Performance of forward error correction and feedback coding schemes

This paper considers the optimal generator matrices of a given binary cyclic code over a binary symmetric channel with crossover probability p → 0 when the goal is to minimize the probability of an information bit error. A given code has many encoder realizations and the information bit error probability is a function of this realization. Our goal here is to seek the optimal realization of encoding functions by taking advantage of the structure of the codes, and to derive the probability of information bit error when possible. We derive some sufficient conditions for a binary cyclic code to have systematic optimal generator matrices under bounded distance decoding and determine many cyclic codes with such properties. We also present some binary cyclic codes whose optimal generator matrices are non-systematic under complete decoding.

This paper evaluates energy level performance of error control strategies in Wireless Sensor Networks (WSNs). More precisely Forward Error Correcting (FEC) and Automatic Repeat Request (ARQ) technique are studied for a square grid WSN. ARQ scheme is compared with FEC scheme in terms of Packet Error Rate (PER), energy efficiency and total energy spent to communicate packetized data. The impact of node spatial density and packet lengths on energy efficiency and energy expenditure is discussed. Further an optimum FEC scheme with the maximal energy efficiency for a given node spatial density and packet size is evaluated. The impact of node spatial density and packet length on optimal error correcting capability is indicated. Energy efficiency for several error correcting capabilities and packet length is also evaluated.

With the exponential growth of video traffic over wireless networked and embedded devices, mechanisms are needed to predict and control perceptual video quality to meet the quality of experience (QoE) requirements in an energy-efficient way. This paper proposes an energy-efficient QoE support framework for wireless video communications. It consists of two components: 1) a perceptual video quality model that allows the prediction of video quality in real-time and with low complexity, and 2) an application layer energy-efficient and content-aware forward error correction (FEC) scheme for preventing quality degradation caused by network packet losses. The perceptual video quality model characterizes factors related to video content as well as distortion caused by compression and transmission. Prediction of perceptual quality is achieved through a decision tree using a set of observable features from the compressed bitstream and the network. The proposed model can achieve prediction accuracy of 88.9% and 90.5% on two distinct testing sets. Based on the proposed quality model, a novel FEC scheme is introduced to protect video packets from losses during transmission. Given a user-defined perceptual quality requirement, the FEC scheme adjusts the level of protection for different components in a video stream to minimize network overhead. Simulation results show that the proposed FEC scheme can enhance the perceptual quality of videos. Compared to conventional FEC methods for video communications, the proposed FEC scheme can reduce network overhead by 41% on average.

In this paper, we use post processing methods to compensate the bit errors occurred in watermark embedding and extracting. Forward error correction (FEC)-based and chirp-based techniques are applied to encode and shape the embedded watermark message so that even at the presence of some bit error rates (BERs) in the extracted watermark, the watermarking algorithm be able to successfully estimate the correct embedded watermark message. Repetition and Bose-Chaudhuri-Hocquenghem (BCH) codings are used as two well-known FEC schemes, and discrete polynomial transform (DPPT) and Hough-Radon transform (HRT) are utilized as two chirp detectors in chirp-based watermarking. Robustness of all the proposed post processing methods are tested for checkmark benchmark attacks, and we found that the chirp-based watermarking using the DPPT chirp detector offers the highest watermark extraction rate, and the best bit error compensation even at BERs of higher than 17%.

Rate-adaptive optical transmission techniques adjust information bit rate based on transmission distance and other factors affecting signal quality. These techniques enable increased bit rates over shorter links, while enabling transmission over longer links when regeneration is not available. They are likely to become more important with increasing network traffic and a continuing evolution toward optically switched mesh networks, which make signal quality more variable. We propose a rate-adaptive scheme using variable-rate forward error correction (FEC) codes and variable constellations with a fixed symbol rate, quantifying how achievable bit rates vary with distance. The scheme uses serially concatenated Reed-Solomon codes and an inner repetition code to vary the code rate, combined with singlecarrier polarization-multiplexed M-ary quadrature amplitude modulation (PM-M-QAM) with variable M and digital coherent detection. A rate adaptation algorithm uses the signal-to-noise ratio (SNR) or the FEC decoder input bit-error ratio (BER) estimated by a receiver to determine the FEC code rate and constellation size that maximizes the information bit rate while satisfying a target FEC decoder output BER and an SNR margin, yielding a peak rate of 200 Gbit/s in a nominal 50-GHz channel bandwidth. We simulate single-channel transmission through a long-haul fiber system incorporating numerous optical switches, evaluating the impact of fiber nonlinearity and bandwidth narrowing. With zero SNR margin, we achieve bit rates of 200/100/50 Gbit/s over distances of 650/2000/3000 km. Compared to an ideal coding scheme, the proposed scheme exhibits a performance gap ranging from about 6.4 dB at 650 km to 7.5 dB at 5000 km.

In this work, we perform an analysis, in the context of channel equalization, of two criteria that can be considered central to the field of information theoretic learning (ITL): the minimum error entropy criterion (MEEC) and the maximum correntropy criterion (MCC). An original derivation of the exact cost function of these criteria in the scenario of interest is provided and used to analyze their robustness and efficiency from a number of relevant standpoints. Another important feature of the paper is an study of the estimated versions of these cost functions, which raises several aspects regarding parameters of the canonical Parzen window estimator. The study is carried out for distinct channel and noise models, both in the combined response and parameter spaces, and also employs as benchmarks crucial metrics like the probability of bit error. The conclusions indicate under what conditions ITL criteria are particularly reliable and a number of factors that can lead to suboptimal performance.

In this chapter, we describe different forward error correction (FEC) schemes currently in use or suitable for use in optical communication systems. We start with the description of standard block codes. The state-of-the-art in optical communication systems standardized by the ITU employ concatenated Bose–Chaudhuri–Hocquenghem (BCH)/RS codes [1, 2]. The RS(255,239), in particular, has been used in a broad range of long-haul communication systems [1, 2], and it is commonly considered as the first-generation of FEC [3, 4]. The elementary FEC schemes (BCH, RS, or convolutional codes) may be combined to design more powerful FEC schemes, e.g., RS(255,239) + RS(255,233). Several classes of concatenation codes are listed in ITU-T G975.1. Different concatenation schemes, such as the concatenation of two RS codes or the concatenation of RS and convolutional codes, are commonly considered as second generation of FEC [3, 4].

This paper shows an important enhancement of TCP behavior over the IEEE 802.11b Wireless Local Area Network (WLAN) if a combination of a Forward Error Correction (FEC) scheme and a Snoop agent is added to the idle Repeat reQuest (RQ) mechanism inherently used by such technology. The FEC scheme has been improved with some smart cross-layer optimizations, and its operation adapts to the channel conditions. Besides, the aim of the Snoop agent is to back up the FEC, overcoming the deficiencies of its adaptation, which are mainly due to the high variability of the channel inside a typical office environment. A complete experimental approach has been followed, and exhaustive measurement campaigns have been carried out over a real platform to derive a large number of performance parameters. Both methods have been implemented as modules belonging to a generic layer-two Performance Enhancing Proxy (PEP).

The performance of MIMO systems is investigated in a flat-fading scenario limited by cochannel interference. It is assumed that both the desired and interferer signals are Rayleigh-faded. We analyze the average probability of bit error of M-ary quadrature amplitude modulation in the presence of multiple independent interferers. The results are applicable to systems employing open-loop transmit diversity, and maximal ratio combining with coherent demodulation. We study the interaction between the number of equal power interferers and the spatial diversity order. The results indicate that the gain introduced by receive antennas is more robust to interference than the spatial diversity gain introduced by multiple transmitters. Moreover, we also show the effect of a varying number of interfering sources when spatial diversity is being exploited. Furthermore we derive a closed form expression of the asymptotic behavior of the average probability of bit error. This expression is then used to analytically explain the relation between number of interferers and diversity.

In recent years, due to the rapid convergence of multimedia services, Internet and wireless communications, there has been a growing trend of heterogeneity (in terms of channel bandwidths, mobility levels of terminals, end-user quality-of-service (QoS) requirements) for emerging integrated wired/wireless networks. Moreover, in nowadays systems, a multitude of users coexists within the same network, each of them with his own QoS requirement and bandwidth availability. In this framework, embedded source coding allowing partial decoding at various resolution is an appealing technique for multimedia transmissions. This dissertation includes my PhD research, mainly devoted to the study of embedded multimedia bitstreams in heterogenous networks, developed at the University of Bologna, advised by Prof. O. Andrisano and Prof. A. Conti, and at the University of California, San Diego (UCSD), where I spent eighteen months as a visiting scholar, advised by Prof. L. B. Milstein and Prof. P. C. Cosman. In order to improve the multimedia transmission quality over wireless channels, joint source and channel coding optimization is investigated in a 2D time-frequency resource block for an OFDM system. We show that knowing the order of diversity in time and/or frequency domain can assist image (video) coding in selecting optimal channel code rates (source and channel code rates). Then, adaptive modulation techniques, aimed at maximizing the spectral efficiency, are investigated as another possible solution for improving multimedia transmissions. For both slow and fast adaptive modulations, the effects of imperfect channel estimation errors are evaluated, showing that the fast technique, optimal in ideal systems, might be outperformed by the slow adaptive modulation, when a real test case is considered. Finally, the effects of co-channel interference and approximated bit error probability (BEP) are evaluated in adaptive modulation techniques, providing new decision regions concepts, and showing how the widely used BEP approximations lead to a substantial loss in the overall performance.

This paper presents an approach for the analysis of gated Gaussian impulsive noise and its effects in M-ary Quadrature Amplitude Modulation (M-QAM) schemes. In the approach, both amplitude variation and noisy pulse duration can be characterized as an amplitude modulation of the impulsive component by a discrete (binary or m-ary) random process. New exact expressions are obtained for the probability density function, autocorrelation function and power spectral density of the noise as well as for the bit error probability of M-QAM considering the maximum {\em a posteriori} probability optimum receiver. An important aspect of the proposed approach is the fact that the discrete random process incorporates the main parameters of the impulsive noise, such as amplitude, duration, instants in which the noise is added and time intervals between instants in which the noise is added.

A hybrid direct-sequence/frequency-hopping spread-spectrum communication modem for burst format transmission of digital data has been developed. A burst consists of a short synchronisation preamble and the data packet. Data modulation is accomplished by assignment of pairs of pseudonoise sequences with low crosscorrelation for message ones and zeros. The spreading code chip pattern is changed from bit to bit in both the preamble and the message portion of a burst. Receiver signal processing is based on the application of surface-acoustic-wave (SAW) elastic convolvers to programmable matched filtering. The performance of the system in an additive white Gaussian noise channel is analysed, measures of performance being the probability of burst loss and the bit error probability in the case of ideal synchronisation. Evaluations for a particular design are presented, and some experimental results obtained with a test system are shown for comparison.

In super-Nyquist wavelength division multiplexed (WDM) systems with frequency spacing smaller than the signal baudrate, the maximum-likelihood (ML) decoder in the receiver is usually introduced to compensate for intersymbol interference due to tight spectral filtering, such as polybinary shaping. After the ML decoder, symbol errors tend to propagate, causing excess continuous errors. Considering that forward error correction (FEC) is commonly introduced, the excess continuous errors degrade bit-error ratio (BER) performance after FEC, so-called post-FEC BER. In order to suppress the performance degradation, we introduce iterative decoding between the first ML decoder for polybinary shaping and the second FEC decoder in the receiver. First, we calculate BER characteristics of polybinary-shaped super-Nyquist WDM quadrature phase-shift keying (QPSK) signals. The results show that iterative decoding is effective for improving post-FEC BER performance. A lager pre-FEC BER threshold for post-FEC BER <; 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> is obtained in super-Nyquist WDM case than in the Nyquist WDM case, although a higher signal-to-noise ratio (SNR) is required. Next, we measure the BER characteristics of three-channel duobinary-shaped super-Nyquist WDM 12.5-Gbaud dual-polarization QPSK signals. The iterative decoding reduces the optical SNR penalty by 0.8 dB. A larger pre-FEC BER threshold of 3.1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> is obtained in the duobinary-shaped super-Nyquist WDM case, compared with the threshold of 2.2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> in the Nyquist WDM case.

We demonstrate experimentally for the first time the impact of forward error correction (FEC) on the performance of 622/1244 Mb/s burst-mode clock and data recovery (BM-CDR) with instantaneous phase acquisition (0 bit) for any phase step (plusmn27pi rads) for gigabit-capable passive optical network (GPON) optical line terminator (OLT) applications with (255, 239) Reed-Solomon (R-S) codes. Our design is based on commercially available SONET CDRs operated in 2times over sampling mode. This burst-mode receiver (BM-RX) provides a ~5 dB coding gain at bit error ratio (BER) of 10-10. We also show that this novel technique of employing FEC on BM-CDRs with fast phase acquisition time, provides a solution for fast burst-error correction giving reliable and predictable BERs in bursty-channels. The BM-RX meets the GPON physical media dependent layer specifications defined in the ITU-T G.984.2 recommendation. The coding gain can be used to increase the optical link budget as specified in the ITU-T G.984.3 standard, that is, support higher bit rates, achieve longer physical reach between the OLT and the optical network units (ONUs), as well as increase the number of splits per single PON tree.

With the volumes of transmitted information growth, the task of increasing the noise immunity and reliability of data transmission networks arises. The presence of interference such as nonlinear loss, chromatic dispersion, polarization mode dispersion, and inter-channel interference decreases the performance of fiber optical communication systems. Forward Error Correction (FEC) codes are vital in optical communication systems to achieve highly efficient and highly reliable communication. The paper presents research on a simulation model where FEC channel-coding schemes based on the Bose-Chaudhuri-Hocquenghem (BCH) cycling block code are integrated with non-return-to-zero on-off-keying (NRZ-OOK) modulated wavelength division multiplexed (WDM) fiber optical communication systems. The results highlight the selection of coding parameters in the adopted FEC approach. In our paper, the BCH (255, 231), BCH (255, 223), and BCH (255,191) FEC channel-coding schemes are chosen for integration in the NRZ-OOK modulated WDM optical transmission system. The paper shows the main advantages and drawbacks of the selected FEC coding scheme and provides a comparison of the proposed schemes based on their main features, such as bit error ratio (BER), which were obtained through the simulations of 25 Gbit/s NRZ-OOK WDM fiber optical system. The dynamics of changes in BER was investigated using the Monte Carlo (MC) method for precise results. The paper shows that integration of FEC channel-coding schemes based on the BCH codes improves the noise immunity and reliability of the WDM Fiber Optical Communication Systems.