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Equation 11 · How AI Datacenter Interconnects Actually Work

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Rline=2 RbaudR_{\mathrm{line}} = 2\,R_{\mathrm{baud}}

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Inputs and operations2R_baud
Result or conditionR_line
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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RlineR_{\mathrm{line}}

Symbol R_line

RlR_line is part of the quantity the equation computes from the expression on the right.

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RbaudR_{\mathrm{baud}}

Symbol R_baud

the writing.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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What the article says around this equation

Modern high-rate Ethernet lanes use PAM4 modulation: instead of encoding one bit per symbol as ordinary NRZ signaling does, PAM4 uses four distinct voltage levels to encode two bits per symbol, so a lane’s bit rate runs at twice its baud (symbol) rate rather than matching it one for one. Writing RbaudR_{\mathrm{baud}} for the symbol rate and RlineR_{\mathrm{line}} for the resulting line rate, Rline=2 RbaudR_{\mathrm{line}} = 2\,R_{\mathrm{baud}}. which is exactly the relationship documented for real 400G optics: a 26.5625 Gbaud lane carries 53.125 Gb/s in an eight-lane configuration, and a 53.125 Gbaud lane carries 106.25 Gb/s in a four-lane configuration [ 8 ] . That doubling is not free. Four voltage levels packed into the same…
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Modern high-rate Ethernet lanes use PAM4 modulation: instead of encoding one bit per symbol as ordinary NRZ signaling does, PAM4 uses four distinct voltage levels to encode two bits per symbol, so a lane’s bit rate runs at twice its baud (symbol) rate rather than matching it one for one. Writing RbaudR_{\mathrm{baud}} for the symbol rate and RlineR_{\mathrm{line}} for the resulting line rate, Rline=2 RbaudR_{\mathrm{line}} = 2\,R_{\mathrm{baud}}. which is exactly the relationship documented for real 400G optics: a 26.5625 Gbaud lane carries 53.125 Gb/s in an eight-lane configuration, and a 53.125 Gbaud lane carries 106.25 Gb/s in a four-lane configuration [ 8 ] . That doubling is not free. Four voltage levels packed into the same signal swing compress the spacing between them, and the same documentation states that PAM4 “considerably reduces the signal-to-noise ratio” relative to NRZ — a roughly 10 dB penalty — which is exactly why a PAM4 transceiver requires a DSP performing equalization and clock recovery, paired with forward error correction, to be usable at all; the guide names RS(544,514) as the industry-standard code, correcting “up to 15 symbol errors within a single codeword” before a frame is considered lost [ 8 ] . The DSP inside a modern transceiver, in other words, is not an incidental feature. It is the component that makes the SNR penalty PAM4 imposes survivable at the rates these fabrics run at.

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