Trellis-based Detection Research Articles

Asynchronous Transmission for Multiple Access Channels: Rate-Region Analysis and System Design for Uplink NOMA

In this work, we thoroughly analyze the rate-region provided by the asynchronous transmission in multiple access channels (MACs). We derive the corresponding capacity-regions, applicable to a wide range of pulse shaping methods. We analytically prove that asynchronous transmission enlarges the capacity-region of MACs. Although successive interference cancellation (SIC) can achieve the optimal sum-rate for the conventional uplink non-orthogonal multiple access (NOMA) methods, it is unable to achieve the boundary of the capacity-region for the asynchronous transmission. We demonstrate that for the asynchronous transmission, the optimal SIC decoding order to achieve the maximum sum-rate is based on the users' channel strengths. This optimal ordering is in contrast to the conventional uplink NOMA, where various decoding orders can result in the maximum sum-rate. Furthermore, we provide practical transceiver designs to approach the capacity-region. The memory induced by asynchronous transmission enables the use of the trellis-based detection methods which improves the performance. In addition, we propose a transceiver design, based on channel diagonalization to exploit the frequency-selectivity introduced by timing offsets. The proposed transceiver design, joint with the turbo principle, enables us to achieve a rate pair that is not achievable by the synchronous transmission.

Sub-Graph Based Joint Sparse Graph for Sparse Code Multiple Access Systems

Sparse code multiple access (SCMA) is a promising air interface candidate technique for next-generation mobile networks, especially for massive machine-type communications. In this paper, we design a low-density parity-check (LDPC) coded SCMA detector by combining the sparse graphs of LDPC and SCMA into one joint sparse graph (JSG). In our proposed scheme, the SCMA sparse graph defined by small size indicator matrix is utilized to construct the JSG, which is termed as sub-graph-based JSG of SCMA (SG-JSG-SCMA). In this paper, we first study the binary-LDPC coded SG-JSG-SCMA system. To combine the SCMA variable node and LDPC variable node into one joint variable node, a non-binary LDPC (NB-LDPC) coded SG-JSG-SCMA is also proposed. Furthermore, to reduce the complexity of NB-LDPC coded SG-JSG-SCMA, a joint trellis representation (JTR) is introduced to represent the search space of NB-LDPC coded SG-JSG-SCMA. Based on JTR, a low complexity joint trellis-based detection and decoding algorithm is proposed to reduce the computational complexity of the NB-LDPC coded SG-JSG-SCMA system. According to the simulation results, SG-JSG-SCMA brings significant performance improvement compare with the conventional receiver using the disjoint approach, and it can also outperform a turbo-structured receiver with comparable complexity. Moreover, the joint approach also has advantages in terms of processing latency compare with the turbo approaches.

Simplification of strip‐wise algorithms applied for two‐dimensional intersymbol interference detection

With the development of the high-speed communication channel or high-capacity storage device, the intersymbol interference (ISI) occurs more frequently in the condensed data. The traditional Bahl – Cocke – Jelineu – Raviv (BCJR) method is capable of solving the two-dimensional (2D) symbol influence problem with extremely high cost. By analysing the complexity in terms of branch, state and path in the 2D trellis-based ISI detection, the authors verify that the system complexity is mainly dominated by the window size. To reduce the detection complexity, the conventional simplifications are applied in the 2D strip-wise ISI detection. In addition, a two-phase strip-wise detection is proposed to achieve a lower complexity than that of the conventional simplifications. In this system, the first detector can be realised by a low-complexity method (like the hard detection or Viterbi algorithm) to provide the mask shrinking with predicted data. After reducing the mask size, the second detector can detect the main portion of ISI by the trellis-based detection (like BCJR algorithm) with a small mask. Under the similar detection performance, the proposed scheme can achieve more than 91.76% saving in the metric computation compared with the 5 × 3-window IRCSDFA (iterative row–column soft-decision feedback algorithm) simplified by the M-algorithm with M = 8.

Detection by multiple trellises

In this paper, we present a novel pragmatic approach, referred to as detection by multiple trellises, to perform trellis-based detection over realistic channels. More precisely, we consider channels with unknown parameters and apply the concept of detection by multiple trellises to forward-backward (FB) algorithms. The key idea of our approach consists, first, of properly quantizing the channel parameters and, then, considering replication of coherent FB algorithms operating on parallel trellises, one per hypothetical quantized value. In order to make the receiver robust against a possibly time-varying channel parameters, the proposed soft-output algorithms perform a proper manipulation of the forward and backward metrics computed by the parallel FB algorithms at regularly spaced trellis steps. We consider two significant examples of application: detection over (i) phase-uncertain channels and (ii) fading channels. The performance of the proposed algorithms is investigated considering differentially encoded (DE) quaternary phase shift keying (QPSK) and iterative detection schemes based on low-density parity-check (LDPC) codes. Besides having a low complexity, the proposed soft-output algorithms turn out to be robust, flexible, blind, in the sense that no knowledge of the channel parameter statistics is required, and highly parallelizable, as it is desirable in high-throughput future wireless communication systems.

Towards Efficient Detection of Two-Dimensional Intersymbol Interference Channels

This paper gives a survey and comparison of algorithms for the detection of binary data in the presence of two-dimensional (2-D) intersymbol interference. This is a general problem of communication theory, because it can be applied to various practical problems in data storage and transmission. Major results on trellis-based detection algorithms, previously disparate are drawn together, and placed into a common framework. All algorithms have better complexity than optimal detection, and complexity is compared. On the one hand, many algorithms perform within 1.0 dB or better of optimal performance. On the other hand, none of these proposed algorithms can find the optimal solution at high SNR, which is surprising. Extensive discussion outlines further open problems.

Complexity Reduction of Iterative Receivers Using Low-Rank Equalization

This paper covers the consideration of an iterative or turbo receiver where the nonlinear trellis-based detection of the interleaved and coded data bits is replaced by linear detection using the Wiener filter (WF), i.e., the optimal linear filter based on the mean-square error (MSE) criterion. The equalization of channels with multiple antennas at the receiver as well as frequency-selective transfer functions requires high-dimensional observation vectors which involve computationally intense detectors. We extend an optimal but computationally efficient algorithm, originally derived for single receive antenna systems, to single-input multiple-output (SIMO) channels. To further reduce computational complexity, we apply the suboptimal low-rank multistage WF (MSWF), i.e., the WF approximation in the low-dimensional Krylov subspace, and replace additionally second-order statistics of nonstationary random processes by their time-invariant averages. Complexity investigations reveal the enormous capability of the proposed algorithms to decrease computational effort. Moreover, the analysis based on extrinsic information transfer (EXIT) charts as well as Monte Carlo simulations show that compared with reduced-rank detection methods based on eigensubspaces, the reduced-rank MSWF behaves near optimum although the rank is drastically reduced to two or even one

On Trellis-Based Truncated-Memory Detection

We propose a general framework for trellis-based detection over channels with infinite memory. A general truncation assumption enables the definition of a trellis diagram, which takes into account a considered portion of the channel memory and possible coding memory at the transmitter side. It is shown that trellis-based maximum a posteriori (MAP) symbol detection algorithms, in the form of forward-backward (FB) algorithms, can be derived on the basis of this memory-truncation assumption. A general approach to the design of truncated-memory (TM) FB algorithms is proposed, and two main classes of algorithms, characterized by coupled and decoupled recursions, respectively, are presented. The complexity of the derived TM-FB algorithms is analyzed in detail. Moreover, it is shown that MAP sequence detection algorithms, based on the Viterbi algorithm, follow easily from one of the proposed classes. Looking backward at this duality between MAP symbol detection algorithms and MAP sequence detection algorithms, it is shown that previous solutions for one case can be systematically extended to the other case. The generality of the proposed framework is shown by considering various examples of stochastic channels. New detection algorithms, as well as generalizations of solutions previously published in the literature, are embedded in the proposed framework. The obtained results do suggest that the performance of the proposed detection algorithms ultimately depends on the truncation depth, almost regardless of the specific detection strategy.

Iterative Detection/Decoding for Two-Track Partial Response Channels

In this letter, we investigate the iterative detection/decoding algorithms for two-track partial response channels. We first describe the iterative algorithm as an iterative message-passing/processing algorithm over a high-level normal graph and then propose two trellis-based detection algorithms. The natural one is based on a joint trellis, which can be implemented for low-order channels. For moderate-order channels, we propose a separated detection, which is based on two single-track trellises. Compared with the joint detection, the separated detection is simpler in most cases. Simulation results show that, for two-track EPR4 channels with minor intertrack interferences, the separated detection causes only marginal degradation in performance.

Receivers with widely linear processing for frequency-selective channels

We propose several equalization schemes based on widely linear processing (WLP). The received signal and its complex conjugate are separately filtered and the results are linearly combined. It is shown that WLP yields a gain in performance if the (noiseless) received signal can be interpreted as the convolution of a real-valued data sequence and an equivalent complex-valued intersymbol interference channel impulse response. Such a model applies to, e.g., amplitude-shift keying, offset quadrature amplitude modulation, and binary minimum-shift keying-type modulation. We consider receivers without and with decision feedback. Finite impulse response filters are derived for these structures, which are optimum with respect to the zero-forcing and minimum mean-squared error (MMSE) criteria, respectively. In the MMSE case, adaptive algorithms for filter adjustment are given. Infinite filter orders are investigated in order to obtain analytical performance results. Furthermore, suboptimum trellis-based detection with widely linear preprocessing is briefly discussed. It is demonstrated analytically and by numerical examples that widely linear schemes may outperform conventional schemes significantly, depending on the considered application.

Adaptive modulation techniques for duplex OFDM transmission

The design tradeoffs of turbo-coded burst-by-burst adaptive orthogonal frequency division multiplex (OFDM) wideband transceivers are analyzed. We demonstrate that upon aiming for a higher throughput a higher proportion of low-quality OFDM subcarriers has to be used for the transmission of inherently vulnerable high-order modem modes, transmitting several bits per subcarrier. Upon invoking turbo coding and adjusting the modem mode switching regime near-error-free performance can be achieved at the cost of a reduced throughput. Various blind modem mode detection techniques have also been investigated and the most complex channel coding trellis-based detection algorithm was found to be the most powerful. Last, the design tradeoffs of spectral pre-equalization have been explored and quantified. We concluded that AOFDM provides a convenient framework for adjusting the required target integrity and throughput both with and without turbo channel coding.