Interleavers and BCH codes for coherent DQPSK systems with laser phase noise

The relatively high phase noise of coherent optical systems poses unique challenges for forward error correction (FEC). In this letter, we propose a novel semianalytical method for selecting combinations of interleaver lengths and binary Bose-Chaudhuri-Hocquenghem (BCH) codes that meet a target post-FEC bit error rate (BER). Our method requires only short pre-FEC simulations, based on which we design interleavers and codes analytically. It is applicable to pre-FEC BER ∼10-3, and any post-FEC BER. In addition, we show that there is a tradeoff between code overhead and interleaver delay. Finally, for a target of 10-5, numerical simulations show that interleaver-code combinations selected using our method have post-FEC BER around 2× target. The target BER is achieved with 0.1 dB extra signal-to-noise ratio

Dimensioning BCH codes for coherent DQPSK systems with laser phase noise and cycle slips

Forward error correction (FEC) plays a vital role in coherent optical systems employing multi-level modulation. However, much of coding theory assumes that additive white Gaussian noise (AWGN) is dominant, whereas coherent optical systems have significant phase noise (PN) in addition to AWGN. This changes the error statistics and impacts FEC performance. In this paper, we propose a novel semianalytical method for dimensioning binary Bose-Chaudhuri-Hocquenghem (BCH) codes for systems with PN. Our method involves extracting statistics from pre-FEC bit error rate (BER) simulations. We use these statistics to parameterize a bivariate binomial model that describes the distribution of bit errors. In this way, we relate pre-FEC statistics to post-FEC BER and BCH codes. Our method is applicable to pre-FEC BER around 10-3 and any post-FEC BER. Using numerical simulations, we evaluate the accuracy of our approach for a target post-FEC BER of 10-5. Codes dimensioned with our bivariate binomial model meet the target within 0.2-dB signal-to-noise ratio

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 (Formula presented.). We evaluate the accuracy of our approach using numerical simulations. For a target post-FEC BER of (Formula presented.), codes selected using our method result in BERs around 3(Formula presented.) target and achieve the target with around 0.2 dB extra signal-to-noise ratio

Coherent Optical Transmission Systems : Performance and Coding Aspects

Since the invention of fiber-optic systems in the 1970s, user demand has driven innovation forward, and each new generation of products has achieved higher data rates than its predecessor. Today, the most promising approach for further increasing data rates is coherent transmission with multi-level modulation and digital signal processing (DSP). By using multi-level modulation, data rates can be increased without increasing the spectral bandwidth of the signal. Digital signal processing has a highly-predictable design flow, and solutions are likely to become more attractive in the future as technology scales. As multi-level modulation is very susceptible to noise and distortions, these systems typically include forward error correction (FEC), which fits well with the DSP structure. In this thesis, we focus on two aspects of DSP-based coherent systems. First, we use a unified approach to analyze theoretical performance limits of coherent optical receivers and microwave receivers, in terms of signal-to-noise ratio (SNR) and bit error rate (BER). By using our general framework, we directly compare the performance of ten coherent optical receiver architectures and five microwave receiver architectures. In addition, we put previous publications into context, and identify areas of agreement and disagreement between them. Second, we consider simple Bose-Chaudhuri-Hocquenghem (BCH) codes for such systems. While most of coding theory is based on the assumption of additive white Gaussian noise (AWGN) channels, fiber-optic systems have other channel impairments in addition to AWGN. For example, there is relatively high phase noise (PN) from the transmitter and local oscillator (LO) lasers. We present a family of straightforward methods for selecting BCH codes for systems with PN. These codes are highly predictable and systematic to construct. They have low-complexity implementations and no error floor. Our methods are based on simple statistical models that can be parameterized from pre-FEC simulations, thus requiring only modest simulation effort. They are suitable for correcting pre-FEC BERs of around 10^−3. We consider differential quadrature phase-shift keying (DQPSK) modulation and higher-order differential quadrature amplitude modulation (DQAM) with star-shaped constellations. This thesis is an extension of our licentiate thesis, and improves upon the latter in two significant ways. First, the methods for code selection that were previously limited to DQPSK are now generalized to higher-order star-shaped DQAM formats, which can potentially deliver higher data rates. Second, we consider block interleavers which yield practical low-complexity implementations. These complement our earlier analysis of uniform interleavers, which provide general theoretical insight.QC 20151119</p

DSP-based Coherent Optical Systems : Receiver Sensitivity and Coding Aspects

User demand for faster access to more data is at a historic high and rising. One of the enabling technologies that makes the information age possible is fiber-optic communications, where light is used to carry information from one place to another over optical fiber. Since the technology was first shown to be feasible in the 1970s, it has been constantly evolving with each new generation of fiber-optic systems achieving higher data rates than its predecessor. Today, the most promising approach for further increasing data rates is digital signal processing (DSP)-based coherent optical transmission with multi-level modulation. As multi-level modulation formats are very susceptible to noise and distortions, forward error correction (FEC) is typically used in such systems. However, FEC has traditionally been designed for additive white Gaussian noise (AWGN) channels, whereas fiber-optic systems also have other impairments. For example, there is relatively high phase noise (PN) from the transmitter and local oscillator (LO) lasers. The contributions of this thesis are in two areas. First, we use a unified approach to analyze theoretical performance limits of coherent optical receivers and microwave receivers, in terms of signal-to-noise ratio (SNR) and bit error rate (BER). By using our general framework, we directly compare the performance of ten coherent optical receiver architectures and five microwave receiver architectures. In addition, we put previous publications into context, and identify areas of agreement and disagreement between them. Second, we propose straightforward methods to select codes for systems with PN. We focus on Bose-Chaudhuri-Hocquenghem (BCH) codes with simple implementations, which correct pre-FEC BERs around 10−3. Our methods are semi-analytical, and need only short pre-FEC simulations to estimate error statistics. We propose statistical models that can be parameterized based on those estimates. Codes can be selected analytically based on our models.QC 20150528</p

Coherent Optical Transmission Systems : Performance and Coding Aspects

Since the invention of fiber-optic systems in the 1970s, user demand has driven innovation forward, and each new generation of products has achieved higher data rates than its predecessor. Today, the most promising approach for further increasing data rates is coherent transmission with multi-level modulation and digital signal processing (DSP). By using multi-level modulation, data rates can be increased without increasing the spectral bandwidth of the signal. Digital signal processing has a highly-predictable design flow, and solutions are likely to become more attractive in the future as technology scales. As multi-level modulation is very susceptible to noise and distortions, these systems typically include forward error correction (FEC), which fits well with the DSP structure. In this thesis, we focus on two aspects of DSP-based coherent systems. First, we use a unified approach to analyze theoretical performance limits of coherent optical receivers and microwave receivers, in terms of signal-to-noise ratio (SNR) and bit error rate (BER). By using our general framework, we directly compare the performance of ten coherent optical receiver architectures and five microwave receiver architectures. In addition, we put previous publications into context, and identify areas of agreement and disagreement between them. Second, we consider simple Bose-Chaudhuri-Hocquenghem (BCH) codes for such systems. While most of coding theory is based on the assumption of additive white Gaussian noise (AWGN) channels, fiber-optic systems have other channel impairments in addition to AWGN. For example, there is relatively high phase noise (PN) from the transmitter and local oscillator (LO) lasers. We present a family of straightforward methods for selecting BCH codes for systems with PN. These codes are highly predictable and systematic to construct. They have low-complexity implementations and no error floor. Our methods are based on simple statistical models that can be parameterized from pre-FEC simulations, thus requiring only modest simulation effort. They are suitable for correcting pre-FEC BERs of around 10^−3. We consider differential quadrature phase-shift keying (DQPSK) modulation and higher-order differential quadrature amplitude modulation (DQAM) with star-shaped constellations. This thesis is an extension of our licentiate thesis, and improves upon the latter in two significant ways. First, the methods for code selection that were previously limited to DQPSK are now generalized to higher-order star-shaped DQAM formats, which can potentially deliver higher data rates. Second, we consider block interleavers which yield practical low-complexity implementations. These complement our earlier analysis of uniform interleavers, which provide general theoretical insight.QC 20151119</p

Coherent Optical Transmission Systems : Performance and Coding Aspects

Since the invention of fiber-optic systems in the 1970s, user demand has driven innovation forward, and each new generation of products has achieved higher data rates than its predecessor. Today, the most promising approach for further increasing data rates is coherent transmission with multi-level modulation and digital signal processing (DSP). By using multi-level modulation, data rates can be increased without increasing the spectral bandwidth of the signal. Digital signal processing has a highly-predictable design flow, and solutions are likely to become more attractive in the future as technology scales. As multi-level modulation is very susceptible to noise and distortions, these systems typically include forward error correction (FEC), which fits well with the DSP structure. In this thesis, we focus on two aspects of DSP-based coherent systems. First, we use a unified approach to analyze theoretical performance limits of coherent optical receivers and microwave receivers, in terms of signal-to-noise ratio (SNR) and bit error rate (BER). By using our general framework, we directly compare the performance of ten coherent optical receiver architectures and five microwave receiver architectures. In addition, we put previous publications into context, and identify areas of agreement and disagreement between them. Second, we consider simple Bose-Chaudhuri-Hocquenghem (BCH) codes for such systems. While most of coding theory is based on the assumption of additive white Gaussian noise (AWGN) channels, fiber-optic systems have other channel impairments in addition to AWGN. For example, there is relatively high phase noise (PN) from the transmitter and local oscillator (LO) lasers. We present a family of straightforward methods for selecting BCH codes for systems with PN. These codes are highly predictable and systematic to construct. They have low-complexity implementations and no error floor. Our methods are based on simple statistical models that can be parameterized from pre-FEC simulations, thus requiring only modest simulation effort. They are suitable for correcting pre-FEC BERs of around 10^−3. We consider differential quadrature phase-shift keying (DQPSK) modulation and higher-order differential quadrature amplitude modulation (DQAM) with star-shaped constellations. This thesis is an extension of our licentiate thesis, and improves upon the latter in two significant ways. First, the methods for code selection that were previously limited to DQPSK are now generalized to higher-order star-shaped DQAM formats, which can potentially deliver higher data rates. Second, we consider block interleavers which yield practical low-complexity implementations. These complement our earlier analysis of uniform interleavers, which provide general theoretical insight.QC 20151119</p