PAM4

PAM4 (pulse amplitude modulation, 4 levels) is a 2-bit-per-symbol modulation format that has become the dominant short-reach optical interconnect modulation since 2018. Compared to traditional NRZ binary signaling, PAM4 doubles the bit rate for the same baud rate (symbol rate) — at the cost of reduced noise margin.

Operating principle. Each transmitted symbol takes one of four optical power levels, encoding two bits:

Bit pair	Symbol level	Gray-coded mapping (typical)
00	Level 0 (lowest)	00
01	Level 1	01
11	Level 2	11
10	Level 3 (highest)	10

The use of Gray coding (adjacent levels differ by one bit) means most decision errors flip only one bit per symbol, improving BER after error correction.

Bit rate vs baud rate. PAM4 carries 2 bits per symbol; at the same baud rate as NRZ, it carries twice the bit rate. Standard PAM4 deployments:

Standard	Baud rate	Bit rate per lane	Bit rate × N lanes
100G-DR4 / FR4	26.5625 Gbaud	53.125 Gb/s	4 lanes = 212.5G
200G-DR4 / FR4	26.5625 Gbaud	53.125 Gb/s	4 lanes = 212.5G (with 800G amplification)
400G-DR4 / FR4	53.125 Gbaud	106.25 Gb/s	4 lanes = 425G
800G-DR8	106.25 Gbaud	106.25 Gb/s	8 lanes = 800G

The 53.125 and 106.25 Gbaud rates accommodate FEC overhead; the "lane rate" (50G, 100G, 200G) refers to the post-FEC user payload.

Why PAM4 displaced NRZ. At baud rates above 25 Gbaud, electronic transceivers face increasingly severe challenges:

• Channel bandwidth (cables, PCB traces, packaging)
• Eye-diagram opening reduces with bandwidth
• SerDes signal integrity becomes harder
• Power consumption per Gb/s scales superlinearly

PAM4 allows the same bit rate at half the baud rate, halving the bandwidth requirement at modest signal-integrity cost. The same 25 Gbaud SerDes that supported 25G NRZ in 100G-SR4 now supports 50G PAM4 in 200G-SR4.

Power penalty vs NRZ. Compared to NRZ at the same average optical power:

• Inner eye amplitude: 1/3 of full swing (in NRZ, 1 of 2 levels has full swing)
• Outer eye SNR penalty: $20 \log_{10}(3) = 9.54$ dB
• PAM4 power penalty after FEC: 4 – 6 dB (FEC closes some of the gap)

This penalty is why PAM4 requires substantial forward error correction (FEC) — typically RS(544,514) or KP4 FEC overhead of ~6%.

Modulator requirements. PAM4 places stricter demands on the optical modulator:

• Linearity: the modulator must produce equally-spaced levels; nonlinearity (e.g., Mach-Zehnder cosine response) requires pre-distortion or DSP compensation
• Extinction ratio: typically 4 – 6 dB for PAM4 vs > 8 dB for NRZ
• Eye height to OMA conversion: PAM4 average power matters more than peak-to-peak swing
• Drive voltage swing: must drive the modulator linearly across 4 levels

Standard PAM4 modulators in deployment:

Modulator type	Bandwidth	$V_\pi L$	Use
Silicon photonic MZ (depletion)	30 – 50 GHz	1.5 – 3 V·cm	100/200G PAM4
InP-based MZ	40 – 60 GHz	1 – 2 V·cm	400/800G PAM4
Lithium niobate on insulator (LNOI)	70 – 110 GHz	1.5 – 2.5 V·cm	800G+ PAM4
Electro-absorption modulator (EAM)	40 – 60 GHz	nonlinear; needs pre-distortion	100/200G PAM4

Receiver requirements. PAM4 receivers need 3 decision levels (vs 1 for NRZ) and tighter linearity:

• Linear TIA: must amplify all 4 levels equally
• High-bandwidth ADC: typically 30 – 60 Gsa/s for PAM4 receivers
• DSP: feedforward equalization, decision-feedback equalization
• Clock recovery: more complex than NRZ due to 4-level transitions

Modern 50/100G PAM4 receivers use chip-scale CMOS/SiGe integration of TIA + ADC + DSP, all in 5/7/12 nm processes.

FEC requirements. PAM4 systems require FEC to recover from the worse pre-FEC BER:

Standard	Pre-FEC BER target	FEC	Post-FEC BER
100G-DR (PAM4)	$\sim 2 \times 10^{-4}$	RS(544,514) "KP4"	$< 10^{-15}$
400G-DR (PAM4)	$\sim 2 \times 10^{-4}$	RS(544,514)	$< 10^{-15}$
800G-DR (PAM4)	$\sim 2 \times 10^{-4}$	Concatenated RS + LDPC	$< 10^{-15}$

The pre-FEC BER threshold (~$2 \times 10^{-4}$) is far higher than NRZ's classical $10^{-12}$ — designed around the FEC's correction capability.

Eye diagram. PAM4 eye diagrams have three eyes vertically (between Levels 0/1, 1/2, 2/3) and one horizontally per symbol. Standard measurements:

• Inner eye height: amplitude of innermost eye (level 1 - level 2 or similar)
• Outer eye heights: amplitudes of edge eyes
• Eye linearity: uniformity of the three eye heights
• Skew: lane-to-lane timing skew

PAM4 eye diagrams are noticeably "noisier" than NRZ even with perfect signals — the 3-level discrimination is inherently less robust.

Optical interconnect roadmap. PAM4 is the standard for current-generation 200G/400G/800G optical:

• 2020 – 2022: 100G PAM4 (50G NRZ replacement)
• 2022 – 2024: 200G PAM4 (100G PAM4 generation)
• 2024 – 2026: 400G/800G PAM4 (200G PAM4 per lane)
• 2026+: 1.6T+ via 8-lane 200G PAM4 or 4-lane 400G PAM4 (with possible move to PAM6 or coherent)

PAM4 vs coherent. PAM4 is "direct detection" — single photodiode per lane, no local oscillator. Coherent uses LO + balanced detection + DSP, supporting higher spectral efficiency (DP-QPSK = 4 bits/symbol; DP-16QAM = 8 bits/symbol) but with higher cost and power. For short reach (< 10 km), PAM4 is preferred for cost; for long reach (> 80 km), coherent is necessary.

Beyond PAM4. Future directions:

• PAM6 / PAM8: 3 or 4 bits per symbol; higher capacity at greater SNR cost
• Probabilistic shaping: non-uniform symbol probabilities to optimize for noise
• Multidimensional codes: jointly encode bits across multiple symbols (DM-PAM4)
• Coherent at short reach: 200G coherent ZR/ZR+ for DC interconnect

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 24 (fiber-optic communications); IEEE 802.3bs and 802.3cd standards for PAM4 specifications; OIF (Optical Internetworking Forum) CEI-56G and CEI-112G specifications; Agrawal, Fiber-Optic Communication Systems (4th ed., 2010) for the underlying modulation theory.