# PAM4 and FEC Push the Limits of the Shannon-Hartley Theorem

2018-10-15  |  5 min read

The Shannon-Hartley theorem states that there is a theoretical maximum amount of error-free data that can be delivered over a specified channel bandwidth in the presence of noise. By increasing either the channel bandwidth or the number of signal levels, it is possible to achieve higher data rates.  Non-return-to-zero (NRZ) and four-level pulse amplitude modulation (PAM4) are two signal modulation technologies used to increase data rate over a channel.

NRZ and PAM4 Modulation

NRZ is the most common signal modulation scheme for 100GE today. It is a two-state transmission system (also referred to as two-level pulse amplitude modulation or PAM2) where positive voltage represents a logical "1", and an equivalent (generally) negative voltage represents "0". 100GE requires four lanes of 25 gigabits per second (Gb/s) NRZ modulated signals. Since NRZ has gradually evolved over the last 50 years, with improved speeds from 110 bits per second to 100 Gb/s, many new concepts and challenges have already been researched and addressed. By applying these same concepts, using eight lanes of 56 Gb/s NRZ signaling to move to 400GE is a logical evolution. However, as speeds of NRZ designs increase above 28 Gb/s, channel loss becomes a limiting factor. PAM4 and forward error correction (FEC) are recommended to reach 400 Gb/s speeds.

PAM4 signals use four amplitude levels with bits 00, 01, 10 and 11 to represent a symbol. The number of symbols transmitted per second (baud rate) is half the number of bits sent per second. For example, a data rate of 28 gigabaud (GBaud) means there are 56 gigabits of data transmitted per second. A 28 GBaud PAM4 signal provides double the data rate (throughput) in the same bandwidth as a 28 GBaud NRZ signal where one bit represents one symbol.

This increased data throughput comes at a cost. PAM4 designs are far more susceptible to noise since an amplitude swing of two represents four signal levels. In PAM4 transceiver designs, the signal-to-noise ratio (SNR) is lower, making noise analysis much more complicated than with NRZ. Testing needs to account for channel return loss, as well as noise from the test instrumentation. Forward error correction (FEC) is used to improve link integrity and counteract physical layer level errors introduced by reduced SNR in PAM4 signals.

Forward Error Correction (FEC)