Low-complexity detection schemes are studied for additive white Gaussian noise channels with an unknown and unbounded offset constant over each memory read. Detectors based on the Pearson distance are analyzed, and a new lower bound on the word error rate of Modified Pearson (MP) detection is derived. Three novel detectors are proposed: the Simplified Pearson (SP), the Ultra-Simplified Pearson (USP), and the Adjusted-Threshold (AT) detectors. The USP and AT detectors are designed to be robust against destructive readings. The proposed schemes are particularly suited for memory systems employing ramp-reading architectures. The analysis demonstrates that the proposed detectors achieve competitive error-rate performance with significantly reduced complexity compared to MP detection.

This work investigates the error performance of detection schemes based on the minimum Pearson distance in the context of additive white Gaussian noise channels with unknown and unbounded offset, constant throughout each channel use. We derive a lower bound on the word error rate under modified Pearson (MP) detection. Additionally, we introduce a new and low-complexity detection strategy, namely the Simplified Pearson (SP) detector. We analyze and compare the error performance of the SP detector with that of the MP detector.

An upper bound on the capacity of multiple-input multiple-output (MIMO) Gaussian fading channels is derived under peak amplitude constraints. The upper bound is obtained borrowing concepts from convex geometry and it extends to MIMO channels notable results from the geometric analysis on the capacity of scalar Gaussian channels. Relying on a sphere packing argument and on the renowned Steiner’s formula, the proposed upper bound depends on the intrinsic volumes of the constraint region, i.e., functionals defining a measure of the geometric features of a convex body. The tightness of the bound is investigated at high signal-to-noise ratio (SNR) for any arbitrary convex amplitude constraint region, for any channel matrix realization, and any dimension of the MIMO system. In addition, two variants of the upper bound are proposed: one is useful to ensure the feasibility in the evaluation of the bound and the other to improve the bound’s performance in the low SNR regime. Finally, the upper bound is specialized for two practical transmitter configurations, either employing a single power amplifier for all transmitting antennas or a power amplifier for each antenna.

Upper bounds on the capacity of vector Gaussian channels affected by fading are derived under peak amplitude constraints at the input. The focus is on constraint regions that can be decomposed in a Cartesian product of sub-regions. This constraint models a transmitter configuration employing a number of power amplifiers less than or equal to the total number of transmitting antennas. In general, the power amplifiers feed distinct subsets of the transmitting antennas and partition the input in independent subspaces. Two upper bounds are derived: The first one is suitable for high signal-to-noise ratio (SNR) values and, as we prove, it is tight in this regime; The second upper bound is accurate at low SNR. Furthermore, the derived upper bounds are applied to the relevant case of amplitude constraints induced by employing a distinct power amplifier for each transmitting antenna.

In this paper an analytical model is introduced to describe the impulse response of the diffusive channel between a pointwise transmitter and a given fully-absorbing (FA) receiver in a molecular communication (MC) system. The presence of neighbouring FA nanomachines in the environment is taken into account by describing them as sources of negative molecules. The channel impulse responses of all the receivers are linked in a system of integral equations. The solution of the system with two receivers is obtained analytically. For a higher number of receivers the system of integral equations is solved numerically. It is also shown that the channel impulse response shape is distorted by the presence of the neighbouring FA interferers. For instance, there is a time shift of the peak in the number of absorbed molecules compared to the case without interference, as predicted by the proposed model. The analytical derivations are validated by means of particle based simulations.

The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented. Furthermore, it is provided an iterative algorithm to numerically evaluate both the information capacity and the optimal input distribution of such channel.

Absorbing sets (ASs) cause the error floor phenomenon in many low-density parity-check (LDPC) codes by entrapping iterative decoders. A recent simplified system model for practical min-sum (MS) LDPC decoding predicts that if all variable nodes in an AS have channel messages above a certain threshold, the AS cannot entrap the decoder. The threshold is an AS parameter that depends on its Tanner graph, and is the result of a nonlinear optimization. In this paper, we analyze the messages exchanged in the directed graph (digraph) of the AS during MS decoding while evaluating the AS threshold. By doing this, we unveil the meaning of the threshold value, which is the minimum channel message for which positive feedback loops in the digraph involve all the messages exchanged.

We evaluate capacity bounds for multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) fading channels subject to input amplitude constraints. We focus on two practical cases, in which the transmitter: (i) employs a single antenna amplifier, which induces a constraint on the norm of the input vector, and (ii) it employs multiple amplifiers, one per antenna, which leads to independent constraints on the amplitude of each input vector entry. For both cases, we evaluate the asymptotic capacity gap between upper and lower bounds at high signal-to-noise ratio.

An upper bound on the capacity of multiple-input multiple-output (MIMO) additive white Gaussian noise fading channels is derived under peak amplitude constraints. The tightness of the bound is investigated at high signal-to-noise ratio (SNR), for any arbitrary convex amplitude constraint region. Moreover, a numerical simulation of the bound for fading MIMO channels is analyzed, at any SNR level, for a practical transmitter configuration employing a single power amplifier for all transmitting antennas.

In this paper, we consider spatially coupled LDPC codes derived from protographs. In particular, we analyze the performance of the window decoder (WD), which allows reducing the complexity, the memory requirements, and the latency of the flood belief-propagation decoder. We show that the performance degradation of WD is due to the fact that it exploits a single decoding wave instead of two. This has effect both in the ideal case of infinite code length, where it may imply a threshold loss, and in the case of finite length, where it affects the slope of the BER curve in the waterfall region. We show how a forward-backward decoder can reduce such problems at the price of a limited increase of average complexity.

In this paper, the definition of threshold of elementary absorbing sets is extended to scaled Min-Sum low-density parity-check (LDPC) decoding. Based on the analysis of the behavior of scaled Min-Sum LDPC decoders in the Tanner graph of the absorbing set, it is proven that correct decoding is guaranteed with received channel messages above threshold. A fast algorithm for the threshold computation is derived. Many examples of absorbing sets taken from LDPC codes of various variable node degrees are investigated, and it is shown that all of them can be deactivated with low enough scaling factors.

Emerging memory technologies (like PCM, MRAM and 3D XPoint) can make data storage as fast as the rest of the system. But to cope with the reliability targets of storage applications, error correcting codes (ECCs) able to correct many errors might be needed anyway. Hierarchical codes, ECCs enabling two levels of correction, can be good candidates to satisfy these reliability targets, without impacting (on average) the low-latency characteristics of these technologies. In particular, an Ultra-Fast (UF) ECC can be used as first trial as long as it is able to flag its failures with high probability and low latency. In this paper we design an UF-ECC able to produce a check for incorrect decoding with probability lower than the typical target uncorrectable bit-error rate (UBER) of storage applications (e.g. 1e-15) and with a latency comparable with the UF-ECC correction process.

Absorbing sets (ASs) cause the error floor phenomenon in many Low-Density Parity-Check (LDPC) codes. A recent, simplified system model for Min-Sum (MS) LDPC decoding [1] predicts that ASs exhibit a threshold behavior: if all variable nodes in an AS have channel messages above the threshold, the AS cannot trap the decoder. The threshold is a real-valued parameter that depends on the topology of the AS, and can be evaluated by a nonlinear optimization. In this paper we describe a simple, fast algorithm for evaluating the AS threshold. Additionally, we show that the algorithm is valid also for scaled-MS decoding. We show with an example that the threshold values under scaled-MS decoding are smaller than under MS decoding. Accordingly, scaling decreases the error floor.

The error floor phenomenon in many low-density parity-check (LDPC) codes is caused by combinatorial objects in their Tanner graph, known as absorbing sets. In this paper, we highlight a threshold behavior for the min-sum decoding algorithm in the graph of an absorbing set with fixed-point representation of messages. For an absorbing set of interest in a binary LDPC code we can compute the threshold, a novel real-valued parameter that is closely related to its harmfulness. We show that absorbing sets with negative thresholds cannot trap the decoder if the dynamic range of the extrinsic messages is large enough. We also prove that, in regular LDPC codes, absorbing sets with negative thresholds exist if the variable node degree is odd. The examples presented in this paper show that odd-column-weight LDPC codes can have many absorbing sets with negative thresholds, but that these absorbing sets do not trap a well-designed decoder. Simulations show a good agreement between the results of the analysis presented in this paper and the performance of practical decoders with fixed-point messages.

High-performance storage class memories could benefit from a fast decoding error correcting code (ECC), able to correct a few errors in just a few nanoseconds. The class of BCH codes provides excellent candidates to play this role. The low latency requirement prevents adopting iterative or sequential processes in the encoding and decoding phases-as traditionally done for storage application based on Flash NAND technology. Therefore, we propose an architecture for fast decoding of double and triple ECCs. In our architecture, any time-consuming iterative computation is eliminated, and the most complex evaluations are isolated and carried in parallel with the other terms, to avoid bottlenecks in the decoder. In particular, the error locator polynomial is computed by a combinatorial logic, and its roots are searched by testing all the bits simultaneously. Here, we describe a gate-level design of these architectures. We also give an in-depth analysis of hardware-oriented implementations of finite field operations, and of bases for element representation.

In this paper, we consider Block Differential Modulation (BDM), to tackle the phase slip problem in digital communication systems. When the received signal phase can drift, the synchronizer can suddenly choose a wrong reference phase, e.g. adding multiples of 2π/M in case of M-ary Phase Shift Keying. Phase slips are detrimental for any coherent system since they cause long error bursts, till an opposite phase slip occurs. BDM is a generalization of Differential Modulation (DM). Neither of them relies on the absolute carrier phase. However, BDM differentially encodes information between small blocks of symbols and exploits couples of adjacent blocks to decode. This allows simple and practical demapping, without sacrificing capacity. We show that for low and moderate phase slip probabilities, BDM approaches the constrained capacity of coherent transmission, in particular at high spectral efficiencies. We provide closed-form results for the constrained capacity in absence of phase slips for Phase Shift Keying and Quadrature Amplitude Modulation, and we evaluate numerically the constrained capacity through an efficient Monte Carlo method, when phase slips occur. Besides, we provide simple upper and lower bounds.

In this paper, we consider joint estimation of the channel length and of the impulse response for OFDM systems, exploiting information criteria to find the best trade-off, in terms of Kullback-Leibler divergence, between noise rejection and channel description accuracy. So far, information criteria have not been used for practical channel length estimation methods, due to their prohibitive complexity. We show how to make them affordable, performing channel estimation in a recursive way that allows to establish the optimal channel length with a moderate incremental cost. With reference to IEEE 802.11 OFDM-based standards for WLAN, we investigate several cases, applying the joint channel length and impulse response estimation to many scenarios, ranging from the simplest pilot-aided channel estimation based on training sequences, to the most challenging data-aided channel tracking, driven either by detected or by decoded symbols. In all cases, the achieved performance and robustness are very good, with a very small increase in complexity w.r.t. estimation methods that assume fixed channel length.

In order to estimate the Hurst parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR). Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with an other method of common use based on wavelet analysis. Here we link it to the wavelets setting and stress why a different analysis for the two approaches is required. We then focus on the asymptotic analysis of the MAVAR log-regression estimator and provide new formulas for the related confidence intervals. By numerical evaluation, we analyze these formulas and make a comparison between three suitable choices on the regression weights, also optimizing over different choices on the data progression.

In this paper, we consider joint estimation of the channel length and of the impulse response for OFDM systems, exploiting information criteria, to find the best trade-off between noise rejection and channel description accuracy. So far, information criteria have not been considered practical channel estimation methods, due to their prohibitive complexity. We show how to make them affordable, performing channel estimation in a recursive way that allows to establish the optimal channel length with a moderate incremental cost. Focusing on the 802.11 wireless LAN family, we investigate several cases, applying the joint channel length and impulse response estimation to many scenarios, ranging from the simplest pilot-aided channel estimation based on training sequences, to the most challenging data-aided channel tracking, driven either by detected or decoded symbols. In all cases, the performance and robustness are very good, with a very small increase in complexity w.r.t. estimation methods that assume fixed channel length.

We investigate a property that we have found in many efficient bilinear cyclic convolutions in GF (2m). We show that this property can reduce the additive complexity of cyclotomic FFTs. We explain how it arises, and why the most common constructions of cyclic convolutions yield this beneficial feature.

This paper is focused on cyclotomic Fourier transforms in GF(2m), and on their applications to algebraic decoding of Reed-Solomon codes, like the evaluation of syndromes and of error locator (or evaluator) polynomials. Cyclotomic transforms are much more efficient than straightforward evaluation. In particular, the number of multiplications is quite small. In this paper it is shown that also the number of additions can be considerably reduced with respect to previous analyses. A simple interpretation of the cyclotomic Fourier transform best suited for the evaluation of syndromes allows to assemble the required matrix easily and quickly, even in large fields. Fast construction of such matrices is important to obtain the best results, since as many matrices as possible must be generated and compared. It is shown that both the structure of the matrix and of bilinear convolutions need to be exploited, to reduce the complexity of the costly part of cyclotomic Fourier transforms, which is a matrix-vector product. Heuristic algorithms for matrix-vector product are to be run as many times as possible to obtain the best transform. It is shown with several examples that very good results can be obtained even with very simple algorithms.

In this paper we introduce an innovative version of the recently proposed Layered ORthogonal lattice Detector (LORD). LORD is an attractive MIMO detection algorithm, which aims to approach the optimal Maximum-Likelihood (ML) detection performance with a reasonable complexity, quadratic in the number of transmitting antennas rather than exponential. LORD is also well suited to a hardware (e.g. ASIC or FPGA) implementation because of its regularity, deterministic latency and parallelism. Nevertheless, its complexity is still high in case of high cardinality constellations, such as the 64-QAM foreseen by the 802.11n standard. We show that, when only global latency constraints exist, e.g. a fixed time to detect the whole OFDM symbol, the LORD complexity can be remarkably reduced (up to 60%), still approaching the ML performance.

We propose a novel family of Soft-Input Soft-Output detectors for iterative, point-to-point, MIMO receivers. Compared to the optimal Maximum A Posteriori receiver, low complexity is achieved restricting the detector search to small subsets of the entire QAM hyper-symbol constellation, through simple criteria. These criteria are applied to an improved version of the non-iterative Layered ORthogonal lattice Detector. We show that, notwithstanding the suboptimal low-complexity implementation, this detector approaches the EXtrinsic Information Transfer of the MAP detector. Therefore, when included in an iterative receiver it delivers the same performance. Furthermore, the deterministic complexity and highly parallelizable structure of the proposed detector are well suited for HDL and ASIC implementation. To focus on a specific setting, we consider the indoor MIMO wireless LAN 802.11n standard, taking into account errors in Channel Estimation and a frequency selective, spatially correlated channel model.

In this paper we introduce an improved version of the turbo layered orthogonal lattice detector (T-LORD), recently presented. This implementation, namely K-Best T-LORD, misses the performance of the turbo MAP detector by only few tenths of dB in various configurations, like the fully enhanced T-LORD. However, its complexity is quadratic in the number of transmitting antennas instead of exponential. Moreover, we show that the K-Best T-LORD is robust also over realistic channels, with correlation between tones and antennas, and with imperfect channel state Information at the receiver. This behavior is shown not only via Monte Carlo simulations, but also with EXIT chart analysis.

We reconsider the role of user selection in multiuser MIMO broadcast channels (downlink), in the relevant regime where the number of users K is linear in the number of transmitter (base station) antennas M. User selection is known to achieve mutually quasi-orthogonal user channels and, at the same time, a multiuser diversity effect in terms of receiver SNR. These goals are achieved in the regime of fixed number of transmit antennas, and very large number of users. In contrast, we show that when K = O(M) these effects cannot be achieved, and the role of user selection is marginal. In terms of system design, our results suggest that only a small number K ¿ M of users should feedback their channel state information at each point in time. This greatly alleviates the burden of the channel state information feedback, while achieving essentially optimal performance.

In this letter we propose rate variable turbo codes based on the parallel concatenation of tailbiting Recursive Systematic multi-binary (m-ary) convolutional codes. Rate variability is not achieved by puncturing, which can have adverse effects on the minimum distance of the code. Using a variable number of input lines of the encoder, we obtain several different overall rates ranging from 1/2 to 7/8. The most suitable Soft-in- Soft-out decoding algorithm for these turbo codes is based on the Dual Reciprocal Code, which is very efficient for high rate codes. A particular interleaver design, namely the "backbone" interleaver, guarantees a high Hamming weight in codewords with information weight 2 and 3, as well as good minimum distances and fairly low multiplicities for higher information weights. Therefore, these codes have very low error floors.

In this paper we deal with Maximum Likelihood (ML) decoding of Turbo Codes on the Binary Erasure Channel. First we describe a new ML decoder. When the standard iterative decoder fails because the set of erasures includes a stopping set, with the component decoders we obtain a linear system of equations that seeks the codeword constrained by both component codes. We evaluate the complexity in terms of equivalent turbo iterations and we show that this ML decoder is implementable. We also modify the algorithm proposed in [6] for LDPC to decode Turbo Codes and we compare the two methods. We find that, in general, our method is more efficient with low memory or punctured codes. Finally, by simulation we show that m-ary Turbo Codes under ML decoding outperform the error exponent bounds for random codes down to WER=10-6, for all rates ranging from 1/3 to 7/8.

In this paper we propose a coding-decoding scheme to be used for II-type hybrid ARQ on a binary erasure channel model, based on rate compatible punctured binary Turbo Codes, DRP interleaver design and ML decoding at the receiver. We carefully design the interleaver and the puncturing mask, and we describe how to achieve low-complexity Maximum Likelihood decoding. We show for the case of an MPEG2 packet size that this scheme overrides random codes upper bounds, providing throughputs within 0.05 bits from capacity at word error rates greater or equal to 10-6.

In this paper a novel Soft-Input Soft-Output detector, namely Turbo-LORD, is proposed for iterative MIMO receivers. This is an improved version, capable of managing a priori information, of the Layered ORthogonal lattice Detector recently presented. The implementation is straight and efficient when there are only two transmitting antennas. However, problems arising with more than two antennas are also discussed, along with possible solutions. It is shown that notwithstanding the suboptimal low-complexity implementation, this iterative receiver misses the performance of the turbo MAP detector by only few tenths of dB in various configurations, with very high spectral efficiency.

In this paper we consider an iterative detection and decoding scheme for Space-Frequency-Bit-Interleaved Coded Modulation (SF-BICM) MIMO-OFDM systems as a candidate receiver architecture for Next Generation Wireless LANs. This work is focused on the implementation complexity reduction of the overall turbo MIMO scheme through the simplification of the three main blocks: the Soft-Interference-Canceller, the MMSE-MIMO detector and the MIMO Soft-Symbol demapper which uses extrinsic soft information, produced by a Soft-Output-Viterbi-Algorithm (SOVA), to perform the LLRs calculation of the coded bits. A new receiver architecture is proposed, its computational complexity is estimated and compared with a more classical turbo MMSE receiver, both for 16-QAM and 64-QAM constellations.

This paper presents a robust method for fast visual tags reading, suitable for augmented reality (AR) environments. Tag detection is based on well known tools of image-processing, but their combination, together with the use of colored markers, allows a robust recognition even with low-cost CMOS or CCD cameras and in poorly illuminated environments. In particular the color mix and the structure of the tag are quite unusual in common environments and can be easily detected with color filtering and geometric analysis. The proposed tag carries binary information encoded in its structure: in the presented implementation a 32-bit code with 12 parity bits is encoded in the tag but extensions to longer codes can be easily devised.

In this letter, a turbo product code (TPC) is combined with multilevel modulations (8-phase-shift keying and 16-quadrature amplitude modulation). The component codes are Bose-Chaudhuri-Hocquengem (BCH) or extended BCH. We derive soft-input/soft-output modules based on the dual code, with exact Euclidean metrics, and we show that the iterative TPC decoder gains no advantage in performance from this. Next, we evaluate asymptotic approximations for maximum-likelihood (ML) decoding from a combinatorial approach that can be applied to any bit-interleaved multilevel modulated code, once the first term (or terms) of the Hamming weight spectrum are known. For the TPCs and modulations studied in this letter, random bit interleaving before modulation leads to improved ML asymptotes. Simulations confirm that this advantage is maintained also under iterative decoding.

We consider turbo decoding of parallel concatenated single parity check (SPC) (K+1,K) codes, with row-column interleaving. The existence and uniqueness of the asymptotic probability density evaluated with the turbo algorithm is proved for every length K and every signal-to-noise ratio (SNR).

We propose a variation of the algorithm for the construction of "spread" or S-random interleavers. This new version guarantees good spread properties that are also maintained under pruning. This makes this kind of interleaver attractive for those applications which require flexible size interleavers, such as flexible block size turbo codes, and flexible rate serially concatenated turbo codes.

The performance of a Reed-Solomon (RS) code has an analytical expression if the errors at the input of the decoder are independent. In concatenated schemes, this condition is often obtained through an interleaving device disrupting the correlation between erroneous symbols. Sometimes the ideal depth of such interleaver is too large to implement, and the RS decoder must operate in suboptimal conditions, for which no analytical formulas are available. In this paper, we present a statistical model that allows analytical evaluation of the performances of a concatenated scheme with an inner turbo code and an outer RS code, in the case of under-dimensioned interleavers. The model requires a statistical analysis of the erroneous symbols at the output of the inner decoder.

An importance sampling technique, tuned for the simulation of ideal or suboptimal MAP bit-per-bit decoding, is applied to some examples of turbo product codes, i.e. to turbo decoding of the product of block codes. The simulation results show the remarkable performances of the suboptimal algorithms. The presence of the so called "knee" in the performance curves, predicted by the maximum likelihood asymptotic bound, is also confirmed.