Bandwidth‐efficient turbo coding over Rayleigh fading channels

Introduced in 1993, turbo codes can achieve high coding gains close to the Shannon limit. In order to design power and bandwidth‐efficient coding schemes, several approaches have been introduced to combine high coding rate turbo codes with multilevel modulations. The coding systems thus obtained have been shown to display near‐capacity performance over additive white Gaussian noise (AWGN) channels. For communications over fading channels requiring large coding gain and high bandwidth efficiency, it is also interesting to study bit error rate (BER) performance of turbo codes combined with high order rectangular QAM modulations. To this end, we investigate, in this paper, error performance of several bandwidth‐efficient schemes designed using the bit‐interleaved coded modulation approach that has proven potentially very attractive when powerful codes, such as turbo codes, are employed. The structure of these coding schemes, termed ‘bit‐interleaved turbo‐coded modulations’ (BITCMs), is presented in a detailed manner and their BER performance is investigated for spectral efficiencies ranging from 2 to 7 bit/s/Hz. Computer simulation results indicate that BITCMs can achieve near‐capacity performance over Rayleigh fading channels, for all spectral efficiencies considered throughout the paper. It is also shown that the combination of turbo coding and rectangular QAM modulation with Gray mapping constitutes inherently a very powerful association, since coding and modulation functions are both optimized for operation in the same signal‐to‐noise ratio region. This means that no BER improvement is obtainable by employing any other signal constellation in place of the rectangular ones. Finally, the actual influence of the interleaving and mapping functions on error performance of BITCM schemes is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

An integrated FEC coding scheme for ATM transmission over regenerative satellite networks

The application of asynchronous transfer mode (ATM) on both wireless and satellite networks requires system adaptation. This adaptation has to improve the overall system's performance, and achieve high quality‐of‐service classes approaching that for fibre‐optic communications. In this paper, a new integrated forward‐error‐correction (FEC) coding scheme is introduced for ATM transmission over regenerative satellite networks. The proposed FEC scheme is a concatenation of two Reed–Solomon codes tailored for the header and payload parts of the ATM cell. This integrated coding scheme is shown to significantly improve the cell loss ratio as compared to the standard CRC code used in the ATM cell header. We obtain both upper and lower performance bounds for the concatenated code and check their accuracy when compared to exact system's performance. Both analytical and simulation results show that a cell loss ratio and bit‐error rate (BER) of 10^?25 and 10^?7 can be, respectively, achieved with minimum delay requirements on the SATCOM link. Finally, an approximation for the system's throughout is obtained. It is shown that using a hybrid selective‐repeat automatic‐repeat‐request (SR‐ARQ) with the RS code, a large throughput of approximately 0.843 can be achieved at BERs lower than 10^?7 for data services. Copyright © 2005 John Wiley & Sons, Ltd.     

Turbo码概率-代数联合解码算法

Turbo码采用修正的BAHL et al.算法实现解码.这是一种基于软值的概率迭代解码算法.本文在保持Turbo码迭代软解码算法优点的基础上,充分利用Turbo码编码器结构这一确知条件,结合代数解码原理,提出了一种Turbo码概率-代数联合解码算法.该算法结合了概率解码和代数解码的优点,又有效避免了误差传播的发生,使Turbo码的纠错性能在原经典算法的基础上得到进一步的提高.该算法不仅为降低Turbo码的比特误码率和误差地板值提供了一种新的研究途径,而且因其更好的纠错性能而具有十分明显的实用价值.仿真实验结果显示,在比特误码率(BER)为10^-3~10^-4时,与经典Turbo码解码算法相比,采用该算法能获得0.1dB左右的编码增益.     

Signalling enhancement on multilevel turbo codes

The design of multilevel turbo codes using M‐PSK is optimized to achieve a low bit error rate (BER). Unequal error protection is employed via group set partitioning in multi‐stage decoding to minimize the error propagation and BER. Simulation results are performed under Gaussian and Rayleigh fading channels to depict the superiority of the new scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

Performance of DS/CDMA-based equatorial LEO satellite system usingturbo-codes

Improving the bit error rate (BER) performance at low elevation angles is a crucial determining factor for the capacity of any low earth orbit (LEO) satellite system. In previous work, it has been demonstrated that the BER performance of a DS/CDMA-based equatorial LEO satellite system on a downlink can be improved significantly by using satellite diversity. The authors address the issue of improving BER at low elevation angles by using turbo codes     

Performance of zero cross correlation resultant weight spectral amplitude codes in lower Earth orbit‐based optical wireless channel system

A consolidated performance investigation and design of newly constructed zero cross correlation resultant weight (ZCCRW) code is presented without mapping over optical wireless channel (OWC) in lower Earth orbit (LEO). Multiple access interference (MAI) is suppressed by incorporating proposed 1‐D code at 10 Gbps with an algorithm. A further state of the art comparison of diverse optical code division multiple access (OCDMA) codes such as multi diagonal codes and diagonal double weight codes is accomplished with proposed code in terms of root mean square (RMS) jitter, extinction ratio, MAI, quality factor (QF), and bit error rate (BER) at different linewidths, chip sizes, link lengths, and active users. It is perceived that for ZCCRW code, QF obtained is 16.5 for chip size (0.1 ns), and at 4000 km, BER 10^‐9 is achieved using the forward error correction (FEC) technique. OWC system in LEO with lasers in spectral amplitude code (SAC) OCDMA is proposed for the first time as per the author's best knowledge.     

Performance of a turbo‐coded CDMA system in a mobile satellite channel

The bit error rate (BER) performance of a turbo‐coded code‐division multiple‐access (CDMA) system operating in a satellite channel is analysed and simulated. The system performance is compared for various constituent decoders, including maximum a posteriori probability (MAP) and Max‐Log‐MAP algorithms, and the soft‐output Viterbi algorithm. The simulation results indicate that the Max‐Log‐MAP algorithm is the most promising among these three algorithms in overall terms of performance and complexity. It is also shown that, for fixed code rate, the BER performance is improved substantially by increasing the number of iterations in the turbo decoder, or by increasing the interleaver length in the turbo encoder. The results in this paper are of interest in CDMA‐based satellite communications applications. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance of transmitted reference pulse cluster ultra‐wideband systems with forward error correction

Recently, an improved transmitted reference (TR) signaling scheme, referred to as transmitted reference pulse cluster (TRPC), was proposed for low‐rate ultra‐wideband (UWB) communications. Compared with conventional TR, TRPC has a more compact and uniform spacing for the reference and data pulses and therefore addresses the implementation problems posed by the long delay line requirement, as well as provides better bit error rate (BER) performance. In this paper, a TRPC‐UWB system, which includes practical forward error correction (FEC) coding such as that specified in the IEEE 802.15.4a standard, as well as more powerful convolutional codes, is developed. A performance analysis, which highlights the importance of selecting appropriate FEC codes, is presented. Results show that with a suitable FEC code, the TRPC‐UWB system is a promising candidate for low‐rate wireless personal area networks. Copyright © 2012 John Wiley & Sons, Ltd.     

Low-complexity BCH codes with optimized interleavers for DQPSK systems with laser phase noise

The presence of high phase noise in addition to additive white Gaussian noise in coherent optical systems affects the performance of forward error correction (FEC) schemes. In this paper, we propose a simple scheme for such systems, using block interleavers and binary Bose–Chaudhuri–Hocquenghem (BCH) codes. The block interleavers are specifically optimized for differential quadrature phase shift keying modulation. We propose a method for selecting BCH codes that, together with the interleavers, achieve a target post-FEC bit error rate (BER). This combination of interleavers and BCH codes has very low implementation complexity. In addition, our approach is straightforward, requiring only short pre-FEC simulations to parameterize a model, based on which we select codes analytically. We aim to correct a pre-FEC BER of around \(10^{-3}\). We evaluate the accuracy of our approach using numerical simulations. For a target post-FEC BER of \(10^{-6}\), codes selected using our method result in BERs around 3\(\times \) target and achieve the target with around 0.2 dB extra signal-to-noise ratio.     

Adaptive predistortion of COFDM signals for a mobile satellite channel

In this paper, we consider the optimization of the performance of QPSK and 16‐QAM coded orthogonal frequency division multiplexing (COFDM) signals over the non‐linear and mobile satellite channel. A high power amplifier and Rician flat fading channel produces non‐linear and linear distortions; an adaptive predistortion technique combined with turbo codes will reduce both types of distortion. The predistorter is based on a feedforward neural network, with the coefficients being derived using an extended Kalman filter (EKF). The conventional turbo code is used to mitigate Rician flat fading distortion and Gaussian noise. The performance over a non‐linear satellite channel indicates that QPSK COFDM followed by a predistorter provides a gain of about 1.7 dB at a BER of 3×10^?3 when compared to QPSK COFDM without the predistortion scheme and 16‐QAM COFDM provides a gain of 0.5 dB output back‐off and 1.2 dB signal to noise ratio at a BER of 3×10^?5 when compared with an adaptive predistorter based on the Harmmerstein model. We also investigate the influence of the guard time interval and Doppler frequency effect on the BER performance. When the guard interval increases from 0 to 0.125T samples and the normalized Doppler frequency is 0.001, there is a gain of 0.7 and 1 dB signal to noise ratio at a BER of 6×10^?4 for QPSK and 16‐QAM COFDM, respectively. Copyright © 2003 John Wiley & Sons, Ltd.     

A spread slotted CDMA/ALOHA system with hybrid ARQ for satellitemultiple access

We propose and investigate a new type of satellite multiple access protocol that combines the characteristics of the spread slotted (SS)-ALOHA protocol, code division multiple access (CDMA), and the hybrid automatic repeat request (ARQ) error controlling and retransmission scheme, in order to increase the throughput by reducing the number of retransmissions and to keep the bit error rate (BER) of the satellite link low when the channel experiences heavy traffic. The main feature of our proposed system is the utilization of two different fields in the analysis of the satellite multiple access problem. Since the hub now possesses the forward error correction (FEC) capability to correct errors that appear after the CDMA despreading of the packets, the satellite does not need to ask so often for the retransmission of erroneous packets and will ask for retransmission only when the FEC error correcting capability is exceeded. This paper also presents the adaptive optimization of the balance between the CDMA processing gain and FEC coding gain in order to obtain a better throughput for the SS-CDMA/ALOHA with hybrid ARQ protocol for satellite multiple access. The optimization is made with the constraint of keeping the bandwidth of the transmitted packets constant during all times. According to this, the effective throughput of the protocol (information bits over total transmitted bits ratio) is improved by adaptively changing the CDMA and FEC codes used in the transmission. This adaptive optimization is done by observing the channel status or load and increasing or decreasing both coding schemes' gains. Computer simulations show the performance of the proposed multiple access scheme     

Performance of Hybrid Error Control Schemes of Satellite Channels

The effectiveness of hybrid error control schemes involving forward error correction (FEC) and automatic repeat request (ARQ) is examined for satellite channels. The principal features of the channel are: large round-trip transmission delay due to the satellite link, and burst errors introduced by the terrestrial links that connect the users to the satellite link. The performance is estimated for two channels described by Fritchman's simple partitioned finite-state Markov model, and is compared to that obtainable if the channel is considered as a binary symmetric channel of the same bit error probability. Results show that the hybrid schemes offer substantial improvement over ARQ and FEC, and that an optimum exists for the number of errors corrected to obtain maximum throughput efficiency.     

Improving energy efficiency using a link adaptation algorithm dedicated for 100 Gbps wireless communication

This paper presents a link adaptation algorithm dedicated for 100 Gbps wireless transmission. Interleaved Reed-Solomon codes are selected as forward error correction (FEC) algorithms. The redundancy of the codes is selected according to the channel bit error rate (BER). The uncomplicated FEC scheme allows implementing a complete data link layer processor in an FPGA (field programmable gate array). In our case, we use the Virtex7 FPGA to validate the functionality of our implementation. The proposed FPGA-processor achieves 169 Gbps throughput. Moreover, the implementation is synthesized into 40 nm CMOS technology and the described link adaptation algorithm allows reducing consumed energy per bit to values below 1 pJ/bit at BER <1e−4. With higher BER, the energy increases up to ∼13 pJ/bit.     

Performance analysis of MIMO systems with multiuser diversity

In this paper, we present a comprehensive performance analysis for multiple‐input multiple‐output (MIMO) systems with multiuser diversity over Rayleigh fading channels. We derive exact closed‐form expressions of the outage probability and the average bit error rate (BER) for different MIMO schemes, including the selective combining (SC), maximum ratio combining (MRC) and space‐time block codes (STBC). We also provide the explicit upper bounds on the BER performance. Finally, the mathematical formalism is verified by numeric results that study the interaction between the antenna diversity and the multiuser diversity. It is observed that the system performance is deteriorated as the number of transmit antennas increases in multiuser scenario, which is unlike the case in single‐user systems. Copyright © 2007 John Wiley & Sons, Ltd.     

Carrier phase recovery for turbo‐coded systems with pre‐coded GMSK modulation

A carrier phase recovery scheme suited for turbo‐coded systems with pre‐coded Gaussian minimum shift keying (GMSK) modulation is proposed and evaluated in terms of bit‐error‐rate (BER) performance. This scheme involves utilizing the extrinsic information obtained from the turbo‐decoder to aid an iterative carrier phase estimation process, based on a maximum‐likelihood (ML) strategy. The phase estimator works jointly with the turbo‐decoder, using the updated extrinsic information from the turbo‐decoder in every iterative decoding. A pre‐coder is used to remove the inherent differential encoding of the GMSK modulation. Two bandwidths of GMSK signals are considered: BT=0.5 and 0.25, which are recommended by the European Cooperation for Space Standardization (ECSS). It is shown that the performance of this technique is quite close to the perfect synchronized system within a wide range of phase errors. This technique is further developed to recover nearly any phase error in [?π,+π] by increasing the number of phase estimators and joint decoding units. This, however, will increase the complexity of the system. Copyright © 2008 John Wiley & Sons, Ltd.     

Performance of truncated type-II hybrid ARQ schemes with noisyfeedback over block fading channels

This paper considers truncated type-II hybrid automatic repeat-request (ARQ) schemes with noisy feedback over block fading channels. With these ARQ techniques, the number of retransmissions is limited, and, similar to forward error correction (FEC), error-free delivery of data packets cannot be guaranteed. Bounds on the average number of transmissions, the average coding rate as well as the reliability of the schemes are derived using random coding techniques, and the performance is compared with FEC. The random coding bounds reveal the achievable performance with block codes and maximum-likelihood soft-decision decoding. Union upper bounds and simulation results show that over block fading channels, these bounds can be closely approached with simple terminated convolutional codes and soft-decision Viterbi decoding. Truncated type-II hybrid ARQ and the corresponding FEC schemes have the same probability of packet erasure; however, the truncated ARQ schemes offer a trade-off between the average coding rate and the probability of undetected error. Truncated ARQ schemes have significantly higher average coding rates than FEC at high and medium signal-to-noise ratio even with noisy feedback. Truncated ARQ can be viewed as adaptive FEC that adapts to the instantaneous channel conditions     

Analysis and performance evaluation of new coding options for space telecommand links ‐ Part I: AWGN channels

We investigate and compare, over the additive white Gaussian noise channel, different options for updating the error correcting code currently used in space mission telecommand links. Besides some more consolidated proposals, using low‐density parity‐check codes, we characterize and assess the performance of alternative schemes, based on parallel turbo codes and soft‐decision decoded Bose‐Chaudhuri‐Hocquenghem (BCH) codes. The analysis considers relevant metrics like the codeword error rate, the frame error rate, and the undetected frame error rate. The considered codes include binary and non‐binary low‐density parity‐check codes, parallel turbo codes and extended BCH codes, with different decoding algorithms. The complexity of the various schemes and possible limits for their application are considered and discussed. Several numerical examples are provided. International Journal of Satellite Communications and Networking. Copyright © 2014 John Wiley & Sons, Ltd.     

Tight error bounds for space-time orthogonal block codes under slow Rayleigh flat fading

The performance of space-time orthogonal block (STOB) codes over slow Rayleigh fading channels and maximum-likelihood (ML) decoding is investigated. Two Bonferroni-type bounds (one upper bound and one lower bound) for the symbol error rate (SER) and bit error rate (BER) of the system are obtained. The bounds are expressed in terms of the pairwise error probabilities (PEPs) and the two-dimensional pairwise error probabilities (2-D PEPs) of the transmitted symbols. Furthermore, the bounds can be efficiently evaluated and they hold for arbitrary (nonstandard) signaling schemes and mappings. Numerical results demonstrate that the bounds are very accurate in estimating the performance of STOB codes. In particular, the upper and lower bounds often coincide even at low channel signal-to-noise ratios, large constellation sizes, and large diversity orders.     

Filter orthogonal frequency-division multiplexing scheme based on polar code in underwater acoustic communication with non-Gaussian distribution noise

The research domain of underwater communication has garnered much interest among researchers exploring underwater activities. The underwater environment differs from the terrestrial setting. Some of the main challenges in underwater communication are limited bandwidth, low data rate, propagation delay, and high bit error rate (BER). As such, this study assessed the underwater acoustic (UWA) aspect and explored the expression of error performance based on t-distribution noise. Filter orthogonal frequency-division multiplexing refers to a new waveform candidate that has been adopted in UWA, along with turbo and polar codes. The empirical outcomes demonstrated that the noise did not adhere to Gaussian distribution, whereas the simulation results revealed that the filter applied in orthogonal frequency-division multiplexing could significantly suppress out-of-band emission. Additionally, the performance of the turbo code was superior to that of the polar code by 2 dB at BER 10⁻³.     

Estimation of packet losses due to propagation impairments: Application to TCP performance over satellite

The transmission control protocol (TCP) is widely used to provide reliable data transmission due to its congestion and flow control mechanisms that provide reliable error recovery in higher layers. In satellite links, various atmospheric phenomena may lead to high packet loss rate (PLR) degrading the TCP throughput. Modern satellite systems operate at frequencies above 10 GHz, where rainfall is the dominant fading mechanism leading to high bit error ratio and correlated packet losses. In this paper, a mathematical analysis is presented to accurately describe the statistical properties of the packet‐error process in a dynamically varying satellite channel. The proposed method is extended to provide PLR estimations when block forward error correction (FEC) is employed. A new Markov‐based method, based on the previous analysis and adapted to the rain‐faded satellite channel, is also presented for the estimation of TCP SACK throughput and tested against simulation results. Based on the information provided by the packet‐error model, a study between the TCP performance under various FEC schemes and a proposed adaptive FEC scheme has provided indications about the superiority of the proposed model. Copyright © 2007 John Wiley & Sons, Ltd.