Visible to the public Forward Error Correction

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Forward Error Correction

Controlling errors in data transmission in noisy or lossy circuits is a problem often solved by channel coding or forward error correction. The articles cited here look at bit error rates, energy efficiency, hybrid networks, and transportation systems. This research was presented in the first three quarters of 2014.

  • Hai Dao Thanh; Morvan, M.; Gravey, P.; Cugini, F.; Cerutti, I, "On the Spectrum-Efficiency Of Transparent Optical Transport Network Design With Variable-Rate Forward Error Correction Codes," Advanced Communication Technology (ICACT), 2014 16th International Conference on, pp.1173, 1177, 16-19 Feb. 2014. doi: 10.1109/ICACT.2014.6779143 We discuss the flexible rate optical transmission enabled by forward error correction (FEC) codes adjustment. The adaptation of FEC codes to given transmission condition gives rise to trade-off between transmission rate and optical reach. In this paper, that compromise is addressed from network planning standpoint. A static transparent network planning taking into account that rate-reach trade-off is formulated. A case study is solved in realistic NSF network with a comparison between mixed line rate (MLR) (10/40/100 Gbps) and flexible rate (FlexRate) by FEC variation (10-100 Gbps with a step of 10 Gbps). The result shows that the maximum link load could be reduced up to ~60% in FlexRate compared with MLR and the reduction becomes evident at high traffic load. Moreover, thanks to finer rate adaptation, the FlexRate could support an amount of traffic around three times higher than MLR.
    Keywords: forward error correction; light transmission; optical fibre networks; telecommunication network planning; telecommunication traffic; variable rate codes; flexible rate optical transmission; mixed line rate; network planning standpoint; static transparent network planning; traffic load; transparent optical transport network design; variable rate forward error correction codes; Adaptive optics; Integrated optics; Optical fiber networks; Optical fibers; Planning; Transponders; Elastic Transponder; Fiber-Optic Communication; Flexible Optical Network; Forward Error Correction; Network Optimization (ID#:14-3083)
  • Ahmed, Q.Z.; Ki-Hong Park; Alouini, M.-S.; Aissa, S., "Linear Transceiver Design for Nonorthogonal Amplify-and-Forward Protocol Using a Bit Error Rate Criterion," Wireless Communications, IEEE Transactions on, vol.13, no.4, pp.1844, 1853, April 2014. doi: 10.1109/TWC.2014.022114.130369 The ever growing demand of higher data rates can now be addressed by exploiting cooperative diversity. This form of diversity has become a fundamental technique for achieving spatial diversity by exploiting the presence of idle users in the network. This has led to new challenges in terms of designing new protocols and detectors for cooperative communications. Among various amplify-and-forward (AF) protocols, the half duplex non-orthogonal amplify-and-forward (NAF) protocol is superior to other AF schemes in terms of error performance and capacity. However, this superiority is achieved at the cost of higher receiver complexity. Furthermore, in order to exploit the full diversity of the system an optimal precoder is required. In this paper, an optimal joint linear transceiver is proposed for the NAF protocol. This transceiver operates on the principles of minimum bit error rate (BER), and is referred as joint bit error rate (JBER) detector. The BER performance of JBER detector is superior to all the proposed linear detectors such as channel inversion, the maximal ratio combining, the biased maximum likelihood detectors, and the minimum mean square error. The proposed transceiver also outperforms previous precoders designed for the NAF protocol.
    Keywords: amplify and forward communication; cooperative communication; detector circuits; diversity reception; error statistics; least mean squares methods; maximum likelihood detection; optimisation; precoding; protocols; radio transceivers; JBER detector; NAF protocols; biased maximum likelihood detectors; bit error rate criterion ;channel inversion; cooperative communications; cooperative diversity; duplex nonorthogonal amplify-and-forward protocol; error performance; idle users; joint bit error rate; linear detectors; linear transceiver design; maximal ratio combining; minimum mean square error; optimal joint linear transceiver; optimal precoder; receiver complexity; spatial diversity; Bit error rate; Complexity theory; Detectors; Diversity reception; Modulation; Protocols; Vectors; Cooperative diversity; bit error rate (BER);minimum mean square error (MMSE); nonorthogonal amplify-and-forward protocol}, (ID#:14-3084)
  • Fareed, M.M.; Uysal, M.; Tsiftsis, T.A, "Error-Rate Performance Analysis of Cooperative OFDMA System With Decode-and-Forward Relaying," Vehicular Technology, IEEE Transactions on, vol.63, no.5, pp.2216,2223, Jun 2014 doi: 10.1109/TVT.2013.2290780 In this paper, we investigate the performance of a cooperative orthogonal frequency-division multiple-access (OFDMA) system with decode-and-forward (DaF) relaying. Specifically, we derive a closed-form approximate symbol-error-rate expression and analyze the achievable diversity orders. Depending on the relay location, a diversity order up to (L(SkD) + 1) + Sm=1M min(L(SkRm) + 1, L(RmD) + 1) is available, where M is the number of relays, and L(SkD) + 1, L(SkRm) + 1, and L(RmD) + 1 are the lengths of channel impulse responses of source-to-destination, source-to-mth relay, and mth relay-to-destination links, respectively. Monte Carlo simulation results are also presented to confirm the analytical findings.
    Keywords: Monte Carlo methods; OFDM modulation; cooperative communication; decode and forward communication; diversity reception; frequency division multiple access; telecommunication channels; transient response; DaF relaying; Monte Carlo simulation; channel impulse responses; closed-form approximate symbol-error-rate expression; cooperative OFDMA system; decode-and-forward relaying; diversity orders; error-rate performance analysis; orthogonal frequency-division multiple-access system; relay location; relay-to-destination links; source-to-destination; source-to-mth relay; Approximation methods; Error analysis; Maximum likelihood decoding; OFDM; Relays; Resource management; Upper bound; Error rate; Orthogonal frequency division multiple access; error rate; orthogonal frequency-division multiple access (OFDMA); power allocation; relay channels (ID#:14-3085)
  • Kaddoum, G.; Gagnon, F., "Lower Bound On The Bit Error Rate Of A Decode-And-Forward Relay Network Under Chaos Shift Keying Communication System," Communications, IET, vol.8, no.2, pp.227,232, January 23 2014. doi: 10.1049/iet-com.2013.0421 This study carries out the first-ever investigation of the analysis of a cooperative decode-and-forward (DF) relay network with chaos shift keying (CSK) modulation. The performance analysis of DF-CSK in this study takes into account the dynamical nature of chaotic signal, which is not similar to a conventional binary modulation performance computation methodology. The expression of a lower bound bit error rate (BER) is derived in order to investigate the performance of the cooperative system under independently and identically distributed Gaussian fading wireless environments. The effect of the non-periodic nature of chaotic sequence leading to a non-constant bit energy of the considered modulation is also investigated. A computation approach of the BER expression based on the probability density function of the bit energy of the chaotic sequence, channel distribution and number of relays is presented. Simulation results prove the accuracy of the authors BER computation methodology.
    Keywords: Gaussian distribution; chaotic communication; cooperative communication; decode and forward communication; error statistics; fading channels; phase shift keying; probability; relay networks (telecommunication);BER;CSK modulation; binary modulation; bit error rate; channel distribution; chaos shift keying communication system; chaotic sequence; chaotic signal; cooperative decode-and-forward relay network; distributed Gaussian fading wireless environments; nonconstant bit energy; nonperiodic nature; probability density function (ID#:14-3086)
  • Al-Kali, M.; Li Yu; Mohammed, AA, "Performance Analysis Of Energy Efficiency And Symbol Error Rate In Amplify-And-Forward Cooperative MIMO Networks," Ubiquitous and Future Networks (ICUFN), 2014 Sixth International Conf. on vol., no., pp.448,453, 8-11 July 2014. doi: 10.1109/ICUFN.2014.6876831 In this paper, we analyze the energy efficiency and the symbol error rate (SER) in the cooperative multiple-input multiple-output (MIMO) relay networks. We employ an amplify-and-forward (AF) relay scheme, where a relay access point occupied with Q antennas cooperatively forwards packets to the destination. Under the assumption of Rayleigh fading channels and time division multiplexing (TDM), we derive new exact closed-form expressions for the outage probability, SER and the energy efficiency valid for Q antennas. Further asymptotic analysis is done in high SNR regime to characterize the energy efficiency in terms of the diversity order and the array gain. Subsequently, our expressions are quantitatively compared with Monte Carlo simulations. Numerical results are provided to validate the exact and the asymptotic expressions. The results show that the energy efficiency decreases with the number of antennas at the relay according to Q+1. The behavior of the energy efficiency with the relay locations is also discussed in this paper.
    Keywords: MIMO communication; Monte Carlo methods; Rayleigh channels; amplify and forward communication; fading channels; probability; relay networks (telecommunication) ;time division multiplexing; AF relay scheme; MIMO relay networks; Monte Carlo simulations; Q antennas; Rayleigh fading channels; SER; TDM; amplify-and-forward cooperative MIMO networks; array gain; asymptotic analysis; energy efficiency; multiple-input multiple-output relay networks; outage probability; performance analysis; relay locations; symbol error rate; time division multiplexing; Antennas; Arrays; Diversity reception; MIMO; Modulation; Relays; Signal to noise ratio; Cooperative MIMO; cooperative diversity; energy efficiency; symbol error rate (ID#:14-3087)
  • Rasmussen, A; Yankov, M.P.; Berger, M.S.; Larsen, K.J.; Ruepp, S., "Improved Energy Efficiency for Optical Transport Networks by Elastic Forward Error Correction," Optical Communications and Networking, IEEE/OSA Journal of, vol. 6, no.4, pp.397, 407, April 2014. doi: 10.1364/JOCN.6.000397 In this paper we propose a scheme for reducing the energy consumption of optical links by means of adaptive forward error correction (FEC). The scheme works by performing on the fly adjustments to the code rate of the FEC, adding extra parity bits to the data stream whenever extra capacity is available. We show that this additional parity information decreases the number of necessary decoding iterations and thus reduces the power consumption in iterative decoders during periods of low load. The code rate adjustments can be done on a frame-by-frame basis and thus make it possible to manipulate the balance between effective data rate and FEC coding gain without any disruption to the live traffic. As a consequence, these automatic adjustments can be performed very often based on the current traffic demand and bit error rate performance of the links through the network. The FEC scheme itself is designed to work as a transparent add-on to transceivers running the optical transport network (OTN) protocol, adding an extra layer of elastic soft-decision FEC to the built-in hard-decision FEC implemented in OTN, while retaining interoperability with existing OTN equipment. In order to facilitate dynamic code rate adaptation, we propose a programmable encoder and decoder design approach, which can implement various codes depending on the desired code rate using the same basic circuitry. This design ensures optimal coding gain performance with a modest overhead for supporting multiple codes with minimal impact on the area and power requirements of the decoder.
    Keywords: access protocols; energy conservation; error statistics; forward error correction; iterative decoding; optical fibre networks; optical links; optical transceivers; power consumption ;telecommunication standards; OTN protocol; adaptive FEC; adaptive forward error correction; bit error rate; built-in hard-decision FEC; data stream; decoding iterations; dynamic code rate adaptation; elastic forward error correction; elastic soft-decision FEC; energy consumption; energy efficiency; iterative decoders; optical links; optical transport network protocol; optimal coding gain performance; parity information ;power consumption; programmable encoder; traffic demand; transceivers; Bit error rate; Decoding; Encoding; Forward error correction; Iterative decoding; Optical fiber communication; Elastic optical networks; Optical transport networks; Optically switched networks; Rate adaptive forward error correction (ID#:14-3088)
  • Ying Zhang; Huapeng Zhao; Chuanyi Pan, "Optimization of an Amplify-and-Forward Relay Network Considering Time Delay and Estimation Error in Channel State Information," Vehicular Technology, IEEE Transactions on, vol.63, no.5, pp. 2483, 2488, Jun 2014. doi: 10.1109/TVT.2013.2292939 This paper presents the optimization of an amplify-and-forward (AF) relay network with time delay and estimation error in channel state information (CSI). The CSI time delay and estimation error are modeled by the channel time variation model and stochastic error model, respectively. The conditional probability density function of the ideal CSI upon the estimated CSI is computed based on these two models, and it is used to derive the conditional expectation of the mean square error (MSE) between estimated and desired signals upon estimated CSI, which is minimized to optimize the beamforming and equalization coefficients. Computer simulations show that the proposed method obtains lower bit error rate (BER) than the conventional minimum MSE and the maxmin SNR strategies when CSI contains time delay and estimation error.
    Keywords: amplify and forward communication; delays; least mean squares methods; optimisation;relay networks (telecommunication); stochastic processes; BER; amplify-and-forward relay network; beamforming; bit error rate; channel state information; channel time variation model; conditional probability density function; equalization coefficients; estimation error; minimum mean square error; stochastic error model; time delay; Bit error rate; Channel estimation; Correlation; Delay effects; Estimation error; Relays; Signal to noise ratio; Amplify and forward (AF); Amplify-and-forward; conditional expectation; estimation error; minimum mean square error; minimum mean square error (MMSE);outdated channel state information; outdated channel state information (CSI);relay network (ID#:14-3089)
  • Rafique, D.; Napoli, A; Calabro, S.; Spinnler, B., "Digital Preemphasis in Optical Communication Systems: On the DAC Requirements for Terabit Transmission Applications," Lightwave Technology, Journal of, vol.32, no.19, pp.3247, 3256, Oct.1, 1 2014. doi: 10.1109/JLT.2014.2343957 Next-generation coherent optical systems are geared to employ high-speed digital-to-analog converters (DAC), allowing for digital preprocessing of the signal and flexible optical transport networks. However, one of the major obstacles in such architectures is the limited resolution (less than 5.5 effective bits) and -3 dB bandwidth of commercial DACs, typically limited to half of the currently commercial baud rates, and even relatively reduced in case of higher baud rate transponders (400 Gb/s and 1 Tb/s). In this paper, we propose a simple digital preemphasis (DPE) algorithm to compensate for DAC-induced signal distortions, and exhaustively investigate the impact of DAC specifications on system performance, both with and without DPE. As an outcome, performance improvements are established across various DAC hardware requirements (effective number of bits and bandwidth) and channel baud rates, for m-state quadrature amplitude modulation (QAM) formats. In particular, we show that lower order modulation formats are least affected by DAC limitations, however, they benefit the most from DPE in extremely challenging hardware conditions. On the contrary, higher order formats are severely limited by DAC distortions, and moderately benefit from DPE across a wide range of DAC specifications. Moreover, effective number of bit requirements are established for m-state QAM, assuming low and high baud rate transmission regimes. Finally, we discuss the application scenarios for the proposed DPE in next-generation terabit transmission systems, and establish maximum transportable baud rates, which are shown to be used toward increasing channel baud rates to reduce terabit subcarrier count or toward increasing forward error correction (FEC) overheads to reduce the pre-FEC bit error rate threshold. Maximum baud rates after DPE are summarized here for polarization multiplexed BPSK, QPSK, 8QAM, and 16QAM, assuming two DACs: Current commer- ial DACs (5.5 effective bits, 16 GHz bandwidth) 57, 54, 51, and 48 Gbaud, respectively. Next-generation DACs (7 effective bits, 22 GHz bandwidth): 62, 61, 60, and 58 Gbaud, respectively.
    Keywords: Bandwidth; Noise; Q-factor; Quadrature amplitude modulation; Receivers; Transfer functions; Coherent detection; Nyquist; digital signal processing; digital-to-analog converter; pre-emphasis (ID#:14-3090)
  • Qiang Huo; Tianxi Liu; Shaohui Sun; Lingyang Song; Bingli Jiao, "Selective Combining For Hybrid Cooperative Networks," Communications, IET, vol.8, no.4, pp.471,482, March 6 2014. doi: 10.1049/iet-com.2013.0323 In this study, we consider the selective combining in hybrid cooperative networks (SCHCNs scheme) with one source node, one destination node and N relay nodes. In the SCHCN scheme, each relay first adaptively chooses between amplify-and-forward protocol and decode-and-forward protocol on a per frame basis by examining the error-detecting code result, and Nc(1 Nc N) relays will be selected to forward their received signals to the destination. We first develop a signal-to-noise ratio (SNR) threshold-based frame error rate (FER) approximation model. Then, the theoretical FER expressions for the SCHCN scheme are derived by utilising the proposed SNR threshold-based FER approximation model. The analytical FER expressions are validated through simulation results.
    Keywords: amplify and forward communication; cooperative communication; decode and forward communication; diversity reception; error detection codes; error statistics ;FER approximation model; SCHCN; amplify-and-forward protocol; decode-and-forward protocol; destination node; error detecting code; frame error rate; hybrid cooperative networks; relay nodes; selective combining; signal-to-noise ratio (ID#:14-3091)
  • Haifeng Zhu; Bajekal, S.; Lakamraju, V.; Murray, B., "A Radio System Design Tool For Forward Error Corrections In Wireless CSMA Networks: Analysis And Economics," Radio and Wireless Symposium (RWS), 2014 IEEE, pp.145,147, 19-23 Jan. 2014. doi: 10.1109/RWS.2014.6830160 As cyber-physical systems become pervasive, their power consumption and system design practices are major concerns. This paper explores problems of deploying Forward Error Correction (FEC) in wireless commercial standards such as IEEE 802.11b and 802.15.4. First, we describe battery life estimation that includes practical factors such as system issues and the negative impact by retransmissions vs. power impact by overhead of encoding schemes. Secondly, we explore the link to design economics and demonstrate a design decision method. Theoretical analyses validated with simulations provide a decision tool for engineers and management during system design. Different from previous unfavorable usage in FEC, we show that for cyber-physical devices FEC should be now strongly considered under proper circumstances, as it provides the opportunity for saving communications-related energy for prolonged battery life, which is critical for devices in hard-to-reach locations and battlefield.
    Keywords: Zigbee; carrier sense multiple access; encoding;forward error correction; power consumption; wireless LAN; wireless channels;FEC; IEEE 802.11b;IEEE 802.15.4;battery life estimation; cyber-physical devices; cyber-physical systems; design decision method; economics; encoding; forward error corrections; power consumption; radio system design tool; wireless CSMA networks; wireless commercial standards; Automatic repeat request; Batteries; Bit error rate; Economics ;Encoding; Forward error correction; Power demand; FEC; Wireless; power consumption; system design (ID#:14-3092)
  • Chang, Shih-Ying; Chiao, Hsin-Ta; Hung, Yu-Hsian, "Ideal Forward Error Correction Codes for High-Speed Rail Multimedia Communications," Vehicular Technology, IEEE Transactions on, vol. PP, no.99, pp.1, 1, March 2014. doi: 10.1109/TVT.2014.2310897 In recent years, Application Layer-Forward Error Correction (AL-FEC), especially rateless AL-FEC, has received a lot of attention due to its superior performance in both transmissional and computational efficiency. Rateless AL-FEC (e.g., Raptor code or LT code) can protect a large data block with an overhead somewhat close to ideal codes. In the meantime, its data processing rates of both encoding and decoding are quite efficient even in software implementations. However, we found that conventional rateless AL-FEC schemes may not be the best candidates when considering streaming over WiMAX networks for high speed rail reception in Taiwan. In this paper, we propose a new ideal AL-FEC scheme based on the Chinese Remainder Theorem (CRT) to facilitate streaming service delivery for highspeed rail reception. The proposed scheme can support the rateless property, but it requires less transmission overhead than conventional rateless codes. Although it requires higher computational cost than conventional rateless codes, the cost is affordable for commodity laptops. Besides measuring the FEC computation, storage, and decoder overhead, we also evaluate its performance in an emulation environment for simulating highspeed rail reception over WiMAX networks. The emulation result shows that the proposed scheme can achieve the same error protection as Raptor codes, but it requires less transmission overhead, suitable for protecting data transmission over bandwidthlimited, high-mobility erasure channels.
    Keywords: Decoding; Digital video broadcasting; Encoding; Forward error correction; Maintenance engineering; Systematics; WiMAX (ID#:14-3093)
  • JongJun Park; Jongsoo Jeong; Hoon Jeong; Liang, C.-J.M.; JeongGil Ko, "Improving the Packet Delivery Performance for Concurrent Packet Transmissions in WSNs," Communications Letters, IEEE , vol.18, no. 1, pp.58,61, January 2014. doi: 10.1109/LCOMM.2013.112013.131974 In this letter, we investigate the properties of packet collisions in IEEE 802.15.4-based wireless sensor networks when packets with the same content are transmitted concurrently. While the nature of wireless transmissions allows the reception of a packet when the same packet is transmitted at different radios with (near) perfect time synchronization, we find that in practical systems, platform specific characteristics, such as the independence and error of the crystal oscillators, cause packets to collide disruptively when the two signals have similar transmission powers (i.e., differences of <;2 dBm). In such scenarios, the packet reception ratio (PRR) of concurrently transmitted packets falls below 10%. Nevertheless, we empirically show that the packet corruption patterns are easily recoverable using forward error correction schemes and validate this using implementations of RS and convolutional codes. Overall, our results show that using such error correction schemes can increase the PRR by more than four-fold.
    Keywords: Reed-Solomon codes; Zigbee; convolutional codes; wireless sensor networks; IEEE 802.15.4-based wireless sensor networks; RS codes; WSN; concurrent packet transmissions; convolutional codes; forward error correction schemes; packet delivery performance; Convolutional codes; Crystals; Forward error correction; IEEE 802.15 Standards; Oscillators; Radio transmitters; Wireless sensor networks; Concurrent transmissions and forward error correction; wireless sensor networks (ID#:14-3094)


Articles listed on these pages have been found on publicly available internet pages and are cited with links to those pages. Some of the information included herein has been reprinted with permission from the authors or data repositories. Direct any requests via Email to SoS.Project (at) for removal of the links or modifications to specific citations. Please include the ID# of the specific citation in your correspondence.