Modulation, Coding and Digital Optical Transmission

Introduction

Digital optical transmission converts information into controlled variations of an optical carrier, transports the resulting waveform through fiber, and reconstructs the data in the presence of attenuation, dispersion, amplified spontaneous-emission noise, nonlinear distortion and transceiver imperfections. Modern links therefore cannot be designed by selecting a modulation format alone. Modulation, pulse shaping, multiplexing, synchronization, detection and forward-error correction (FEC) form an interdependent system.

Intensity-modulated direct-detection links remain important in access networks and short-reach interconnects because of their simplicity. Coherent systems dominate high-capacity transport because they recover both quadratures and polarizations of the optical field, enabling spectrally efficient formats such as dual-polarization quadrature amplitude modulation (DP-QAM). Performance is evaluated through eye diagrams, constellation statistics, Q-factor, optical signal-to-noise ratio (OSNR), error-vector magnitude (EVM), generalized mutual information (GMI) and bit-error ratio (BER).

Learning Objectives

After studying this chapter, readers should be able to:

• distinguish intensity, phase, frequency and polarization modulation;
• calculate gross and net bit rates for single- and dual-polarization formats;
• evaluate line coding and pulse-shaping alternatives;
• explain time-, wavelength-, frequency- and polarization-division multiplexing;
• interpret eye diagrams, constellations, Q-factor, OSNR and BER;
• compare hard-decision and soft-decision FEC code families and decoders;
• quantify FEC overhead, coding gain and net throughput; and
• integrate modulation, filtering, multiplexing and coding in an optical-link design.

1. Optical Carrier Representation

A narrowband optical field may be represented as

E(t) = Re{A(t)e^(j2πf₀t)},

where f₀ is the optical carrier frequency and A(t) is the complex envelope. Writing

A(t) = √P(t)e^(jφ(t))

shows three directly controllable attributes: optical power P(t), phase φ(t), and instantaneous frequency

fᵢ(t) = f₀ + (1/2π)dφ(t)/dt.

The field also has a state of polarization. In a coherent dual-polarization model, its envelope is the Jones vector

A(t) = [Aₓ(t), Aᵧ(t)]ᵀ,

where Aₓ and Aᵧ are complex envelopes on two orthogonal polarization axes.

A direct detector produces a current approximately proportional to incident optical power:

i(t) = ℛP(t) + n(t),

where ℛ is photodiode responsivity in A/W and n(t) represents receiver noise. Direct detection does not ordinarily preserve absolute optical phase. A coherent receiver mixes the signal with a local oscillator and recovers in-phase and quadrature components, allowing estimation of the complete complex field.

2. Modulation of the Optical Carrier

2.1 Intensity modulation

In intensity modulation, information controls optical power. Common formats include on–off keying (OOK), pulse-amplitude modulation with M levels (PAM-M), and subcarrier-modulated signals. Since physical optical intensity is nonnegative, an intensity-modulated waveform must satisfy P(t) ≥ 0.

Non-return-to-zero OOK assigns one power level to binary zero and another to binary one. PAM-4 carries two bits per symbol but uses four closely spaced levels; for the same average optical power and receiver bandwidth, its reduced level separation makes it more sensitive to noise and nonlinearity than OOK.

An ideal push-pull Mach–Zehnder modulator can be described, under a commonly used normalization, by

Pout/Pin = ½[1 + cos(πV/Vπ + φb)],

where V is the differential drive voltage, Vπ is the half-wave voltage, and φb is the bias phase. The exact transfer expression depends on electrode and voltage conventions. Bias drift creates level distortion and chirp, so practical transmitters require bias control.

Intensity-modulation/direct-detection systems are inexpensive but suffer from square-law detection, signal–signal beating and limited access to phase information. Chromatic dispersion can also produce frequency-selective fading in double-sideband links.

2.2 Phase modulation

Phase-shift keying selects one of several carrier phases. Binary PSK carries one bit per symbol; quadrature PSK carries two. Differential PSK detects phase changes rather than absolute phase and may simplify carrier recovery, although differential detection usually incurs a sensitivity penalty compared with ideal coherent detection.

Quadrature amplitude modulation varies both quadratures:

aₖ = Iₖ + jQₖ.

Square M-QAM carries log₂M bits per symbol when M is a power of two. Higher-order QAM improves spectral efficiency but reduces Euclidean distance between normalized constellation points and consequently requires higher signal-to-noise ratio and better control of laser phase noise, modulator linearity and equalization error.

For symbol rate Rₛ, modulation order M, and Npol independently modulated polarizations, the uncoded gross bit rate is

Rgross = Npol Rₛ log₂M.

Thus, DP-16-QAM at 25 GBd carries

Rgross = 2 × 25 × 4 = 200 Gb/s.

FEC and framing reduce the client data rate below this gross value.

2.3 Frequency modulation and frequency-shift keying

Frequency modulation changes instantaneous frequency through a time-varying phase. In M-ary frequency-shift keying, symbols correspond to distinct frequencies. Orthogonal coherent tones separated by 1/Tₛ, where Tₛ is symbol duration, are orthogonal over one symbol interval under rectangular pulse observation. Other detection models can require different spacing.

Optical frequency modulation may be generated by direct laser modulation or phase modulation. Direct laser modulation commonly produces both intensity modulation and frequency chirp because carrier-density changes affect gain and refractive index. FSK can support robust noncoherent reception, but conventional M-FSK generally consumes more bandwidth as M increases.

2.4 Polarization modulation and dual-polarization transmission

The state of polarization may itself encode data, but modern coherent systems more commonly transmit independent complex symbols on two nominally orthogonal polarizations. This doubles gross bit rate without doubling symbol rate or occupied optical bandwidth.

Fiber birefringence randomly rotates and mixes the polarizations. A coherent receiver therefore uses a multiple-input multiple-output equalizer, often a 2 × 2 finite-impulse-response filter, to estimate the inverse channel. Polarization-mode dispersion makes this channel frequency dependent. Polarization-dependent loss cannot generally be removed perfectly because it produces unequal attenuation and can reduce channel capacity.

3. Line Coding and Digital Framing

Line coding maps source bits into a transmission sequence chosen for synchronization, spectrum control, transition density or error detection.

NRZ coding is bandwidth efficient but can contain long runs without transitions. Return-to-zero coding offers more timing transitions but occupies greater bandwidth. Manchester coding guarantees a mid-bit transition and has no DC component for balanced data, but its bandwidth requirement is high.

Block codes such as 8b/10b provide bounded disparity and adequate transition density at 25% overhead. The rate is 8/10 = 0.8. Modern high-rate systems often use scrambling with lightweight framing rather than highly redundant line codes. A self-synchronizing scrambler whitens data statistically but does not guarantee strict run-length limits; it may also multiply isolated channel errors depending on its structure.

Line coding must not be confused with FEC. Line codes primarily control waveform properties, whereas FEC introduces structured redundancy to correct errors. Some schemes perform both functions, but their roles should still be distinguished analytically.

4. Pulse Shaping and Spectral Efficiency

Symbols transmitted as abrupt rectangular pulses have slowly decaying spectra. Pulse shaping limits occupied bandwidth and controls intersymbol interference (ISI). For symbols aₖ and pulse p(t), the waveform is

s(t) = Σₖ aₖp(t − kTₛ).

The Nyquist zero-ISI criterion requires the combined transmit-channel-receive response sampled at symbol times to satisfy

g(nTₛ) = 1 for n = 0, and 0 for nonzero integer n.

A raised-cosine response satisfies this criterion. Its roll-off factor α lies between 0 and 1. For a complex modulated signal, its null-to-null passband bandwidth is

B = (1 + α)Rₛ.

Root-raised-cosine (RRC) filters are commonly split between transmitter and receiver; the cascade forms a raised-cosine response. A smaller α improves spectral efficiency but increases filter length and sensitivity to timing error, frequency offset and component bandwidth limitations.

Chromatic dispersion, polarization-mode dispersion, filtering and bandwidth-limited electronics destroy the ideal Nyquist condition. Adaptive equalizers compensate residual ISI. Linear equalization cannot fully reverse noise enhancement, severe nonlinear distortion or information lost through narrow filtering.

Probabilistic constellation shaping provides another efficiency mechanism. Rather than transmitting all constellation points equally often, it favors lower-energy points. This can approach the Gaussian input distribution desirable for an additive white Gaussian noise channel and permits finer rate adaptation. Its gain is reduced when implementation constraints or fiber nonlinearities dominate.

5. Multiplexing

5.1 Time-division multiplexing

Time-division multiplexing interleaves tributaries into distinct time slots. It requires accurate clock alignment and framing. Optical time-division multiplexing can achieve very high aggregate rates, but ultrashort-pulse generation and demultiplexing are demanding.

5.2 Wavelength-division multiplexing

Wavelength-division multiplexing assigns channels to different optical carrier wavelengths. Dense WDM supports many closely spaced channels over the same fiber. Channel spacing must accommodate the modulated spectrum, laser drift, filter transition bands and nonlinear interactions. Flexible-grid networks allocate spectrum in frequency slots rather than fixed wavelength channels, enabling variable symbol rates and modulation orders.

5.3 Frequency-division and orthogonal multiplexing

Orthogonal frequency-division multiplexing divides a high-rate stream among orthogonal subcarriers. With a useful symbol duration T, the ideal subcarrier spacing is 1/T. A cyclic prefix converts sufficiently short linear channel memory into circular convolution, enabling one-tap frequency-domain equalization. The prefix must exceed the effective channel impulse-response duration to avoid intersymbol and intercarrier interference. OFDM has high peak-to-average power ratio, which stresses optical modulators and amplifiers.

Nyquist subcarrier multiplexing uses tightly packed, pulse-shaped subcarriers and may avoid the cyclic-prefix overhead, but it requires accurate filtering and carrier management.

5.4 Space-division multiplexing

Space-division multiplexing uses multiple cores, modes or fibers. Coupled spatial channels require MIMO processing. It can overcome the capacity limit of a single fiber, although component complexity, intermodal crosstalk and amplifier integration remain substantial challenges.

6. Receiver Performance Metrics

6.1 Eye diagram

An eye diagram overlays waveform segments one or more symbol periods long. Eye height indicates vertical noise margin; eye width indicates timing margin. Closure can result from noise, ISI, jitter, bandwidth limitation, reflections or nonlinear distortion. Crossing asymmetry can reveal duty-cycle distortion.

An eye diagram is most directly useful for scalar signaling such as OOK or PAM. Coherent QAM is more naturally evaluated using constellation plots, EVM and bit-wise soft information. An apparently open eye does not alone establish an acceptable BER because rare events, pattern dependence and non-Gaussian tails may be hidden.

6.2 Q-factor and BER

For binary OOK with Gaussian level distributions, means μ₁ and μ₀, standard deviations σ₁ and σ₀, equal prior probabilities, and an optimum threshold under the standard Gaussian approximation, the electrical Q-factor is

Q = (μ₁ − μ₀)/(σ₁ + σ₀).

The corresponding approximate BER is

BER ≈ ½ erfc(Q/√2) = QN(Q),

where QN(·) denotes the standard Gaussian tail probability. For Q = 6, BER ≈ 9.87 × 10⁻¹⁰. Some instruments report Q in decibels as 20log₁₀Q. This relationship should not be applied uncritically to unequal priors, non-Gaussian noise, severe ISI or multilevel modulation.

For coherent constellations, EVM is often defined as

EVMrms = √[Σ|rₖ − ŝₖ|² / Σ|ŝₖ|²],

where rₖ is the equalized received symbol and ŝₖ is the associated ideal reference symbol after permitted normalization. Under ideal additive noise and consistent normalization, EVM relates to SNR approximately as EVMrms² ≈ 1/SNR. Phase noise and decision errors can invalidate this simple interpretation.

6.3 OSNR

OSNR compares optical signal power with optical noise power measured in a specified reference bandwidth:

OSNR = Ps/(NASEBref),

where Ps is channel signal power, NASE is the optical noise power spectral density under the stated polarization convention, and Bref is the reference bandwidth. Around 1550 nm, 0.1 nm corresponds approximately to 12.5 GHz.

With consistent signal, polarization and noise conventions, a useful idealized conversion is

Es/N0 ≈ OSNR × Bref/Rₛ.

All quantities in this equation are linear ratios. Practical conversion may include polarization, matched-filter, implementation and measurement-correction factors. Therefore, an OSNR value is incomplete unless reference bandwidth, resolution bandwidth, polarization convention and measurement method are specified.

OSNR is highly useful in amplified links but does not uniquely predict BER when nonlinear interference, filtering penalties, phase noise or transceiver distortion are significant.

6.4 Pre-FEC and post-FEC BER

Pre-FEC BER is measured at the decoder input after demodulation; post-FEC BER is measured after decoding. Two systems with the same pre-FEC BER can have different post-FEC performance because error correlation and reliability distributions differ. Modern soft-decision systems are more accurately predicted by GMI or normalized GMI than by a single pre-FEC BER threshold.

7. Forward-Error Correction

7.1 Code parameters and overhead

An (n,k) block code maps k information bits or symbols into n coded bits or symbols. Its rate is

Rc = k/n,

and FEC overhead relative to information data is

OH = (n − k)/k = 1/Rc − 1.

For Rc = 0.8, overhead is 25%, not 20%. Twenty percent of the transmitted bits are parity, but parity is 25% of the information-bit count.

For a binary linear block code with minimum Hamming distance dmin, guaranteed correction of arbitrary errors is

t = floor[(dmin − 1)/2].

This is a bounded-distance hard-decision result; soft decoders can perform beyond this guaranteed radius probabilistically.

7.2 Algebraic block codes

Bose–Chaudhuri–Hocquenghem (BCH) codes are cyclic codes designed to correct multiple random bit errors. Decoding commonly involves syndrome computation, determination of an error-locator polynomial, and identification of error positions.

Reed–Solomon (RS) codes operate on multibit symbols and are effective against burst errors. An RS(n,k) code with minimum distance n − k + 1 corrects up to floor[(n − k)/2] unknown symbol errors, or up to n − k known symbol erasures. Interleaving spreads a physical burst across several codewords.

Hard-decision BCH and RS decoders have moderate complexity and were widely used in earlier optical systems, but their net coding gain is typically lower than that of modern soft-decision codes.

7.3 Convolutional, turbo and polar codes

A convolutional encoder has memory; each output depends on current and previous input bits. The Viterbi algorithm performs maximum-likelihood sequence estimation for manageable constraint lengths. The BCJR algorithm computes symbol-wise a posteriori probabilities and supports iterative decoding.

Turbo codes concatenate recursive convolutional codes through an interleaver. Their constituent decoders iteratively exchange extrinsic log-likelihood information. Turbo codes can approach capacity but may exhibit error floors and substantial latency.

Polar codes transform channels into synthesized bit channels of differing reliability. Information is assigned to reliable positions and frozen values to the remainder. Successive-cancellation list decoding, often aided by a cyclic-redundancy check, greatly improves finite-length performance. Polar codes are important in communication standards, although LDPC and product-like codes remain especially prominent in optical transport.

7.4 LDPC codes and soft-decision decoding

A low-density parity-check code is defined by a sparse parity-check matrix H. A valid codeword c satisfies

Hcᵀ = 0 over GF(2).

Its Tanner graph contains variable nodes and check nodes. Belief-propagation decoding exchanges reliability messages between them. For a received observation y, the channel log-likelihood ratio for bit b is

L(y) = ln[P(y|b = 0)/P(y|b = 1)].

The sum-product check-node update combines incoming messages through the tanh rule. Min-sum decoding replaces this nonlinear operation with signed minimum-magnitude calculations, reducing complexity but generally requiring normalization or offset correction.

Decoder performance depends on block length, degree distribution, graph cycles, quantization, iteration count and stopping criteria. Short cycles produce correlated messages; trapping or absorbing sets can cause error floors. Spatially coupled LDPC codes improve thresholds through structured coupling and windowed decoding, at the cost of termination overhead and latency considerations.

7.5 Product, staircase and braided codes

Product codes arrange data in an array and apply component block codes to rows and columns. Iterative bounded-distance decoding alternates between dimensions. Staircase codes couple adjacent blocks, providing strong hard-decision performance with high throughput and relatively simple component decoders. Miscorrections by bounded-distance decoders can limit performance; reliability-assisted and soft-aided variants improve results.

Hard-decision FEC is attractive where power and latency are constrained. Soft-decision FEC typically offers greater coding gain but requires demapper reliability values, more memory, higher data movement and iterative processing. Decoder energy, rather than arithmetic count alone, is often the implementation bottleneck.

7.6 Coding gain and bounds

At a specified output BER, coding gain is the reduction in required SNR relative to an uncoded reference using consistent definitions. Net coding gain accounts for code rate and is the more meaningful system measure.

For uncoded coherent BPSK in an additive white Gaussian noise channel,

Pb = QN(√(2Eb/N0)).

At Pb = 10⁻¹², QN⁻¹(10⁻¹²) ≈ 7.034, giving

Eb/N0 = 7.034²/2 ≈ 24.74 = 13.93 dB.

If a rate-0.8 coded implementation achieves post-FEC BER 10⁻¹² at an information-bit Eb/N0 of 7.0 dB under the same channel and measurement convention, its measured net coding gain is approximately

13.93 − 7.0 = 6.93 dB.

This result is a performance comparison, not a universal property of all rate-0.8 codes.

For a binary linear code with coherent BPSK over AWGN, a union bound can be written in terms of its bit-weight spectrum:

Pb ≤ (1/k)Σd Bd QN(√(2dRcEb/N0)),

where Bd is the total information-bit weight associated with codewords of Hamming weight d. The bound is most informative at high SNR and may be loose elsewhere.

Coding cannot provide unlimited gain. For a memoryless channel, reliable transmission requires an information rate below channel capacity. Practical code design seeks a small gap to capacity while satisfying constraints on latency, power, complexity and error floor.

8. Worked Design Example

A transmitter uses DP-16-QAM at 64 GBd with RRC pulse shaping and α = 0.10.

Gross bit rate:

Rgross = 2 × 64 × 4 = 512 Gb/s.

With a rate-0.8 FEC code:

Rafter FEC = 512 × 0.8 = 409.6 Gb/s.

If framing consumes 2% of the post-FEC information rate, client payload is

Rpayload = 409.6 × 0.98 = 401.408 Gb/s.

The null-to-null occupied bandwidth is approximately

B = 64 × 1.10 = 70.4 GHz.

A 75 GHz channel allocation leaves only 4.6 GHz total nominal guard bandwidth, so laser drift and filter tolerances must be tightly controlled.

Suppose the required Es/N0 is 12 dB. In linear form this is 15.85. Using a 12.5 GHz OSNR reference bandwidth and consistent conventions,

OSNR ≈ 15.85 × 64/12.5 = 81.15,

or 10log₁₀(81.15) ≈ 19.09 dB. With a 2 dB implementation margin, the design target becomes approximately 21.1 dB. This estimate must be adjusted if the laboratory OSNR convention differs or nonlinear distortion is substantial.

9. Illustrative Case Study: Upgrading a Regional WDM Link

Background

This fictional case concerns a network operator upgrading a 600 km amplified fiber route. Existing 100 Gb/s channels use lower-order coherent modulation. The operator seeks approximately 400 Gb/s client capacity per wavelength without replacing the installed line system.

Problem

The available flexible-grid slot is 75 GHz. Measurements indicate end-of-life OSNR near 22 dB in a 0.1 nm reference bandwidth. The route also exhibits wavelength-dependent filtering and moderate nonlinear penalties.

Analysis

DP-16-QAM at 64 GBd provides 512 Gb/s gross capacity. With rate-0.8 soft-decision FEC and 2% framing, its payload is approximately 401.4 Gb/s. An RRC roll-off of 0.10 produces a nominal 70.4 GHz bandwidth, fitting within the slot but leaving little filtering margin.

The idealized OSNR target from the worked calculation is 19.1 dB before implementation margin. Adding 2 dB gives 21.1 dB, leaving only 0.9 dB against the measured end-of-life OSNR. Such a narrow margin is vulnerable to nonlinear noise, polarization-dependent loss and component ageing.

Approach and Solution

The operator performs transponder trials using GMI rather than relying solely on pre-FEC BER. Launch power is optimized to balance ASE noise against Kerr nonlinearity. Filter concatenation is included in the laboratory channel emulator. A rate-adaptive LDPC mode is selected so that difficult spans can use slightly stronger coding, while easier routes retain higher net throughput. Telemetry records OSNR, GMI, decoder iteration count and corrected-codeword statistics.

Outcome

Most channels support the target rate, but two wavelengths near filter edges require spectrum reassignment. The upgrade proceeds without line-system replacement. Operational alarms are based on declining GMI and increasing decoder workload rather than waiting for post-FEC errors.

Learning Points

• Gross bit rate alone does not establish deployable payload.
• OSNR must be interpreted with bandwidth and polarization conventions.
• Filter shape and nonlinear noise can invalidate an ASE-only budget.
• GMI and decoder telemetry provide earlier warning than post-FEC BER.
• Rate-adaptive FEC converts physical-layer margin into operational flexibility.

10. Design Challenges, Governance and Contemporary Directions

Higher-order modulation improves spectral efficiency but tightens requirements on lasers, converters, clocks and digital signal processing. Stronger FEC improves sensitivity but increases overhead, latency, decoder power and heat. Very narrow pulse shaping saves spectrum while increasing implementation sensitivity. System optimization is therefore multi-objective.

Interoperability requires explicit agreement on framing, constellation labeling, FEC structure, soft-metric scaling, OSNR reference bandwidth and management telemetry. Vendor-neutral conformance testing reduces lock-in and prevents misleading performance comparisons.

FEC provides error control, not confidentiality or authenticity. Optical transport carrying sensitive data requires cryptographic protection and secure key management. Telemetry used by AI-based impairment prediction can expose network topology and traffic conditions; access control, retention policies and model validation are therefore necessary.

Contemporary research includes probabilistic and geometric constellation shaping, coherent pluggable optics, neural-network equalizers, learned demappers, spatially coupled codes, nonbinary LDPC codes and joint optimization of shaping and FEC. Machine learning can assist impairment estimation and launch-power control, but it must be tested against distribution shifts and rare failure modes. Deterministic safety limits remain necessary for laser power, equipment operation and service availability.

Chapter Summary

Digital optical transmission jointly depends on modulation, pulse shaping, multiplexing, detection and coding. Intensity modulation supports economical direct detection, whereas coherent phase-and-amplitude modulation enables high spectral efficiency. Dual-polarization transmission doubles gross bit rate but requires polarization-demultiplexing equalizers.

Line coding controls transitions and spectrum, while Nyquist pulse shaping controls bandwidth and ISI. WDM, OFDM and spatial multiplexing increase aggregate capacity through different physical dimensions. Eye diagrams, EVM, Q-factor, OSNR, GMI and BER reveal complementary aspects of performance and must be interpreted under their stated assumptions.

FEC converts controlled redundancy into coding gain. BCH, Reed–Solomon, convolutional, turbo, polar, LDPC, product and staircase codes offer different trade-offs among gain, complexity, latency and error floor. Modern coherent systems increasingly rely on soft information and information-theoretic metrics rather than a universal pre-FEC BER threshold. Effective design balances net throughput, bandwidth, OSNR margin, nonlinear tolerance, implementation power and operational reliability.

Key Terms

Intensity modulation: Encoding information by varying optical power.

Direct detection: Photodetection that primarily recovers optical intensity.

Coherent detection: Detection using a local oscillator to recover field quadratures.

QAM: Modulation that encodes symbols through in-phase and quadrature amplitudes.

Dual polarization: Independent transmission on two orthogonal polarization states.

Symbol rate: Number of transmitted modulation symbols per second.

Line coding: Mapping bits into sequences with controlled waveform properties.

Nyquist pulse: Pulse satisfying the zero-ISI sampling criterion.

Roll-off factor: Excess-bandwidth parameter of a raised-cosine filter.

WDM: Multiplexing using distinct optical carrier wavelengths.

Eye diagram: Overlaid waveform display used to assess timing and amplitude margins.

OSNR: Ratio of optical signal power to optical noise in a specified bandwidth.

Q-factor: Gaussian decision-quality measure related to binary BER under stated assumptions.

EVM: Root-mean-square constellation error normalized to reference-symbol energy.

Pre-FEC BER: Error ratio measured before FEC decoding.

Coding gain: Reduction in required SNR produced by coding at a specified error rate.

LDPC code: Linear block code defined by a sparse parity-check matrix.

Log-likelihood ratio: Soft measure comparing the probabilities of two bit hypotheses.

GMI: Achievable-rate metric for bit-interleaved coded modulation with a specified receiver.

Error floor: Region where BER improvement slows because of harmful code or decoder structures.

Review Questions

Short Answer Questions

1. Why must an intensity-modulated optical waveform remain nonnegative?

2. Distinguish symbol rate from gross bit rate.

3. What information does an eye diagram provide?

4. Why must an OSNR value include its reference bandwidth?

5. Distinguish hard-decision from soft-decision FEC.

Long Answer Questions

1. Compare intensity, phase, frequency and polarization modulation in terms of detection, bandwidth and implementation complexity.

2. Explain the Nyquist zero-ISI criterion and the role of root-raised-cosine filtering.

3. Discuss WDM, OFDM and space-division multiplexing for future optical networks.

4. Compare BCH, Reed–Solomon, turbo, polar, LDPC and staircase codes for optical transmission.

5. Explain the relationships and limitations of eye diagrams, Q-factor, OSNR, EVM, GMI and BER.

Analytical / Application Questions

1. A DP-64-QAM transmitter operates at 50 GBd with code rate 0.85 and 3% framing overhead. Calculate gross and client payload rates.

2. Design a pulse-shaping and channel-spacing plan for a 60 GBd coherent signal, explicitly stating roll-off and guard-band assumptions.

3. Given measured OSNR, nonlinear penalty, GMI and decoder iteration data from several wavelengths, formulate a rational criterion for selecting modulation order and FEC rate.

Multiple Choice Questions with Answers

Question 1

What is the uncoded gross bit rate of DP-16-QAM operating at 25 GBd?

A. 100 Gb/s

B. 150 Gb/s

C. 200 Gb/s

D. 400 Gb/s

Correct Answer: C. 200 Gb/s

Question 2

A code has rate Rc = 0.8. What is its FEC overhead relative to the information-bit count?

A. 20%

B. 25%

C. 40%

D. 80%

Correct Answer: B. 25%

Question 3

What is the approximate null-to-null bandwidth of a 64 GBd signal shaped by a raised-cosine response with roll-off 0.10?

A. 57.6 GHz

B. 64.0 GHz

C. 70.4 GHz

D. 76.8 GHz

Correct Answer: C. 70.4 GHz

Question 4

Which receiver type recovers both in-phase and quadrature components of an optical field?

A. Coherent receiver

B. Envelope-only photodiode receiver

C. Optical power meter

D. Passive wavelength filter

Correct Answer: A. Coherent receiver

Question 5

Under the Gaussian binary OOK approximation, which expression relates Q-factor to BER?

A. BER = Q²

B. BER = exp(Q)/2

C. BER = 1/Q

D. BER ≈ 0.5 erfc(Q/√2)

Correct Answer: D. BER ≈ 0.5 erfc(Q/√2)

Question 6

Which code family is defined by a sparse parity-check matrix and is commonly decoded by belief propagation?

A. Manchester code

B. LDPC code

C. Repetition-free line code

D. Differential phase code

Correct Answer: B. LDPC code

Question 7

An RS(255,239) code can correct how many unknown symbol errors per codeword?

A. 8

B. 16

C. 32

D. 239

Correct Answer: A. 8

Question 8

Which metric generally preserves more predictive information for a soft-decision coherent system than pre-FEC hard-bit BER alone?

A. Laser wavelength label

B. Fiber length alone

C. Generalized mutual information

D. Average launch power alone

Correct Answer: C. Generalized mutual information

Question 9

A DP-QPSK system operates at 40 GBd. What is its uncoded gross bit rate?

A. 80 Gb/s

B. 160 Gb/s

C. 240 Gb/s

D. 320 Gb/s

Correct Answer: B. 160 Gb/s

Question 10

What is the principal purpose of a cyclic prefix in conventional OFDM?

A. To increase constellation order

B. To eliminate all optical noise

C. To double polarization capacity

D. To mitigate channel memory and enable simple frequency-domain equalization

Correct Answer: D. To mitigate channel memory and enable simple frequency-domain equalization