Performance Improvement of Multi-Stage Threshold Decoding with Difference Register

Spatial modulation (SM) is a promising multiple- input multiple-output system used to increase spectral efficiency. The maximum likelihood (ML) decoder jointly detects the transmitted SM symbol, which is of high complexity. In this paper, a novel reliable sphere decoder (RSD) algorithm based on tree-search is proposed for the SM system. The basic idea of the proposed RSD algorithm is to reduce the size of the tree- search, and then, a smart searching method inside the reduced tree-search is performed to find the solution. The proposed RSD algorithm provides a significant reduction in decoding complexity compared to the ML decoder and existent decoders as well. Moreover, the RSD algorithm provides a flexible tradeoff between the bit error rate (BER) performance and decoding complexity, so as to be reliable for a wide range of practical hardware implementations. The BER performance and decoding complexity analysis for the RSD algorithm are studied, and Monte Carlo simulations are then provided to demonstrate the findings.

Irregular LDPC codes can achieve better error rate performance than regular LDPC codes. However, irregular LDPC codes have higher error floors than regular LDPC codes. The Ordered Statistic Decoding (OSD) algorithm achieves approximate Maximum Likelihood (ML) decoding. ML decoding is effective to lower error floors. However, the OSD estimates satisfy the parity check equation of the LDPC code even the estimates are wrong. Hybrid decoder combining LLR-BP decoding algorithm and the OSD algorithm cannot also lower error floors, because wrong estimates also satisfy the LDPC parity check equation. We proposed the concatenated code constructed with an inner irregular LDPC code and an outer Cyclic Redundancy Check (CRC). Owing to CRC, we can detect wrong codewords from OSD estimates. Our CRC-LDPC code with hybrid decoder can lower error floors in an AWGN channel. In wireless communications, we cannot neglect the effects of the channel. The OSD algorithm needs the ordering of each bit based on the reliability. The Channel State Information (CSI) is used for deciding reliability of each bit. In this paper, we evaluate the Block Error Rate (BLER) of the CRC-LDPC code with hybrid decoder in a fast fading channel with perfect and imperfect CSIs where 'imperfect CSI' means that the distribution of channel and those statistical average of the fading amplitudes are known at the receiver. By computer simulation, we show that the CRC-LDPC code with hybrid decoder can lower error floors than the conventional LDPC code with hybrid decoder in the fast fading channel with perfect and imperfect CSIs. We also show that combining error detection with the OSD algorithm is effective not only for lowering the error floor but also for reducing computational complexity of the OSD algorithm.

For space-time bit-interleaved coded modulation (ST-BICM) systems with iterative decoding, the overall perfor- mance is affected by the chosen mapping. In bit error rate (BER) curves, one mapping reaches an error floor at a low signal- to-noise ratio (SNR), while other mappings result in a lower error floor at a higher SNR. The constellation mappings are divided into groups where each group exhibits a distinctive BER curve. We show that the convergence abscissa of the system depends on the average total bit errors and the harmonic mean of the minimum squared Euclidean distance. In this paper, we characterize all mapping groups for ST-BICM with 8PSK and present the optimal selection for each mapping group over independent fading channels. I. INTRODUCTION Space-time coding techniques significantly improve trans- mission efficiency in radio channels by using multiple transmit and/or receive antennas and coordination of the signaling over these antennas. Bit-interleaved coded modulation with iterative decoding (BICM-ID) gives good diversity gains and Euclidean distance property with higher order modulation schemes using well known binary convolutional codes (1). Tonello (2) combined these two schemes as space-time BICM (ST-BICM) with Gray mapping. In this paper, we will first show that the asymptotic BER performance of ST-BICM system is equivalent to the single antenna BICM-ID case even when the throughput of ST-BICM is higher. This indicates that the total data rate of ST-BICM can be increased linearly with the number of transmit antennas while maintaining the same error probability as BICM-ID. This demonstrates the superior performance of ST-BICM. Motivated by the fact that the ST-BICM performance can be characterized by BICM-ID with the same code and mapping, we optimize the ST-BICM mappings based on the BICM-ID parameters. While the error floor (EF) bound (1) offers a good match for an error floor region, a heuristic analysis is still needed to study BER curve behaviors of BICM-ID for the water fall region. Thus, we derive design considerations based on both

In this paper, we propose a near maximum likelihood (ML) decoding technique, which reduces the computational complexity of the exact ML decoding algorithm. The computations needed for the tree search in the ML decoding is simplified by reducing the dimension of the search space prior to the tree search. In order to compensate performance loss due to the dimension reduction, a list stack algorithm (LSA) is considered, which produces a list of the top K closest points. The combination of both approaches, called reduced dimension list stack algorithm (RD-LSA), is shown to provide flexibility and offers a performance-complexity trade-off. Simulations performed for V-BLAST transmission demonstrate that significant complexity reduction can be achieved compared to the sphere decoding algorithm (SDA) while keeping the performance loss below an acceptable level.

In this paper, Multiple Input Multiple Output (MIMO) system with Space-Time Block Code (STBC) technique is used to satisfy the recent demands in the wireless communication system. That means the system should support the system’s high data rate, reliability, and performance in terms of the bit error rates. For achieving high data rates and high reliability, the antennas at the transmitter and the receiver side of the communication system should increase. Here we consider the 8 × 8 system it consists of eight antennas at both transmitter and receiver side. This 8 × 8 system matrix will design based on almouti codes. This almouti code with the STBC technique gives full data rates and high reliability. So by increasing the antennas, the high data rates by splitting the among the transmitter antennas. In this system at the receiver, the linear processing of the maximum likelihood (ML) decoding technique simplifies the decoding complexity. The simulation result shows the achieving high bit error rate (BER) and the channel capacity. The (8, 8) system outperforms the previous system without increasing the receiver decoding complexity.KeywordsMIMOSTBCML decoding

The increasing demand for high-density and high-speed digital optical recording systems has made the development of advanced coding and signal processing techniques for fast and reliable data recovery increasingly important. In recent years, the parity-check (PC)-code-based reception technique has been widely studied for magnetic recording systems, and it is projected to be highly promising for high-density optical recording. The PC code is an inner error correction code (ECC), which can detect dominant short error events of the system, using only a few parity bits. This reduces the loss in error correction capability of the outer ECC due to random short errors and results in a simple and efficient solution to improve the overall performance. This thesis is dedicated to the design and analysis of PCcode- based recording systems to achieve higher recording capacity with low implementation complexity, for high-density blue laser disc systems. In particular, most of the key components of the PC-code-based optical recording system have been designed and optimized for different recording densities, and different proportions of white noise and media noise. During the development of advanced coding and detection techniques, it becomes necessary to investigate the system’s performance with different coding schemes and recording densities. In Chapter 2 of the thesis, we propose a generalized Braat-Hopkins model for optical recording channels, which provides a fair basis for the performance comparison of detection schemes over different coding schemes and recording densities, for channels with additive, white Gaussian noise (AWGN) and media noise. Various basic issues associated with the PC-code-based systems are investigated in Chapter 3. These include bounds for bit error rates and error event probabilities, the dominant error events at channel detector output, different PC codes, simple and efficient post-processors, the impact of error events that are split across data block boundaries and the corresponding remedy, as well as the effects of code rates and recording densities. Simulation results show that a 4-bit PC code achieves the best performance. The corresponding bit error rates (BERs) are very close to the performance bounds, at both nominal and high densities. Constrained codes, which serve as a key component in the read-write channel of data storage systems, are desired to have a high code rate with low-complexity encoder/decoder. In Chapter 4, we investigate the design of certain capacity-approaching constrained codes for optical recording systems. In particular, we derive analytically the relationship between the number of encoder states and the maximum size of these codes. We identify the minimum number of encoder states that maximizes the code rate, for any desired codeword length. The design of constrained PC codes is key to the development of PCcode- based systems, and the systematic design of efficient constrained PC codes remains a challenging problem. In Chapter 5, we propose a general and systematic code design technique for constructing capacity-approaching constrained PC codes, which can detect any type of error events of the system, with the minimum code rate loss. Compared to the rate 2/3 code without parity, the newly designed constrained 4-bit PC code achieves a performance gain of 2 dB at nominal density, and 1.5 dB at high density, at BER = 10-5. As the dominant noise for high-density optical recording systems, media noise severely degrades the performance of channel detectors and postprocessors that are designed for AWGN. In Chapter 6, we propose two novel modifications to the bit detector to combat media noise. We further develop a data-dependent post-processing scheme for error correction. Compared to the system designed without considering media noise and without PC codes, the overall performance gain of the developed scheme can be more than 11 dB at high media noise levels. In data storage systems, the ECC failure rate (EFR) serves as the ultimate measure of the data recovery performance. In Chapter 7, we develop semi-analytical approaches for estimating the EFR, and analyze EFRs for the developed PC-code-based systems, for the cases without and with interleaving. Our analysis shows that with the optimum interleaving degrees, compared to the rate 9/13 code without parity, the 2-bit PC code achieves a gain of around 0.5 dB, and the 4-bit PC code gains 0.6 dB, at high record ing density and EFR = 10-16. The thesis concludes in Chapter 8 with some suggestions for further work.

We study the maximum a posteriori (MAP) decoding of memoryless non-uniform sources over multiple-antenna channels. Our model is general enough to include space-time coding, BLAST architectures, and single-transmit multi-receive antenna systems which employ any type of channel coding. We derive a closed-form expression for the codeword pairwise error probability (PEP) of general multi-antenna codes using moment generating function and Laplace transform arguments. We then consider space-time orthogonal block (STOB) coding and prove that, similar to the maximum likelihood (ML) decoding case, detection of symbols is decoupled in MAP decoding. We also derive the symbol PEP in closed-form for STOB codes. We apply these results in several scenarios. First, we design a binary antipodal signaling scheme which minimizes the system bit error rate (BER) under STOB coding. At a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> , this constellation has a channel signal-to-noise ratio (CSNR) gain of 4.7 dB over conventional BPSK signaling for a binary nonuniform source with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> Delta <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">=</sub> P(0) = 0.9. We next design space-time linear dispersion (LD) codes which are optimized for the source distribution under the criterion of minimizing the union upper bound on the frame error rate (FER). Two codes are given here: one outperforms V-BLAST by 3.5 dB and Alamouti's code by 12.3 dB at an FER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> for a binary source with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 0.9, and the other outperforms V-BLAST by 4.2 dB at an FER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> for a uniform source. These codes also outperform the LD codes of constructed under a different criteria. Finally, the problem of bit-to-signal mapping is studied. It is shown that for a binary source with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 0.9, 64-QAM signaling, and SER = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , a gain of 3.7 dB can be achieved using a better-than-Gray mapping. For a system with one transmit and two receive antennas that uses trellis coding with 16-QAM signaling, a 1.8 dB gain over quasi-Gray mapping and ML decoding is observed when MAP decoding is used for binary sources with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 0.9.

We are motivated by many applications such as problems that arise in online marketing applications, where the observations are governed by non-homogeneous Poisson models. We analyze the performance of a Maximum Likelihood (ML) decoder. We prove consistency and show an exponential rate of converge for sparse recovery in the high-dimensional Poisson setting. After verifying the efficiency of ML estimator empirically, we apply the ML decoder to study the dynamics of online marketing methods over time.

This paper proposes an efficient pruning algorithm for MIMO detector, which not only achieves the same performance of the maximum likelihood (ML) decoder, but also massively reduces the number of visiting nodes. The proposed algorithm applies correct sorting order so that it achieves the same performance of the ML decoder. Thanks to the use of the correct ordering, both child and sibling nodes can be pruned efficiently. As a result, the number of visiting nodes is significantly reduced. To acquire properly sorted order, we propose fast sorting algorithms that generate the exact sorted sequence. Furthermore, the proposed schemes can be applied in SISO MIMO detector. The advantages of the proposed sphere decoder become more pronounced in high-order modulation schemes.

We consider the topic of universal decoding with a decoder that does not have direct access to the codebook, but only to noisy versions of the various randomly generated codewords, a problem motivated by biometrical identification systems. Both the source that generates the original (clean) codewords, and the channel that corrupts them in generating the noisy codewords, as well as the main channel for communicating the messages, are all modeled by non–unifilar, finite–state systems (hidden Markov models). As in previous works on universal decoding, here too, the average error probability of our proposed universal decoder is shown to be as small as that of the optimal maximum likelihood (ML) decoder, up to a multiplicative factor that is a sub–exponential function of the block length. It therefore has the same error exponent, whenever the ML decoder has a positive error exponent. The universal decoding metric is based on Lempel–Ziv incremental parsing of each noisy codeword jointly with the given channel output vector, but this metric is somewhat different from the one proposed in earlier works on universal decoding for finite–state channels, by Ziv (1985) and by Lapidoth and Ziv (1998). The reason for the difference is that here, unlike in those earlier works, the probability distribution that governs the (noisy) codewords is, in general, not uniform across its support. This non–uniformity of the codeword distribution also makes our derivation more challenging. Another reason for the more challenging analysis is the fact that the effective induced channel between the noisy codeword of the transmitted message and the main channel output is not a finite–state channel in general.

Classical Turbo code suffers from high error floor due to its small minimum Hamming distance (MHD). Newly-proposed 3D-Turbo code can effectively increase the MHD and achieve a lower error floor by adding a rate-1 post encoder, through which part of the parity bits from the classical Turbo encoder are further encoded. In this paper, a novel bit-interleaved coded modulation (BICM) system is proposed by combining rotated mapping QAM and 3D-Turbo code to effectively improve the performance of 3D-Turbo code over Raleigh fading channels. A 2D iterative soft demodulating-decoding algorithm is developed for the proposed BICM system. Simulation results show that the proposed system can obtain about 0.8-1.0 dB gain at bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> , compared with the existing BICM system with Gray mapping QAM.

We propose Low Density Parity Check (LDPC) coded optical wireless communication systems with multiple subcarrier modulation (BPSK and QPSK). Upper bounds on the bit-error rate (BER) for maximum likelihood (ML) decoding of LDPC coded systems have been obtained on atmospheric optical channels where the effects of the scintillation exist. We also show that LDPC coded atmospheric optical systems have better BER than Turbo coded atmospheric optical systems.

In this paper, we derive a maximum-likelihood (ML) decoder of the differential data in a decode-and-forward (DF)-based cooperative communication system utilizing uncoded transmissions. This decoder is applicable to complex-valued unitary and nonunitary constellations suitable for differential modulation. The ML decoder helps to improve the diversity of the DF-based differential cooperative system using an erroneous relaying node. We also derive a piecewise linear (PL) decoder of the differential data transmitted in the DF-based cooperative system. The proposed PL decoder significantly reduces the decoding complexity, as compared with the proposed ML decoder, with no significant degradation in the receiver performance. Existing ML and PL decoders of the differentially modulated uncoded data in the DF-based cooperative communication system are only applicable to binary modulated signals like binary phase shift keying and binary frequency shift keying, whereas the proposed decoders are applicable to complex-valued unitary and nonunitary constellations suitable for differential modulation under uncoded transmissions. We derive a closed-form expression of the uncoded average symbol error rate (SER) of the proposed PL decoder with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M$</tex></formula> phase-shift keying constellation in a cooperative communication system with a single relay and one source–destination pair. An approximate average SER by ignoring higher order noise terms is also derived for this setup. It is analytically shown on the basis of the derived approximate SER that the proposed PL decoder provides full diversity of second order. In addition, we also derive the approximate SER of the differential DF system with multiple relays at asymptotically high signal-to-noise ratio (SNR) of the source–relay links. It is shown by simulations that the proposed PL decoder in the differential DF cooperative system with more than one relay also achieves the maximum possible diversity.

We consider an asynchronous cooperative communication system where two distributed transmitters are communicating with one destination. In this paper, a bounded delay-tolerant time interleave reversal Alamouti code (BDT-TIR AC) is proposed. BDT-TIR AC achieves full diversity, given that the path delay difference is within a tolerance limit. Furthermore, we design an efficient maximum-likelihood (ML) decoder. By employing a divide-and-conquer strategy, the original decoding problem is decoupled into several sub-problems in small size. In fact, these sub-problems contain either Alamouti code structure or only four symbols. By parallel decoding on the sub-problems, the proposed ML decoder exhibits low complexity advantage in large scale problems. Simulations of BDT-TIR AC confirm the full diversity gain. The bit error rate performance of BDT-TIR AC in the considered asynchronous scenarios is comparable with that of synchronized Alamouti code, and outperforms the latest delay-tolerant space-time code.

Space-time block codes from orthogonal designs proposed by Alamouti (1998), and Tarokh-Jafarkhani-Calderbank (199) have attracted much attention lately due to their fast maximum-likelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of a space-time block code from complex orthogonal designs for complex constellations is only 3/4 for three and four transmit antennas. Jafarkhani (see IEEE Trans. Commun., vol.49, no.1, p.1-4, 2001), and Tirkkonen-Boariu-Hottinen (see ISSSTA 2000, pp.429-432, September 2000) proposed space-time block codes from quasi-orthogonal designs, where the orthogonality is relaxed to provide higher symbol transmission rates. With the quasi-orthogonal structure, these codes still have a fast ML decoding, but do not have the full diversity. In this paper, we design quasi-orthogonal space-time block codes with full diversity by properly choosing the signal constellations. In particular, we propose that half symbols in a quasi-orthogonal design are from a signal constellation A and another half of them are optimal selections from the rotated constellation e/sup j/spl phi// A. The optimal rotation angles /spl phi/ are obtained for some commonly used signal constellations. The resulting codes have both full diversity and fast ML decoding.