded OFDM transmissions over underwater acoustic channels with large Doppler spread. We use a signal design that enables separate sparse channel estimation and data detection, rendering a low complexity receiver. Based on both simulation and experimental results, we observe that the receiver with frequency-domain oversampling outperforms the conventional one considerably in channels with moderate and large Doppler spreads, and the gain increases as the Doppler spread increases. Although a raised-cosine pulse-shaping window can be used to improve the system performance relative to a rectangular window at the expense of data rate reduction, the performance gain is much less than that brought by frequency-domain oversampling in the considered OFDM system for Doppler spread channels.

In this paper, we construct nonbinary quasi-cyclic low-density parity-check (QC-LDPC) codes whose parity check matrices consist of an array of square sub-matrices which are either zero matrices or circulant permutation matrices. We propose a novel method to design the shift offset values of the circulant permutation sub-matrices, so that the code length can vary while maintaining a large girth. Extensive Monte Carlo simulations demonstrate that the obtained codes of a wide range of rates (from 1/2 to 8/9) with length from 1000 to 10000 bits have very good performance over both AWGN and Rayleigh fading channels. Furthermore, the proposed method is extended to design multiple nonbinary QC-LDPC codes simultaneously where each individual code can achieve large girth with variable lengths. The proposed codes are appealing to practical adaptive systems where the block length and code rate need to be adaptively adjusted depending on traffic characteristics and channel conditions.

In this paper, we study nonbinary regular LDPC cycle codes whose parity check matrix H has fixed column weight j = 2 and fixed row weight d. Through graph analysis, we show that the parity check matrix H of a regular cycle code can be put into an equivalent structure in the form of concatenation of row-permuted block-diagonal matrices if d is even, or, if d is odd and the code's associated graph contains at least one spanning subgraph that consists of disjoint edges. This equivalent structure of H enables: i) parallel processing in lineartime encoding; ii) considerable resource reduction on the code storage for encoding and decoding; and iii) parallel processing in sequential belief-propagation decoding, which increases the throughput without compromising performance or complexity. On the code's structure design, we propose a novel design methodology based on the equivalent structure of H. Finally, we present various numerical results on the code performance and the decoding complexity.

In this paper, we present a novel method to construct nonbinary irregular LDPC codes whose parity check matrix has only column weights of 2 and t, where t ¿ 3. The constructed codes can be encoded in linear time and in a parallel fashion. Also, they can achieve near-Shannon-limit performance over both AWGN and Rayleigh fading channels with a moderate field size. Analysis based on nonbinary EXIT charts is presented. Codes constructed by the proposed method with block lengths ranging from 1, 000 bits to 10, 000 bits are simulated. Simulation results show that codes of rate 1/2 and length 10, 000 bits can achieve block-error-rate (BLER) of 10-5within 1.1 dB and 1.3 dB away from the Shannon limits of the AWGN and Rayleigh channels, respectively. In an AWGN channel, codes of rate r = 8/9 and length around 4,000 bits can achieve BLER of 10-5within 1.1 dB from the Shannon limit, while codes of rate r = 15/16 and length around 9,000 bits can achieve BLER of 10-5within 1.0 dB from the Shannon limit. We conjecture that to further lower the error floor (e.g., to a BLER of 10-10), a column weight no less than 3 is preferred and may be necessary, especially for codes with high rate and over Galois fields of small to moderate sizes.

In this paper, we propose a practical scheme, called Non-Binary Joint Network-Channel Decoding (NB-JNCD) for reliable communication in wireless networks. It seamlessly couples channel coding and network coding, and can effectively combat the detrimental effect of fading of wireless channels, especially in large networks. On a high order Galois field, NB-JNCD combines non-binary LDPC channel coding and random linear network coding through iterative joint decoding, which helps fully exploit the spatial diversity and redundancy residing in both codes. Furthermore, the scheme can unify non-binary source coding and high order modulation without the need of any bit-to-symbol conversion and its inverse. Through analysis and simulation, we demonstrate the significant performance improvement of NB-JNCD against other schemes.

Using group theory, we analyze cycle GF(2p) codes that use Cayley graphs as their associated graphs. First, we show that through row and column permutations the parity check matrix H can be put in a concatenation form of row-permuted block-diagonal matrices. Encoding utilizing this form can be performed in linear time and in parallel. Second, we derive a rule to determine the nonzero entries of H and present determinate and semi-determinate codes. Our simulations show that the determinate and semi-determinate codes have better performance than codes with randomly generated nonzero entries for GF(16) and GF(64), and have similar performance for GF(256). The constructed determinate and semi-determinate codes over GF(64) and GF(256) can outperform the binary irregular counterparts of the same block lengths. One distinct advantage for determinate and semi-determinate codes is that they greatly reduce the storage cost of H for decoding. The results in this correspondence are appealing for the implementation of efficient encoders and decoders for this class of promising LDPC codes, especially when the block length is large.

In this paper, we study non-binary regular LDPC cycle codes whose parity check matrix has fixed column weight 2 and fixed row weight d. We prove that the parity check matrix of any regular cycle code can be put into a concatenation form of row-permuted block-diagonal matrices after row and column permutations if d is even, or, if d is odd and the code's associated graph contains at least one spanning subgraph that consists of disjoint edges. Utilizing this structure enables parallel processing in linear-time encoding, and parallel processing in sequential belief-propagation decoding, which increases the throughput without compromising performance or complexity. Numerical results are presented to compare the code performance and the decoding complexity.

Multicarrier modulation in the form of OFDM has been actively pursued for underwater acoustic communication recently. In this paper, we present a desirable property of OFDM that one signal design can be easily scaled to fit into different transmission bandwidths with negligible changes on the receiver. We have tested the proposed design with data collected from experiments at AUV Fest, Panama City, FL, June 2007, and at the Buzzards Bay, MA, Aug. 2007. With QPSK modulation, we have used different bandwidths from 3 kHz to 50 kHz, leading to data rates from 1.5 kbps to 25 kbps after rate 1/2 coding. With 16-QAM modulation, we have used different bandwidths from 12 kHz to 50 kHz, leading to data rates from 12 kbps to 50 kbps. Excellent BER performance has been achieved, which confirms the flexibility of OFDM under different system setups.

Recently, multicarrier modulation in the form of orthogonal frequency division multiplexing (OFDM) has been shown feasible for underwater acoustic communications via effective algorithms to handle the channel time-variability. In this paper, we propose to use nonbinary low density parity check (LDPC) codes to address two other main issues in OFDM: (i) plain (or uncoded) OFDM has poor performance in fading channels, and (ii) OFDM transmission has high peak to average power ratio (PAPR). We develop new methods to construct nonbinary regular and irregular LDPC codes that achieve excellent performance, match well with the underlying modulation, and can be encoded in linear time and in a parallel fashion. Based on the fact that the generator matrix of LDPC codes has high density, we further show how to reduce the PAPR considerably with minimal overhead. Experimental results confirm the excellent performance of the proposed nonbinary LDPC codes in multicarrier underwater acoustic communications.