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In this paper, we focus on near-optimal designs for variable-length error-correcting (VLEC) codes, while considering the performance in terms of both the average codeword length (ACL) and the symbol-error rate (SER). The criteria for narrowing the search space and enhancing the SER performance are investigated. An efficient code construction algorithm is then devised based on a random search process. Taking advantage of the significantly reduced search complexity, we are able to construct near-optimal VLEC codes for large source alphabets. Numerical results obtained for various free distance values and alphabet sizes show that constructed VLEC codes have both reduced ACL values and enhanced SER performances. Performance improvement is more notable for large source alphabets.

In this paper, based on the technique of LDPC (low-density parity-check)-like sparse graphs for the Polar codes, we propose a Polar decoding method which provides the schedule diversity. The investigated decoding schedules outperforms Arikan’s belief propagation (BP) algorithm performed on the original encoding factor graph. Secondly, based on both the layered BP (LBP) and the modified node-wise residual BP (NW-RBP) schedules, we are able produce several sequential decoding schedules that are executed in serial. It is shown through simulations that when compared to the successive cancellation list (SCL) decoding, the proposed scheme achieves a lower complexity level, while a gap of 0.2 dB still exists in BER performance in the high-SNR region. However, the enhanced BP-based decoding method provides a flexible decoding latency, and is able to generate soft-in/soft-out information, which makes it suitable for the schemes which perform iterative decoding and detection processes.

Aimed at the emerging massive multiple-input multiple-output (MIMO) systems, both hard-decision and soft-decision detectors are investigated for the generalized space shift keying (GSSK) modulation scheme, where a codebook-assisted technique is used to reduce the tree-search complexity. Furthermore, the outer low-density parity-check (LDPC) code is optimized such that the proposed system design can provide an error performance, which is almost the same as that of the scheme that uses the maximum a posteriori (MAP) soft detector, but with a much lower computational complexity.

In this paper, we investigate Raptor-coded distributed unitary space–time modulation (USTM) schemes, where both the amplify-and-forward (AF) and decode-and-forward (DF) relaying scenarios are considered, under a wireless relay network with arbitrary path gains for the channel fading coefficients. First, the AF and DF relaying procedures are investigated based on the use of an inner USTM signal and an outer Raptor code, and the related noncoherent detectors are also derived. The constellation search for the USTM signal, as well as the optimization for the Raptor code, is then investigated in order to enhance the system performance. It is shown that the designed systems effectively approach the predicted limit in throughput performances and outperform the noncoherent distributed MIMO scheme reported in the previous literature.

In the paper, we investigate LDPC-coded differential amplitude/phase modulation (APM) schemes for correlated Rayleigh fading channels. Through the observation for the mutual information of the extrinsic log-likelihood ratio (LLR) values of the variable nodes in the LDPC decoder, it is found that the code design methods investigated in the previous literature loses their accuracy. Consequently, a modified code design method for the outer LDPC code is proposed in this paper. It is shown that the searched LDPC code effectively improves the error performance, when compared to the convolutional-coded scheme investigated in the previous literature.

In this paper, a coded modulation scheme using extremely sparse low-density parity-check (LDPC) codes is proposed for the stored signal of triple-level-cell (TLC) NAND flash, where both the encoding and the decoding complexity can be significantly reduced with the advantage of the extremely sparse code graph. In order to enhance the performance of decoder, iterative detection decoding (IDD) is introduced to extract the extrinsic information from the symbol detector, and the cooperative non-Gray mapping is also designed. In addition, for error floor lowering, an interleaver is inserted to ensure the cascaded degree-2 variable nodes are separated to individual symbols. The simulation results show that the proposed coded modulation scheme can provide a practical error floor performance with a low decoding complexity.

In this paper, we investigate differential amplitude/ phase modulation (APM) schemes for correlated Rayleigh fading channels. Considering the noncoherent maximum-likelihood receiver, a theoretical pairwise error probability (PEP) formula for differential signal vectors with arbitrary power values is derived. The design criterion for the signal set of differential vectors is then proposed based on the asymptotic analysis of the PEP. For both uncoded and coded APM schemes, the design criteria and optimization procedures for bit labeling rules are investigated. The designed differential APM schemes are shown to provide significant improvement in bit-error-rate performance, particularly in the error-floor regions.

It is known that low-density parity-check (LDPC) codes are widely used to provide capacity-approaching performances in various transmission systems. However, the Gaussian assumption for soft messages in conventional EXIT (extrinsic information transfer)-chart-based optimization algorithms result in prediction gaps in the decoding threshold for certain transmission systems. In this letter, we propose an EXIT-chart-based optimization method, in which all the Gaussian assumptions for soft messages can be avoided. Compared to the conventional design methods, the proposed method provides a more accurate threshold prediction and can be used to design LDPC-coded schemes with better error performances.

In this paper, we investigate noncoherent transmission schemes using amplitude/phase modulation. For uncoded transmission schemes, we derive the pairwise error probability (PEP) and its high-SNR approximation for signal vectors with unequal power values using a noncoherent maximum-likelihood detector under Rayleigh block fading channels. For coded transmission schemes, we consider differential amplitude/phase modulated signals and introduce a codeword-interleaving strategy to improve the error performance. The design criteria for the signal labelling and bit interleaving are also derived via the high-SNR approximation of the PEP. At the receiver, we devise an iterative channel amplitude estimator to enhance the detection reliability. With the help of a specially-designed iterative receiving algorithm, the designed noncoherent coded scheme can provide a significant improvement, either in the error-floor or the waterfall region.

In this paper, we propose the use of a convolutional interleaver employing a variety of block delay parameters as the bit interleaver in a multiple-input-multiple-output (MIMO) bit-interleaved coded-modulation (BICM) scheme. The associated iterative decoding-detection algorithm is proposed, and the design criteria for the outer convolutional code are derived. The cases for both the perfect channel-state information (CSI) and the estimated CSI are investigated. In the proposed MIMO-BICM scheme, the MIMO detector and the channel estimator utilize the soft information passed from the sliding-window convolutional decoder within the same iteration, and hence, the convergence speed can be increased. Compared with the conventional scheme using various interleaver designs, the proposed scheme not only achieves better error performance for the first iteration but also has lower decoding latency. Consequently, the proposed scheme is suitable for delay-sensitive applications.

A novel noncoherent block coding scheme, called noncoherent block-coded MPSK (NBC-MPSK), was proposed recently. In this paper, we present further research results on NBC-MPSK. We first focus on the rotational invariance (RI) of NBC-MPSK. Based on the RI property of NBC-MPSK with multistage decoding, a noncoherent near-optimal linear complexity multistage decoder for NBC-MPSK is proposed. Then we investigate a tree-search ML decoding algorithm for NBCMPSK. The derived algorithm is shown to have low complexity and excellent error performance. In this paper, we also utilize the idea of the NBC-MPSK to design noncoherent space-time block codes, called noncoherent space-time block-coded MPSK (NSTBC-MPSK). For two transmit antennas, we propose a signal set with set partitioning and derive the minimum noncohent distance of NSTBC-MPSK with this signal set. For the decoding of NSTBC-MPSK, we modify the ML decoding algorithm of NBC-MPSK and propose an iterative hard-decision decoding algorithm. Compared with training codes and unitary space-time modulation, NBC-MPSK and NSTBC-MPSK have larger minimum noncoherent distance and thus better error performance for the noncoherent ML decoder.

This paper presents a listed maximum mutual information increase (LM2I2)-based algorithm, which is used to arrange low-density parity-check (LDPC) decoding schedules for faster convergence. The increments in the predicted mutual information for the messages to be updated is used to guide the arrangement of the fixed decoding schedule. Consequently, by looking ahead for several decoding stages, a high-order prediction can be realized. For each decoding stages, the searching branches can be trimmed to fit a predetermined size of list, and the efficiency in the selection of update candidates is thus increased. Comparing to previous algorithms, the proposed LM2I2-based algorithm can be used to arrange the decoding schedules converged in the same speed with lower complexity, or accelerate the convergence with the same computation cost.

In this paper, we investigate the design procedures of the bit labelling rule as well as the outer channel code for the table-based bit-interleaved coded differential amplitude/phase modulation (BICD-APM) scheme under correlated Rayleigh fading channels. Based on the asymptotic pairwise error probability (PEP) formula reported in the previous work, the design criteria for the generator polynomials of the outer convolutional encoder, and for the bit labelling strategy of the inner differential modulator, are investigated for the table-based differential APM schemes when considering two different types of bit interleavers. It is shown that the designed scheme which considers parallel bit interleavers is able to achieve the best bit error rate (BER) performance, and provides a significant SNR gain under the same BER value, when compared to the conventional BICD-APM scheme reported in the previous literature.

In this paper, we focus on the design of differential amplitude/phase modulation schemes by a look-up table for Rayleigh fading channels. In the first part of this paper, we first propose the noncoherent distance measure for each two signal vectors based on the maximum-likelihood (ML) signal detection under Rayleigh fading channels. The design criterion/procedure of the look-up table is then investigated. In the second part of this paper, linear dispersion codes are used to construct a multi-dimensional differential amplitude/phase modulation scheme, with the aid of the genetic algorithm. Both schemes are shown to provide improvements in error performance, when comparing to the conventional scheme provided in the literature.

In this paper, an efficient implementation of the Chase II soft-input/soft-output (SISO) decoder using the distance-based decoding algorithm is proposed, where a piece-wise-linear based method is proposed to simplify the calculation of the extrinsic values. As a demonstration, a (64; 51; 6)2 block turbo decoder is implemented. Compared to the DBD-based decoder presented in the previous literature, the proposed decoder achieves a higher throughput and a higher efficiency.

In the encoding of Luby transform (LT) codes, information bits (variable nodes) are randomly connected to the check nodes. Although the check-node degrees have been optimized for error-rate performance, the arbitrary connections in the code graph cannot guarantee efficient propagation of the channel information (intrinsic messages), and may slow down the convergence speed of the iterative decoding. This paper presents a design for a generator matrix such that the intrinsic messages can be efficiently propagated through the arranged connections. In addition, the convergence speed of rateless codes can also be accelerated using the proposed degree-oriented scheduling (DOS), where the intrinsic messages are propagated based on the order of check node degrees. An improvement in the convergence speed can be achieved without sacrificing the error-rate performance. In the case of Raptor codes, the BER performance can be significantly improved.

Recently, a turbo-coded noncoherent space-time modulation scheme, which is aimed at providing both a high data transmission rate and a low receiving complexity, was proposed for noncoherent block fading channels. However, in cases where a large number of transmit antennas exist, the turbo code does not match well with the noncoherent space-time modulation scheme, and results in performance degradation. In this paper, we first investigate a coded noncoherent space-time modulation scheme using an irregular low-density parity-check (LDPC) code. We also design a turbo-coded noncoherent space-time modulation scheme based on the codeword-interleaving strategy. The coded symbols mapped from adjacent codewords are interleaved into the same signal vectors, and the soft information from adjacent codewords are allowed to be exchanged at the receiver. When comparing to the conventional turbo-coded scheme, both proposed schemes achieve a significant improvement in BER performance.

As part of the tradeoff between error performance, decoding complexity and the overhead of rateless codes, the combination of incremental decoding (ID) and informed dynamic scheduling (IDS), known as IDIDS (incremental decoding with informed dynamic scheduling), is an attractive solution in binary symmetric channels (BSC). However, applying IDIDS in the AWGN (additive white Gaussian noise) channel may cause a degradation in BER performance, since the incrementally received symbols from the AWGN channel may not be immediately utilized in the decoding process directed by IDS. In addition, a stopping criterion combined with IDS may cause the current decoding attempt to terminate too early, and the channel information contained in the originally received codeword will not be used efficiently. In this paper, a dynamic decoding schedule strategy is proposed. In the proposed decoder, the new received symbols can be immediately utilized in the decoding process. For Luby transform (LT) codes and Raptor codes over the AWGN channel, the proposed algorithm provides a more balanced tradeoff. In the case of Raptor codes, the BER performance is obviously improved.

It is known that partial transmit sequence (PTS) is an effective technique to mitigate the problem of high peak-to-average power ratio (PAPR) in an orthogonal frequency-division multiplexing (OFDM) system. One of the major drawbacks of PTS lies in the high complexity for searching the optimal weighting-factor (phase-rotation) vector. In this paper, a trellis-based iterative algorithm is proposed to choose an appropriate weighting-factor vector. Compared to a previously-proposed non-iterative trellis-based algorithm, the proposed iterative algorithm can achieve a comparable PAPR performance with a lower search complexity. Since explicit side information is not transmitted to the receiver of the OFDM system under investigation, we use a phase-quantization-based receiver, which was originally used in noncoherent receivers, to recover the transmit data. Using such a blind receiver, we can achieve a comparable error performance with a lower complexity compared to previously-proposed blind and semi-blind receivers.

In non-coherent multiple-input multiple-output (MIMO) systems, the conventional noncoherent MAP detector is too complex to be performed if the number of labelling bits conveyed within one single coherence block is high. In order to overcome this difficulty, in this paper, we propose a noncoherent MAP (maximum a posteriori) detector with very low complexity for orthogonally designed USTM (unitary space-time modulation) schemes. In addition, we show that the detected soft values are independent of the extrinsic information fed back from the turbo decoder. As a result, iterative detection and decoding between the noncoherent detector and the turbo decoder can be avoided without performance degradation. Compared to the scheme using the exhaustive-search-based noncoherent MAP detector, the proposed scheme achieves the same error performance, and has a much lower detection complexity.

In this paper, we propose to approach the capacity limit for channels with fast phase variation by using a serial concatenation scheme with an outer turbo encoder and an inner block modulator. A distinct feature of the proposed transmission scheme is that coded symbols from adjacent codewords are interleaved into the same input vectors of the block modulator. At the receiver, we not only perform the iterative noncoherent demodulation and decoding algorithm, but also exchange extrinsic information between adjacent codewords due to the codeword interleaved structure. It is shown through the extrinsic information transfer (EXIT) chart that the resultant block demodulator and channel decoder can match well with each other, and can achieve a near-capacity performance.

A modified recursive least-squares algorithm is proposed for estimating the parameters of a linear system, including ill-conditioned situations. The proposed algorithm is obtained by minimizing the modified cost function in which the initial guess in the cost function of an ordinary recursive least-squares (RLS) algorithm is replaced by the latest estimate. Analysis of the convergence shows that the proposed algorithm has a better convergence rate than the ordinary RLS alorithm. The extension of the algorithm to the time-varying case has also been considered.

In this paper, we propose to mitigate the effect of inter-symbol interference (ISI) by first interleaving symbols la­belled by bits in one codeword with symbols respectively labelled by bits in the two adjacent codewords and then transmitting the interleaved symbol vectors through the ISI channel. At the receiver, we not only perform turbo equalization between the equalizer and the channel decoder, but also exchange extrinsic information between adjacent codewords since the interleaved structure of the proposed scheme. If the adjacent codewords are decoded reliably, we can cancel the interference from adjacent codewords and hence the performance can be improved. Simu­lation results show that the proposed scheme can achieve better error performance as compared to the conventional scheme based on either the same code length or the same decoding latency.

A novel noncoherent block coding scheme, called noncoherent block-coded MPSK (NBC-MPSK), was proposed in [1] recently. This NBC-MPSK scheme was generalized to multiple-antenna systems in [2] as well. In this paper, we present further research results on NBC-MPSK and its generalization. We first focus on the rotational invariance (RI) of NBC-MPSK. Based on the RI property of NBC-MPSK with multistage decoding, a noncoherent near-optimal linear-complexity multistage decoder for NBC-MPSK is proposed. Then we propose a tree-search ML decoding algorithm for NBC-MPSK. The proposed algorithm is shown to have low complexity and excellent error performance. This ML decoding algorithm can also be applied to the generalized NBC-MPSK for multiple antennas. In addition, we propose a new signal set with partitioning for the generalized NBC-MPSK. Error performance and complexity of decoding algorithms is verified by simulations.

A factored form of a Boolean function is a common representation to express the complexity of a Boolean function in multi-level logic. However, a factored form which inhibits the appearance of the inversion operation is still a restricted way of representing a multi-level circuit. In this paper, we present a novel representation of a Boolean function, called the invert factored form representation. This representation mainly takes advantage of the inversion of whole or part of a Boolean function so that fewer literals and better multi-level circuit implementation can be obtained. Based on this novel presentation, our algorithm attempts to find a minimal expression. Experimental results also show the literal counts based on the novel representation are smaller than those on the traditional factored form representation.