Gain division multiple access (GDMA), low density spreading code division multiple access (LDS-CDMA) and Sparse code multiple access (SCMA) are non-orthogonal multiple access methods, where SCMA is a method derived from LDS-CDMA with a special design of signal constellation. We compare their performances for transmission over Rayleigh fading channels. Simulation results show that the special constellation design of SCMA does not provide any gain in Rayleigh fading channels. We show that the error performances of a 6-user LDS-CDMA scheme based on 4 resources can be evaluated by applying diversity-2 concept to the 3-user GDMA based on a single resource. However, by using more resources and error-correcting codes, GDMA can also achieve diversity and hence provide error rates similar to LDS-CDMA. In addition, GDMA has the advantage of low complexity.

We construct polar codes for OFDM systems over the frequency selective channel. The channel coefficients are assumed to be available to the transmitter such that the encoder of polar codes can correctly distinguish the input reliabilities and make proper arrangement of frozen bits and message bits. Instead of using the well-known Gaussian approximation method to construct polar codes, we propose a curve fitting method which not only closely approximate the corresponding channel capacity function but also significantly reduce the computational complexity. With the proposed method, the polar coded OFDM systems can achieve good error performances for systems using high- rate polar codes.

A* algorithm is a kind of tree search algorithm which aims to decode short block codes. In the A* algorithm, a stack is needed to store the partially computed paths. The cost of maintaining the stack is very significant. As the size of the stack increases, the computation cost to maintain it will grow quadratically. In this paper, we propose methods which classify paths in the tree according to the deviation from the hard decision path to restrict the stack size. Such a design can reduce the needed stack size and meanwhile avoid the degradation of error performances.

Binary physical-layer Raptor (PLR) codes are known to be capable of approaching the channel capacity over the binary-input additive white Gaussian noise (BIAWGN) channel efficiently. It is desired to apply PLR codes to high order modulations to achieve good spectral efficiency. Herein we study the designs of using conventional PLR codes and protograph-based PLR codes by taking standard Gray-mapped 16QAM into consideration. Simulation results are presented to show the advantages of various designs.

In this paper, the unequal error protection (UEP) capability of convolutional encoders, in terms of the separation vector, is studied from an algebraic viewpoint. A simple procedure is presented for constructing a generator matrix, which is basic and has the largest separation vector for every convolutional code. Such a generator matrix would be desirable, since the corresponding encoder not only achieves UEP optimality, but also avoids undesired catastrophic error propagation. In addition, canonical generator matrices, which are both basic and reduced, are even more preferable for encoding, since they attain the lowest complexity for Viterbi decoding. However, the direct transformation from a UEP-optimal generator matrix to a canonical generator matrix may come with an unexpected loss of the separation vector. We also propose a specific type of transformation matrix that reduces the external degrees of the generator matrices, from which canonical generator matrices can be constructed that include the mitigated degradation of the separation vector. Finally, beneficial UEP convolutional codes that achieve the maximum free distances for the given code parameters are provided.

The A* algorithm for decoding linear block codes is an efficient tree-search method for decoding short linear block codes. The information contained in the parity bits are potentially useful for reducing the edges needed in the tree search. We propose to extract the information embedded in the parity bits by considering sums of parity bits which can be decided by part of the message bits. Analysis for the number of required message bits for obtaining sums of parity bits is provided. The information contained in the parity bits can help to reduce the number of search tree edges.

The A* algorithm is an efficient method for decoding short linear block code based on tree search. However, it may suffer very long decoding latency in the worst-case channel condition. In this paper, we propose to apply some restrictions on the Hamming weights of search paths in the tree-search decoding. Simulation results show that with proper selection of path constraints in the A* algorithm, the worst-case decoding complexity (or latency) can be significantly reduced with only slight sacrifice of the bit error rates.

The A* algorithm for decoding linear block codes is known to be an efficient tree-search method for decoding short linear block codes. We propose to employ the early acquired information of some parity bits to speed up the tree search. Analysis for the number of required information bits for obtaining the parity bits is provided. In addition, two versions of the modified A* algorithm which take advantage of the advanced information of parity bits are provided. Simulation results show that there is advantage in reducing the number of search tree edges in each proposed version as compared with two existing A* algorithms which do not consider the early information of parity bits.

A physical-layer network coding (PNC) scheme based on MIMO linear detection is proposed in this paper for a two-way relay channel with a multi-antenna relay. We apply a real-valued linear combiner to the output symbols of the MIMO linear detector to obtain a superimposed constellation for which the labelling is obtained from the exclusive or operation on the two transmitted symbols. The superimposed constellation is QAM-like which can facilitate the SER (symbol error rate) analysis.

Applying interblock memory to binary linear block codes is a method to increase the transmission reliability by increasing the correlation among codewords. In this paper, we consider short block coding with interblock memory. Since short block codes can be efficiently decoded by employing the A* Algorithm, we investigate the performance of short block coding with interblock memory using the A* decoding. In addition, we propose a simple method which can alleviate the effect of error propagation resulting from interblock memory.

In this paper, a low-density parity-check (LDPC) coded recording system is investigated, for which the run-length-limited (RLL) constraint is satisfied by deliberate flipping at the write side and by estimating the flipped bits at the read side. Two approaches are proposed for enhancing the error performance of such a system. The first approach is to alleviate the negative effect of incorrect estimation of the flipped bits by adjusting the soft information. The second approach is to increase the likelihood of the correct detection of flipped bits by designing a flipped-bit detection algorithm that utilizes both the RLL constraint and the parity-check constraint of the LDPC code. These two approaches can be combined to obtain significant improvement in performance over previously proposed methods.

We propose a hybrid ARQ (HARQ) scheme for which a rate-1/2 error-correcting code with code length equal to the packet length is used in the HARQ operation, where each packet comprises two subpackets of equal lengths. For the HARQ system with constant packet lengths, the utilization of subpackets enables the flexibility of carrying new message (or data) in the retransmissions. Hence, such a system can gain additional throughput as compared to the system using all-redundancy retransmissions under the conditions of moderate to high signal-to-noise ratios (SNR). In the proposed HARQ scheme, each of the subpackets can be chosen as a data part, or a redundancy part, or a function of two subpackets, where the data part or the redundancy part may belong to different codewords of the rate-1/2 error-correcting code. With a proper design of the function subpacket, we can adaptively control the error-correcting capability used in the HARQ operation. The key idea is that there is possibility of recovering three data subpackets in one retransmission and hence increasing the throughput. The price is that in each retransmission, up to three bits are needed in the feedback channel to indicate which subpacket is successfully recovered.

Interleave-division multiple-access (IDMA) is a multiple-access technique, which uses an elementary signal estimator (ESE) to achieve simple chip-by-chip detection. In this paper, we propose a new ESE which can be calculated directly based on the two-dimensional received signals. Hence, the proposed ESE can be applied to IDMA using signal modulation with either Gray labelling or non-Gray labelling. In contrast, the original ESE is calculated either based on the one-dimensional received signals or separately based on the real parts and the imaginary parts of the two-dimensional received signals. In fact, the original ESE can only be applied to IDMA using BPSK or Gray-labelled QPSK. From the proposed ESE, we can predict that the IDMA using the non-Gray labelling will be superior to the IDMA using the Gray labelling at the high signal-to-noise ratio (SNR) region. With EXIT (extrinsic information transfer) chart analysis, we can estimate the SNR region for which there is advantage of using non-Gray labelling for IDMA. The simulation results fit well with the theoretical analysis.

For the implementation of low-density parity-check (LDPC) decoders, the associated error performance and the complexity are significantly affected by the number of quantization bits used. In this paper, we propose an adaptive quantization scheme, which uses different quantization schemes at different iteration numbers based on a fixed number of quantization bits. Simulation results show that the proposed adaptive quantization can reduce the number of quantization bits without error performance degradation.

In this paper, we investigate the soft iterative decoding technique for ternary recoding systems with run-length-limited (RLL) constraints. We employ a simple binary-to-ternary RLL encoder following the LDPC (low density parity check) encoder. In the decoder, the iteratively passing of soft information between the LDPC decoder and a detector is used, where the detector is constructed for a combination of the RLL encoder, PLM (pulse length modulation) precoder and the partial response channel. We provide two different decoding algorithms. For one of the decoding algorithm, we are able to obtain bit-error-rate performance which is inferior to the comparable system without considering the RLL constraint for the high sign-to-noise ratio (SNR) regime and is better for the low-to-moderate SNR regime.

In this paper, a modified version of the A* algorithm for decoding linear block codes is proposed. By employing the early acquired information for some parity bits, we can improve the efficiency of the A* decoding algorithm.

We propose a multiple-candidate shaping technique for turbo coded modulation systems. Shaping gains are obtained by encoding each message into multiple turbo coded modulation sequences, called candidates, and then selecting the candidate with the lowest energy for transmission. Multiple candidates are generated by adding various scrambling sequences to each message sequence. The proposed shaping technique can also be applied to turbo coded modulation systems equipped with some other shaping methods to obtain additional shaping gains.

We investigate a binary code, which is implemented by serially concatenating a multiplexer, a multilevel delay processor, and a signal mapper to a binary turbo encoder. To achieve improved convergence behavior, we modify the binary code by passing only a fraction of the bits in the turbo code through the multilevel delay processor and the signal mapper. Two decoding methods are discussed and their performances are evaluated.

For a turbo coded BLAST (Bell LAbs Space-Time architecture) system with Nttransmit antennas and Nrreceive antennas, there is a significant gap between its detection threshold and the capacity in case Nt> Nr. In this paper, we show that by introducing a convolutional interleaver with block delay between the BLAST mapper and the turbo encoder, the threshold can be improved. Near-capacity thresholds can be achieved for some cases. To take advantage of the low detector complexity in Alamouti STBC (space-time block code), we also investigate a STBC system, which is the concatenation of the Alamouti STBC with a turbo trellis coded modulation. By using a proper labelling and adding a convolutional interleaver with block delay to such a STBC system, we achieve both lower error floors and lower thresholds.

A selective-mapping (SLM) scheme which does not require the transmission of side information and can reduce the peak to average power ratio (PAPR) in turbo coded orthogonal frequency-division multiplexing (OFDM) systems is proposed. The candidates of the proposed SLM are respectively generated by a turbo encoder using various interleavers. The waiver of side information can avoid the degradation of error rate performance which results from the incorrect recovery of side information at receiver in the conventional SLM OFDM system.

In this paper, we investigate detection-decoding algorithms for the near-capacity performances of turbo coded MIMO (multiple-input multiple-output) schemes in the fast fading channel. Both the conventional turbo coded MIMO scheme Gamma0and turbo coded MIMO scheme with interblock memory which is denoted by Gamma are investigated. Gamma is implemented by introducing some delay elements between the BLAST mapper and the turbo encoder. We show that, unlike Gamma0, the extrinsic information transfer (EXIT) curves of detector and turbo decoder in Gamma can match well. Hence, Gamma can provide error performances much better than Gamma0. In particular, we find an improved detection and decoding algorithm which can closely approach the Shannon capacity.

We investigate the performance of binary codes T constructed from turbo coding with interblock memory. The encoding of T is implemented by serially concatenating a multiplexer, a multilevel delay processor, and a signal mapper to the encoder of a conventional binary turbo code C. With such a construction, in T, there is some irregularity for the code bits in C. To provide more variety of irregularity, we can construct TCwhich is obtained by passing only a fraction of C through a multilevel delay processor and a signal mapper. We propose iterative decoding between adjacent codewords (IDAC), which provides error performance much better than the iterative decoding within a single codeword (IDSC). Simulation shows that T can have a lower error floor than C for either short or long code length. In some cases, TCcan provide better error floors and waterfall regions than C.

Repeated clipping and filtering (RCF) is a simple method for reducing the peak-to-average power ratio (PAPR) of the signal in the orthogonal frequency-division modulation (OFDM) system. We propose to modify RCF by limiting the distortion on each tone of the OFDM so that both low PAPR and low error can be achieved

In a paper authored by Ashikhmin, et. al., a low-density parity-check (LDPC) coded transmission scheme operated on multiple-input multiple-output (MIMO) fading channel was proposed, which can achieve capacity-approaching performance in case the code length is 100000 bits. In this paper, we add interblock memory to the LDPC or turbo coded MIMO system, in which only the receiver knows the channel. The simulation results show that this technique gives advantage in case that the code is short.

In this correspondence, it is shown that some convolutional codes with distinct memory sizes of minimal encoders are equivalent in the sense that the minimal trellises of these codes are the shifted versions of one another. For an$(n,k)$binary convolutional code, the weight spectrum obtained from the minimal trellis may be slightly different from that obtained from the conventional code trellis with$n$-bit branches. Code search is conducted to find some good$(n,n-1)$binary convolutional codes. Bounds on the trellis complexity, measured by the number of states and the number of branches in the minimal trellis module, of any convolutional code and its equivalent codes are also derived.

We propose a new PAPR reduction scheme for OFDM systems. The idea is to reduce PAPR and control clipping distortion simultaneously. The procedure includes setting a proper distortion bound and recursive operations of clipping, filtering and distortion control. The proposed scheme can achieve significant PAPR reduction while maintaining low error rate. For this scheme, PAPR reduction is obtained without any redundancy and no side information is needed in the OFDM receiver. Hence, OFDM systems using this scheme do not pay the price of the reduction of transmission rate or reliability for achieving PAPR reduction.

We show that the state complexity profile of a convolutional code C is the same as that of the reciprocal of the dual code of C in case that minimal encoders for both codes are used. Then, we propose an optimum permutation for any given (n, n-1) binary convolutional code that will yield an equivalent code with the lowest state complexity. With this permutation, we are able to find many (n, n-1) binary convolutional codes which are better than punctured convolutional codes of the same code rate and memory size by either lower decoding complexity or better weight spectra.

It is already known that a trellis code T, which is constructed by using the encoder of a convolutional code C with short constraint length followed by a delay processor and a signal mapper, is equivalent to a trellis code with large constraint length. In this paper, we derive a new lower bound on the free distance of T, which, in some cases, is better than the previously derived bound. Moreover, instead of the decoding used in earlier publications, we apply iterative decoding on both tailbiting and zero-tail representations of T to take advantage of the new lower bound and, in the meantime, to decrease the associated error coefficient caused by the decoding used in earlier publications. Comparisons among various designs of such a trellis code and some well-known coding methods are also provided.

This letter shows several methods for improving the decoding of noncoherent trellis-coded M-ary phase-shift keying. We propose two new metrics for the basic decision-feedback algorithm. These metrics are derived based on the idea of reducing the effect of incorrect amplitude of the reference signal. We also propose a new decoding algorithm that uses a simple way to estimate the metric of the future sequence.

A trellis code encoded by using the encoder of a convolutional code C with a short constraint length followed by an additional processing unit is equivalent to a trellis code with a large constraint-length. In 1993, Hellstern proposed a trellis coding scheme for which the processing unit consists of a delay processor and a signal mapper. With Hellstern's scheme, trellis codes with large free distances can be constructed. In this paper, we propose two trellis coding schemes. For the first scheme, the processing unit is composed of multiple pairs of delay processors and signal mappers. For the second scheme, the processing unit is composed of a convolutional processor and a signal mapper, where a convolutional processor is a rate 1 convolutional code. The trellis code constructed from each of the proposed schemes can be suboptimally decoded by using the trellis of the convolutional code C with some feedback information. Either of the proposed schemes can produce a trellis code that has a larger bound on free distance and better error performance as compared to the trellis code constructed from Hellstern's scheme based on the same convolutional code C.

Block-coded modulation with interblock memory (BCMIM) is a variation of block-coded modulation (BCM) which is designed for multilevel coding. By providing interblock memory between adjacent blocks, the coding rate of a BCMIM scheme can be increased without decreasing the minimum squared Euclidean distance (MSED) as compared to the original BCM. In an early version of BCMIM, interblock coding is provided only between the first two coding levels of adjacent blocks. In this paper, we design BCMIM with a more general form for which interblock coding can be introduced among many coding levels. In this way, we can further increase the coding rate of BCMIM without decreasing the MSED. We provide many examples to show the advantages of BCMIM with the general form. Most of the examples are designed based on multidimensional signal sets, since a multidimensional signal set can provide more coding levels than a two-dimensional (2-D) signal set.

We propose a trellis-coding scheme for which large free distances and low decoding complexities can be easily achieved. The proposed trellis-coding scheme is a generalization of the trellis-coding scheme proposed by Hellstern (1993). With the proposed trellis-coding scheme, we have the flexibility of controlling the decoding delay.

We show that decision-feedback differential phase detection (DFDPD) is equivalent to a technique which generates a phase reference by averaging several primitive phase references. We then modify the DFDPD into a differential phase detection (DPD) technique which generates the phase reference using a simple recursive form. The proposed technique can be easily implemented and has satisfactory error performance.

We derive a new upper bound on the pairwise error probability for MPSK sequences over the Rayleigh fading channel when channel state information (CSI) is not available. This is obtained by adding weight factors in calculating the symbol metrics. Simulation shows that the weight factors which optimize the upper bound are likely to optimize the error rate too. We also design multilevel coded MPSK schemes which are suitable for the Rayleigh fading channel. These schemes are basically in the form of block coded modulation with interblock memory (BCMIM), which was originally designed for an additive white Gaussian noise (AWGN) channel. The added weight factors are found to be effective in improving the error performance of these BCMIM schemes in case that CSI is not available.

A conventional decision feedback differential detection technique can be regarded as a technique using L previously received signal samples and L-1 previously decided data phases to generate a phase reference for the phase detection operation of a currently received MPSK signal sample. With this observation, we propose a differential detection technique which uses a new way to generate the phase reference. In the proposed technique, the phase reference called weighted phase reference is the weighted sum of primitive phase references derived from previously received signal samples. The weighted phase reference can be generated using a simple recursive form. The proposed detection technique can be easily implemented and has satisfactory error performance.

We propose a very powerful trellis coded modulation (TCM) scheme which has the structure of multilevel and single-stage coding.For the proposed TCM scheme, the encoder consists of a binary convolutional encoder which is followed by a multilevel delay processor and a signal mapper.By computer search, we find many useful TCM systems which are good for AWGN channels.

We propose a hybrid ARQ scheme which uses QPSK modulation for the first transmission and BPSK modulation for retransmissions. The throughput performance of the proposed ARQ scheme is better that those of ARQ schemes purely using QPSK modulation or purely using BPSK modulation for transmissions. Furthermore, the proposed scheme does not require any operation of error correction as usually required in hybrid ARQ schemes. Therefore, the ARQ scheme proposed in this paper can be easily implemented.>

Proposes a coded modulation scheme with interblock memory. The proposed scheme has a multi-stage coding structure. However, at some coding stage, the coding designs for every two adjacent blocks are related. Compared to coded modulation schemes for which each block is independent of the others, the introduction of interblock coding provides additional flexibility in the design. In this way, for the proposed scheme, one can achieve a large minimum Euclidean distance while the number of nearest neighbors is not too large. The authors also design a multi-stage decoding algorithm, which is optimum in each stage and has low decoding complexity. Three specific examples are provided to demonstrate the advantages of the proposed scheme.>

Proposes a new trellis coded modulation scheme which is constructed by combining a convolutional code and a variation of block coded modulation called block coded modulation with interblock memory. In the proposed scheme, each coded multidimensional signal point has a kind of two-fold dependency on other coded multidimensional signal points. In addition to the dependency on other coded multidimensional signal points described by the trellis of a convolutional code, each coded multidimensional signal point has another form of dependency on one previously coded multidimensional signal point. The additional dependency comes from the design of block coded modulation with interblock memory.>

The authors analyze an ARQ (automatic repeat request) scheme using parity retransmissions. By dividing each transmission block into subblocks, the combination of a transmission block and its retransmission block has the structure of a concatenated code. They derive formulae for calculating an upper bound on the probability of undetected errors and a lower bound on the throughput for such an ARQ scheme. Numerical results show that even with extremely simple code design, such an ARQ scheme has satisfactory performance.>