Error Rate Improvement in Underwater MIMO Communications Using Sparse Partial Response Equalization

Severe intersymbol interference (ISI) is one of the main obstacles for reliable signal reception in ATSC DTV systems. Decision feedback equalizers (DFEs) are commonly used to suppress the ISI. However, DFEs may suffer from error propagation due to incorrect symbol decisions from the symbol slicer. This phenomenon deteriorates the performance even more when the post-cursor ISI is strong. In order to reduce error propagation, we present a novel hybrid equalization scheme for ATSC channels. The proposed scheme consists of an adaptive decision feedback sparsening filter (DFSF), and an iterative maximum a posteriori (MAP) equalizer based on the belief propagation (BP) algorithm. In the first stage, instead of removing all the ISI from post cursors, the DFSF employs a modified feedback filter which leaves the strongest post-cursor ISI taps uncorrected. As a result, a long ISI channel is equalized to a sparse channel having only a small number of nonzero taps. In the second stage, a belief propagation algorithm is applied to mitigate the residual ISI. Since the channel is typically time-varying and suffers from Doppler fading, the DFSF is adapted using the least mean square (LMS) algorithm, such that the amplitude and the locations of the nonzero taps of the equalized sparse channel appear to be fixed. As such, the channel appears to be static during the second stage of equalization which consists of the BP detector. Simulation results demonstrate that the proposed scheme outperforms the traditional DFE in symbol error rate, under both static channels and dynamic ATSC channels.

We proposed two improved decoding algorithms for Low-Density Parity-Check (LDPC) codes based on the Belief-Propagation (BP) algorithm combined with Genetic Algorithm (GA). After giving a genetic interpretation of Tanner graph, GA is adopted to efficiently use the information passing from the variable nodes to the check nodes. Simulation results assert the superiority of our proposed algorithms over the BP algorithm both in BER (Bit Error Rate) and FER (Frame Error Rate). At last, optimization of the key parameter of the developed algorithms is given.

Point-to-point links using multiple transmitters and receivers or MIMO (multiple input, multiple output) configurations and associated signal processing at the receiver, can provide significant improvements in both data rate and reliability and is a promising technology for enhancing communications in the band-limited and highly-dynamic underwater acoustic (UWA) channel. Although the underwater channel impulse response extent can span tens to hundreds of symbols, it is generally sparse in nature and well suited for sparse partial response equalization (sPRE). This equalization scheme, which is not restricted to MIMO configurations, does not attempt to suppress intersymbol interference completely, rather it retains residual ISI in a controlled manner. This is accomplished by setting a sparse residual impulse response target generally similar in magnitude and time to the dominant, yet also sparse, arrivals within the actual channel impulse response. The resultant partial response equalizer is followed by a complexity-reduction detection scheme known as "belief propagation (BP)" which is an alternative to the optimal Viterbi or MAP (maximum a-posteriori probability) detector. The complexity of the optimal schemes grows exponentially with the total number of taps, regardless of structure; whereas the complexity of BP grows exponentially only with the non-zero taps. Thus the entire receiver structure, sPRE followed by BP, is suitable for the long, sparse channels since it allows more efficient exploitation of the channel structure. The proposed symbol recovery scheme was applied to data collected during a comprehensive multi-institution MIMO Experiment conducted within the Makai Experiment in 2005 off the northwest coast of Kauai, Hawaii. We have demonstrated a reduction in error rates over receiver algorithms using conventional decision feedback equalization techniques due to increased multipath diversity

In this paper, we have investigated the effect of differentiators on the performance of partial response maximum likelihood detection for optical recording under various noise conditions. Computer simulations and experiments with real signals have been conducted to compare the performance of Direct PRML and Differential PRML. It is seen that Direct PRML outperforms Differential PRML in electronic noise dominated system, while Differential PRML has better performance in media noise dominated system.

This paper is devoted to detection of signals with intentionally introduced intersymbol interference (ISI). Faster-than-Nyquist (FTN) signaling and optimal partial response signaling (PRS) are considered. As the detection algorithm it is used a sub-optimal modification of BCJR algorithm, named Max-Log-M-BCJR. Signals are compared in the plane of spectral efficiency and energy consumptions for the fixed value of bit error rate (BER) and different grades of detection algorithm complexity. It is shown that using the sub-optimal BCJR algorithm provides a noticeable decrease in the computational complexity of the detection. For deep ISI optimal PR signaling provides higher spectral efficiency as compared with FTN signaling and vise versa.

The major obstacle to shallow water acoustic communication is the interference of multipath signal results from surface and bottom reflections. Channel coding is indispensable in practical system to accommodate these adverse channel transmission characteristics due to the coding gain. In this paper, a channel model including time-varying fading, multipath and additive noise for the shallow water acoustic channels is built. Based on the channel model, the Probability Density Function (PDF) of initial decoding messages with Belief Propagation (BP) algorithm of LowDensity Parity-Check (LDPC) codes is deduced. The performance of the LDPC codes with BP algorithm is simulated, and the effects of multipath, fading velocity and channel interleaver on the decoding performance are studied. As the result, the following conclusions can be given: The performance of LDPC codes is excellent (Bit Error Rate (BER) is less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> ) over three-multipath shallow water acoustic channels, with 3~5 iterative decoding times and about 1000 bits code lengths; The BER of LDPC codes degrades with the increasing of the number of multipath; The BER of LDPC codes degrades slowly with the decreasing of the fading velocity, which shows the proposed channel code is not sensitive to the fading velocity of the channel.

In this presentation the issues concerning the impact of channel structure and dynamics on the design and performance of a decision feedback equalizer (DFE) type of the receiver for coherent underwater acoustic (UWA) telemetry is discussed. The receiver, developed as a part of the feasibility analysis of coherent communications over UWA telemetry channels, consists of a fractionally spaced DFE and a passband digital phase-locked loop. The adaptive algorithm for updating the receiver parameters is a combination of the recursive least-squares algorithm for the equalizer tap weights and a second-order phase update for carrier recovery. The receiver jointly performs channel equalization, symbol timing, and carrier phase synchronization, using the minimum mean-squared error criterion. Besides processing the single-channel signal, the receiver structure and the algorithm are extended to the multichannel case in which coherent diversity combining of different spatially distributed signals is performed. This receiver algorithm was applied to the experimental data originating from the three fundamentally different ocean environments, namely long range–deep water, long range–shallow water, and short range–shallow water channels. The experiments, conducted by the Woods Hole Oceanographic Institution, were performed in the deep waters off the coast of northern California (long range), at New England Continental Shelf (long range–shallow water), and in the Buzzards Bay (short range). Propagation in deep water, which occurs in convergence zones, results in long, but fairly stable multipath structures. Channel impulse responses, which are typically nonminimum phase, span several tens of milliseconds, requiring at least 40 taps in the feedforward section of the equalizer at data rates of 300 symbols per second. In the cases of strictly maximum phase channel responses, some reduction in complexity can be achieved by time-reversed equalization. The multipath structure of the shallow water channel is much less stable than that of the deep water channel, due to the presence of large amount of bottom and surface reverberation. The impulse responses are again nonminimum phase, typically characterized by extended multipath propagation following the main arrival. Equalizer lengths of as many as 100 feedforward and 80 feedback taps were needed in some cases of transmission at 1000 symbols per second. In all of the mentioned UWA channels, successful operation of the receiver algorithm for joint synchronization and equalization has been achieved. Experimental results assert the feasibility of coherently combining multiple arrivals at the expense of high computational complexity of the receiver. With the transmitted power constraint, performance limitations encountered at very high data rates lie both in the increased noise levels, as well as in the increased computational complexity of extremely long equalizer structures needed to overcome the intersymbol interference problem caused by multipath propagation. Future work should be directed towards finding the ways to reduce the equalizer complexity, which will result in the improved performance by virtue of reducing the noise enhancement in the equalizer.

In this paper, we consider the decoding of fountain codes where the received symbols may have errors. It is motivated by the application of fountain codes in DNA-based data storage systems where the inner code decoding, which generally has undetectable errors, is performed before the outer fountain code decoding. We propose a novel and efficient decoding algorithm, namely basis-finding algorithm (BFA), followed by three implementations. The key idea of the BFA is to find a basis of the received symbols, and then use the most reliable basis elements to recover the source symbols with the inactivation decoding. Gaussian elimination is used to find the basis and to identify the most reliable basis elements. As a result, the BFA has polynomial time complexity. For random fountain codes, we are able to derive some theoretical bounds for the frame error rate (FER) of the BFA. Extensive simulations with Luby transform (LT) codes show that, the BFA has significantly lower FER than the belief propagation (BP) algorithm except for an extremely large amount of received symbols, and the FER of the BFA generally decreases as the average weight of basis elements increases.

In this paper, we describe an improved adaptive partial response maximum likelihood (PRML) method combining modulation code for signal waveform modulation multi-level disc. This improved adaptive PRML method employs partial response equalizer and adaptive viterbi detector combining modulation code. Compared with the traditional adaptive PRML detector, the improved PRML detector additionally employs illogical sequence detector and corrector. Illogical sequence detector and corrector can avoid the appearance of illogical sequences effectively, which do not follow the law of modulation code for signal waveform modulation multi-level disc, and obtain the correct sequences. We implement the improved PRML detector using a DSP and an FPGA chip. The experimental results show good performance. The higher efficient and lower complexity can be obtained by using the improved PRML method than by using the previous PRML method. Meanwhile, resource utilization of the improved PRML detector is not changed, but the bit error rate (BER) is reduced by more than 20%.

Partial response maximum likelihood (PRML) detector chips are used in magnetic hard-disk drives. This paper describes the digital chip in a two-chip, 64 Mb/s PRML detector for magnetic hard-disk drives that use multi-zoned, variable-data-rate recording and embedded servo information. This PRML detector is incorporated in a high-capacity disk drive.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

For serial wireline communication beyond 56 Gb/s, bandwidth-efficient modulation is needed. Four-level pulse amplitude modulation (4-PAM) has become the standard technique at 56–64 and 112 Gb/s. However, whereas decision feedback equalization (DFE) with 5 taps or more was common for 2-PAM links at lower data rates, the speculative look-ahead techniques required to satisfy a DFE's timing requirements at 56 Gb/s increase power consumption exponentially with the number of taps and the number of modulation levels. Thus, 4-PAM DFEs at 56 Gb/s are generally limited to 2 taps or fewer. This limitation, in turn, necessitates the use of long (10 taps or more) finite impulse response (FIR) feed-forward equalization (FFE) to accurately eliminate the intersymbol interference in long reach (LR) channels. Thus, LR receivers at 56–64 and 112 Gb/s comprise an analog-to-digital converter (ADC) followed by digital equalization, and the transmitters increasingly use a digital-to-analog converter (DAC) preceded by a digital filter. Discrete multitone (DMT) signalling obviates the need for a long FIR FFE and DFE, and has demonstrated better spectral efficiency than 4-PAM above 50 Gb/s. In this work, we consider the potential of DMT for wireline communication beyond 100 Gb/s. For example, a spectral efficiency of 2.5 bits/sample is achievable over an IEEE P802.3ck channel with 18 dB loss at 40 GHz, affording an aggregate data rate of 200 Gb/s at 80 GS/s with 150 fs of jitter and 1.26 mV of noise at the input to the receiver. Significant improvement in bit error rate (BER) is obtained by increasing DAC resolution to 8 bits.

The fading caused by multipath and the effect of delay spread affect broadband wireless personal communications channels by introducing intersymbol interference, which appear when the root-mean-squared (rms) delay spread is significant in comparison to the duration of the transmitted symbols. This results, in the absence of equalizing, in an irreducible error probability. In this paper, we show that it is easy to obtain, for given power-delay profile models, the variance of the interference components at the output of a QPSK receiver. Using Gaussian approximations, a general form for a “fading factor” is defined. This approach is applied, in the particular cases of exponential and Maxwell power-delay profiles, to analyze the performance of coherent QPSK modulation over frequency-selective fading channels.

Two dimensional magnetic recording (TDMR) technology aims at achieving recording densities as high as 10 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with the current interest in achieving >1 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . In TDMR, the size of a bit is reduced to the order of the size of magnetic grains. The effects of this are two-fold: a) increased interference in cross-track as well as down-track directions and b) ultra high jitter noise due to irregular grain positions. Channel models that include the grain distributions on the medium give a more accurate jitter noise characteristics than the first order linear approximations of the jitter noise. Signal detection for 2D-ISI channels is well known to be NP-hard. JTED algorithm, proposed in [3], is proved to iteratively achieve maximum aposterior (MAP) performance. Partial response maximum likelihood (PRML) detection is a well known technique for reducing signal detection complexity by using a linear equalizer before maximum likelihood (ML) detection. The linear equalizer allows partial ISI as seen at the input of the ML detector. At high areal densities, the jitter noise is the dominant component of the noise observed in the read back signal. Noise predictive maximum likelihood (NPML) detection improves upon the PRML detection by decorrelating the noise. In this paper, we study the effects of grain density (average number of grains per channel bit) and jitter noise using a low complexity 2D NPML detector recently proposed in [2] over the granular media model. By using correlation properties of the jitter noise, we could achieve >1 .5dB gain in SNR at a chosen grain density. Gains in channel bit densities (CBD) of up to 10% are also observed.

The cache-enabled D2D network supports direct interconnection among users and can help to offload the data traffic through user caching. In this paper, we consider a reasonable caching strategy design in the cache-enabled D2D network to improve its performance. First we formulate an optimization problem aiming to minimize the average file download time of the users. Next we transform the original problem to a max-product form that can be distributed solved. Then we introduce the factor graph and the conventional belief propagation (BP) algorithm. Finally, we show how we design a BP algorithm with Randomized Gaussian Message Passing scheme and Weighting mechanism (BP-RW) to improve its convergence and performance. The distributed BP-RW algorithm can assign almost all computations to each user in the network, which will help to reduce the heavy computational overhead of the central controller. Meanwhile, simulation results show that the BP-RW algorithm performs better than the conventional BP algorithm, and performs very closely to the centralized greedy algorithm with much lower computational complexity.

In this paper, we develop a Belief Propagation (BP) algorithm for similarity computation to improve the recommendation accuracy of the neighborhood method, which is one of the most popular Collaborative Filtering (CF) recommendation algorithms. We formulate a probabilistic inference problem as to compute the marginal posterior distributions of similarity variables from their joint posterior distribution given the observed ratings. However, direct computation is prohibitive in large-scale recommender systems. Therefore, we introduce an appropriate chosen factor graph to express the factorization of the joint distribution function, and utilize the BP algorithm that operates in the factor graph to exploit the factorization for efficient inference. In addition, since the high degree at the factor node incurs an exponential increase in computational complexity, we also propose a complexity-reduction technique. The overall complexity of the proposed BP algorithm on a factor graph is linear in the number of variables, which ensures scalability. Finally, through experiments on the MovieLens dataset, we show the superior prediction accuracy of the proposed BP-based similarity computation algorithm for recommendation.