A Belief Propagation Based Framework for Soft Multiple-Symbol Differential Detection

Soft noncoherent detection, which relies on calculating the \textit{a posteriori} probabilities (APPs) of the bits transmitted with no channel estimation, is imperative for achieving excellent detection performance in high-dimensional wireless communications. In this paper, a high-performance belief propagation (BP)-based soft multiple-symbol differential detection (MSDD) framework, dubbed BP-MSDD, is proposed with its illustrative application in differential space-time block-code (DSTBC)-aided ultra-wideband impulse radio (UWB-IR) systems. Firstly, we revisit the signal sampling with the aid of a trellis structure and decompose the trellis into multiple subtrellises. Furthermore, we derive an APP calculation algorithm, in which the forward-and-backward message passing mechanism of BP operates on the subtrellises. The proposed BP-MSDD is capable of significantly outperforming the conventional hard-decision MSDDs. However, the computational complexity of the BP-MSDD increases exponentially with the number of MSDD trellis states. To circumvent this excessive complexity for practical implementations, we reformulate the BP-MSDD, and additionally propose a Viterbi algorithm (VA)-based hard-decision MSDD (VA-HMSDD) and a VA-based soft-decision MSDD (VA-SMSDD). Moreover, both the proposed BP-MSDD and VA-SMSDD can be exploited in conjunction with soft channel decoding to obtain powerful iterative detection and decoding based receivers. Simulation results demonstrate the effectiveness of the proposed algorithms in DSTBC-aided UWB-IR systems.Comment: 14 pages, 12 figures, 3 tables, accepted to appear on IEEE Transactions on Wireless Communications, Aug. 201

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 (mMTC). In this paper, we design a LDPC coded SCMA detector by combining the sparse graphs of LDPC and SCMA into one joint sparse graph (JSG). In our proposed scheme, SCMA sparse graph (SSG) defined by small size indicator matrix is utilized to construct the JSG, which is termed as sub-graph based joint sparse graph of SCMA (SG-JSG-SCMA). In this paper, we first study the binary-LDPC (B-LDPC) coded SGJSG- SCMA system. To combine the SCMA variable node (SVN) and LDPC variable node (LVN) into one joint variable node (JVN), a non-binary LDPC (NB-LDPC) coded SG-JSG-SCMA is also proposed. Furthermore, to reduce the complexity of NBLDPC 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 (JTDD) algorithm is proposed to reduce the computational complexity of NB-LDPC coded SGJSG- SCMA system. According to the simulation results, SG-JSGSCMA brings significant performance improvement compare to 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 to the Turbo approaches

Turbo Decoding and Detection for Wireless Applications

A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannon’s visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannon’s capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted

Low-Complexity LP Decoding of Nonbinary Linear Codes

Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most important problem with LP decoding for both binary and nonbinary linear codes is that the complexity of standard LP solvers such as the simplex algorithm remains prohibitively large for codes of moderate to large block length. To address this problem, two low-complexity LP (LCLP) decoding algorithms for binary linear codes have been proposed by Vontobel and Koetter, henceforth called the basic LCLP decoding algorithm and the subgradient LCLP decoding algorithm. In this paper, we generalize these LCLP decoding algorithms to nonbinary linear codes. The computational complexity per iteration of the proposed nonbinary LCLP decoding algorithms scales linearly with the block length of the code. A modified BCJR algorithm for efficient check-node calculations in the nonbinary basic LCLP decoding algorithm is also proposed, which has complexity linear in the check node degree. Several simulation results are presented for nonbinary LDPC codes defined over Z_4, GF(4), and GF(8) using quaternary phase-shift keying and 8-phase-shift keying, respectively, over the AWGN channel. It is shown that for some group-structured LDPC codes, the error-correcting performance of the nonbinary LCLP decoding algorithms is similar to or better than that of the min-sum decoding algorithm.Comment: To appear in IEEE Transactions on Communications, 201

Synchronization recovery and state model reduction for soft decoding of variable length codes

Variable length codes exhibit de-synchronization problems when transmitted over noisy channels. Trellis decoding techniques based on Maximum A Posteriori (MAP) estimators are often used to minimize the error rate on the estimated sequence. If the number of symbols and/or bits transmitted are known by the decoder, termination constraints can be incorporated in the decoding process. All the paths in the trellis which do not lead to a valid sequence length are suppressed. This paper presents an analytic method to assess the expected error resilience of a VLC when trellis decoding with a sequence length constraint is used. The approach is based on the computation, for a given code, of the amount of information brought by the constraint. It is then shown that this quantity as well as the probability that the VLC decoder does not re-synchronize in a strict sense, are not significantly altered by appropriate trellis states aggregation. This proves that the performance obtained by running a length-constrained Viterbi decoder on aggregated state models approaches the one obtained with the bit/symbol trellis, with a significantly reduced complexity. It is then shown that the complexity can be further decreased by projecting the state model on two state models of reduced size