NRZ and PAM4: Levels, Bandwidth, and SNR

Best viewed on a laptop or desktop. These panels are built so you can move a slider and watch several charts answer at once. A phone has no room to put them side by side.

Traditional digital communications rely on Non-Return-to-Zero (NRZ) signalling: two voltage states representing a binary 0 or 1. To transmit more data across an NRZ interconnect, the intuitive approach is to clock the bits faster. But copper transmission lines push back ruthlessly against higher toggle rates: conductor skin-effect and dielectric loss scale aggressively with frequency. Doubling a lane's throughput from 28 Gbps to 56 Gbps under NRZ would require doubling the Nyquist frequency from 14 GHz to 28 GHz, often introducing 15 to 25 dB of additional loss that completely swallows the signal.

PAM4 (4-level Pulse Amplitude Modulation) escapes this frequency barrier by trading amplitude resolution for spectral efficiency. Instead of transmitting one bit per clock cycle, PAM4 transmits two bits per symbol by establishing four distinct voltage levels. Because each symbol carries twice the payload, a 56 Gbps link operates at 28 GBaud, keeping its Nyquist frequency at 14 GHz. The channel sees a much gentler attenuation curve.

The engineering catch is that splitting the total supply swing into four levels creates three stacked eyes, each approximately one-third the vertical height of an equivalent NRZ eye. That geometric compression imposes an immediate ~9.54 dB signal-to-noise ratio (SNR) penalty, transforming the link from one dominated by insertion loss to one dominated by noise, linearity, and statistical error rates.

Why anyone would want four levels

A binary signal carries one bit per symbol: high or low. To send twice as much data you send symbols twice as fast, which doubles the bandwidth the channel has to carry.

That is the problem. Channel loss climbs steeply with frequency, so doubling the symbol rate does not cost twice the loss — it costs considerably more, and eventually the channel simply cannot carry it over any useful distance.

PAM4 takes the other route. Instead of sending symbols faster, send more information per symbol: four voltage levels, each encoding two bits. The same data rate now needs half the symbol rate, and therefore half the Nyquist frequency, and the channel gets an easier job at the price of a harder decision at the receiver.

The trade, stated precisely

NRZ has two levels and one bit per symbol, so the symbol rate equals the bit rate and the Nyquist frequency is half of it. PAM4 has four levels and two bits per symbol, so the same bit rate is carried at half the symbol rate — and therefore half the Nyquist frequency.

Because copper loss rises steeply with frequency, halving Nyquist is worth a great deal. It is the only reason 64 GT/s over a connectorised board channel is possible at all; the NRZ version would need 32 GHz, where the loss is prohibitive over any useful distance.

penalty = 20·log₁₀(3) ≈ 9.5 dB Three eyes stacked in the swing that previously held one leaves each a third the height. State the normalisation, because that is what the number depends on: this compares ADJACENT-LEVEL SPACING at EQUAL TOTAL PEAK-TO-PEAK SWING. It is not a complete system penalty — bandwidth, noise, equaliser behaviour, threshold placement and coding all move the real comparison, and PAM4 halves the Nyquist frequency, which gives a good deal of it back.

What 9.5 dB is, and what it is not It is the ratio of adjacent-level spacing, at equal total swing: 20·log₁₀(3), because three gaps now occupy the range that held one. Change the normalisation and the number changes — comparing at equal average power, or at equal outer-eye amplitude, gives a different figure.

It is not the end-to-end penalty. Against it, PAM4 runs at half the symbol rate for the same bit rate, so the channel is worked at half the Nyquist frequency and delivers far less loss — which is the entire reason to do it. Set against it again are level-dependent non-linearity, more transitions, and error statistics that cluster. The net answer is a link-budget question, not a single constant.

What else changes

Three eyes, not one. They are not identical. Driver non-linearity makes the outer and inner eyes behave differently, so transmitter linearity becomes a specified parameter — measured as level separation — in a way it never was for NRZ.
Gray coding. Adjacent levels differ by one bit, so the most likely symbol error costs one bit error rather than two. It is free and it roughly halves the bit error rate for a given symbol error rate.
Error statistics change shape. Errors cluster by level, and a DFE mistake can produce a burst. This interacts badly with lightweight FEC, which is why precoding is used to break the correlation.
Crosstalk hurts three times as much. The same absolute millivolts of coupled noise eat three times the fraction of a PAM4 eye. Every geometry decision gets stricter.

Why FEC becomes mandatory Nine and a half decibels cannot be recovered from the channel, so the standards move the target instead: a raw error rate around 10⁻⁶, corrected back to 10⁻¹² and beyond by FEC. That makes error correction part of the electrical budget rather than a protocol layer above it — and, usefully, makes the raw error rate large enough to measure directly instead of extrapolating.

The rule of thumb worth carrying: PAM4 is the right answer when the channel is loss-limited, because halving Nyquist buys more than the amplitude penalty costs. It is the wrong answer when the channel is noise- or crosstalk-limited, because there the penalty is pure loss and the frequency relief buys nothing.

Why this decides how your board behaves

It changes what limits you. An NRZ link at the same data rate is usually loss-limited. A PAM4 link, with half the loss to fight and a third the eye height, is far more often noise- and crosstalk-limited. The same board can be adequate for one and not the other.
Crosstalk hurts three times as much. The same coupled millivolts now eat three times the fraction of an eye. Spacing and shielding decisions that were comfortable at NRZ may not survive the transition.
Reflections hurt three times as much, for exactly the same reason — which makes return loss and via design disproportionately more important.
Raw error rates are much higher, and that is expected. PAM4 links are designed to run at a raw BER around 10⁻⁶ and rely on forward error correction to reach the required rate. A raw number that would be alarming on an NRZ link is normal here.

What to do about it

Re-budget noise and crosstalk, not just loss. The instinct is to celebrate the halved Nyquist and reuse the channel. The eye height penalty means the noise budget has changed by more than the loss budget improved.

Attack return loss harder than you would at NRZ. Backdrilling, via design and connector launches all matter more when a reflection costs three times its previous share.

Expect three eyes, and check all three. They are not identical: the levels are not perfectly evenly spaced in a real transmitter, and the middle eye sees different threshold noise from the outer ones. Reporting one eye height for a PAM4 link is incomplete.

Report raw and post-FEC error rates separately, and never quote one as if it were the other. The gap between them is the entire design.

Using this to find a fault

One eye much worse than the other two. Level non-linearity in the transmitter, or threshold placement at the receiver. It is a device problem, not a channel one — the channel treats all three the same.
Errors clustering on particular symbol transitions. Transitions spanning three levels have the largest slew and the most ISI. Gray coding means such a transition is still only one bit in error, which is itself diagnostic.
Post-FEC errors with an acceptable raw rate. Suspect bursts. FEC has a limited burst-correcting capacity, and DFE error propagation or a periodic aggressor produces exactly the burst structure it copes worst with.
A channel that was fine at NRZ and marginal at PAM4. Check crosstalk before loss. The loss got better; the sensitivity to everything else got worse.

Go deeper — Gray coding, the 9.5 dB trade, and why PAM4 requires FEC

Gray coding and error mapping. The four PAM4 voltage levels (conventionally denoted -3, -1, +1, +3, or L0, L1, L2, L3) are labelled so that adjacent levels differ in only a single bit: 00 → 01 → 11 → 10. In any real transmission line contaminated by Gaussian thermal noise or minor residual ISI, the vast majority of slicer mistakes occur between immediately adjacent thresholds (e.g. mistaking an L1 for an L2). With Gray coding, that single-level mistake flips exactly one bit in the decoded stream rather than two. In the adjacent-error-dominated regime, this coding trick halves the raw Bit Error Rate (BER ≈ SER / 2) at zero hardware cost.

Why PAM4 links fundamentally require FEC. In the NRZ era, high-speed standards demanded an "error-free" raw physical layer, mandating an uncorrected BER of 10^-12 or 10^-15. With PAM4's 9.5 dB SNR penalty, building a receiver front end capable of achieving an uncorrected 10^-12 BER across a 30 dB copper backplane is economically and physically unfeasible — it would demand unsustainable transmit power and impractically low receiver noise floors.

The architectural solution is Forward Error Correction (FEC). Standards like PCIe Gen 6 and 100G/400G Ethernet intentionally relax the target raw (pre-FEC) BER to 10^-4 or 10^-5. At this relaxed threshold, the eyes do not need to be wide open; they only need to yield a manageable trickle of random errors. Powerful digital logic at the receiver — typically Reed-Solomon codes like RS(544, 514) — then consumes the raw symbol stream, detects the errors, and mathematically reconstructs the original bits to deliver a post-FEC BER below 10^-12. The trade-off is algorithmic processing latency (several tens of nanoseconds) and roughly 3% to 6% of channel bandwidth consumed by parity overhead.

DFE error bursts and FEC interleaving. The vulnerability of this architecture is burst errors. Reed-Solomon FEC can correct up to a fixed number of corrupted symbol blocks per codeword (for RS(544, 514), up to 15 ten-bit symbols per 544-symbol codeword). But if a receiver DFE makes an error on an inner PAM4 eye, feedback tap propagation causes the decision slicer to misfire on successive unit intervals, producing a concentrated burst of consecutive bit errors. If a single burst corrupts more symbols than the FEC's correction budget, the entire codeword fails, causing a catastrophic packet drop. To mitigate this, modern protocols use 1-to-2 or 1-to-4 symbol interleaving, distributing adjacent temporal bits across distinct FEC codewords so no single burst overwhelms a single decoder block.

What the 9.5 dB is not. It is a clean statement about one thing: adjacent level spacing at equal total swing. Three system effects move the real comparison, and two of them favour PAM4:

Half the Nyquist frequency gives back a large part of the penalty on a lossy channel — often more than all of it, which is the whole reason PAM4 exists.
Noise bandwidth halves too, because the receiver's front end only needs half the bandwidth. That is worth about 3 dB of noise on its own.
Threshold placement and level linearity cost something the ideal calculation does not include: three decision thresholds have to be placed accurately, and real transmitters do not produce perfectly even levels.

So quoting 9.5 dB as "the PAM4 penalty" without saying what it is a penalty in is the most common error on this topic. It is an amplitude ratio at equal swing, not a system margin comparison.

In the real world

The move to PAM4 changes the character of signal integrity work more than any other transition on this site. NRZ debugging is mostly about loss and reflections — things you fix with geometry and materials. PAM4 debugging is mostly about noise, linearity and error statistics — things you fix with silicon settings, shielding and coding.

Which means the useful instinct changes too. On an NRZ link, a marginal channel is usually asking for less loss. On a PAM4 link, it is usually asking for less noise, and reaching for the loss lever first is how a week disappears.