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Error Analysis of PAM4 Signals

Application Notes


Increasing demands for a connected world with instant data access continue to drive Ethernet, 64G fiber channel, CEI-56G and other next-generation data center networking links. With data rates continuously increasing, emerging data center standards like OIF, CEI, and IEEE 802.3 Ethernet are moving to PAM4 (pulse-amplitude modulation with four levels) multilevel signaling formats. The next step in the continuing need for increased network bandwidth in data centers is 400 Gb/s links. Multilevel signaling formats such as PAM4 are enabling technology to implement 400G. The switch from NRZ (non-returned to zero) to PAM4 is revolutionary, rather than evolutionary from 100G, presenting many new concepts and design challenges. The design and systems characterization of transmission using PAM4 and NRZ signals is challenging at high data rates. The scope of this application note is to provide detailed insights into PAM4 signal generation and analysis techniques; only error analysis techniques and not TDECQ. Before getting into the details, let’s first have a look at the basic definitions. 

Basic Definitions 

NRZ signal: This is a type of line coding used to represent the bits 0 and 1. Positive voltage represents logical 1s, and the equivalent negative voltage represents 0s. 

PAM4 signal: This is a type of line coding which uses a pulse amplitude modulation technique. PAM4 signals have four voltage levels wherein each amplitude level corresponds to the logical bits 00, 01, 10, and 11. In other words, each symbol of PAM4 coding consists of 2 bits which correspond to one voltage level which is amplitude. 

Gray code: The Gray code, or reflected binary code, is the coding pattern where successive symbols differ by one binary bit. In the case of PAM4, 00,01,10 and 11 are the binary bit sequences to represent levels 0, 1, 2, and 3 shown in Table 1. The Gray code representation for the same symbols would be 00, 01, 11, and 10 for the levels 0, 1, 2, and 3. 

PAM4 encoding is also created using a Gray coding pattern because it facilitates error correction. The Gray coding adheres to IEEE and OIF standards. 

With the introduction of bits and symbols, it is worth mentioning the difference between bits per second and Baud. The bits per second unit is used to denote the total number of bits (1s or 0s) transmitted per second. Baud is used to denote the number of symbols transmitted per second. In the case of an NRZ signal, the symbols are the same as that of the bits; Baud and bps (bits per second) mean the same. However, in the case of PAM4, they are different. 

PAM4 has 2 bits per symbol. Therefore, some symbols transmitted per second (Baud) are half as that of the number of bits transmitted per second. In the case of PAM4, if the symbol rate is 28 Gbaud, then it means there are 56 Gigabits transmitted per second. 

List of content: 

  • Need for PAM4  
  • PAM4 Error Analysis 
  • Bit Error Ratio 
  • SER (Symbol Error Ratio) 
  • Importance of SER in PAM4 Context 
  • BERT System 
  • Generating PAM4 Signals Using Two NRZ Channels 
  • Challenges of PAM4 Generation Using Two NRZ Channels 
  • Error Detection Techniques 
  • Operation of an NRZ ED 
  • PAM4 Error Analysis Using an NRZ ED for PAM4 
  • NRZ ED Challenges 
  • Direct PAM4 Analysis 
  • Advantages of Direct PAM4 Detection 
  • Error Ratio Analysis Using M8040A 
  • Introduction to M8040A 
  • PAM4 Analysis Using M8040A BERT 

PAM4 Error Analysis 

The integrity of a serial data link is generally specified by the bit error rate (BER). Note that the term here is ‘rate’ and not ‘ratio’. Bit errors are measured per unit time. Most of the bit errors in real systems are the result of random noise and occur at random times as opposed to an evenly distributed rate [2]. 

Systems that employ decision feedback equalizers (DFE) may generate burst errors that are not randomly distributed. 

The BER is an estimate assessed by taking the ratio of the number of errored bits to the number of transmitted bits. To characterize the randomness of bit errors in real systems, the more convenient way is to explain BER as the bit error ratio at the output of the receiver which is a statistical measurement. The BER is a measure of the receiver’s quality. In practice, BER measurements are important for characterization testing, also because standard consortia define BER compliance requirements. Analyzing specific errors on only 0s or 1s is useful for troubleshooting problems in the receiver or elsewhere in the link. 

The BER measurement is a statistical process, and the measured BER only approaches the actual BER as the number of bits tested approaches infinity. Fortunately, the BER is tested with a predefined threshold; which is the target BER. The number of bits required to reach the predefined threshold i.e. target BER depends on the required confidence level. The confidence level is the probability that ascertains the system’s true BER with the specified BER which is the target BER. The confidence level does not reach 100 percent as this would require an infinite number of bits that are not measurable. For most applications, a typical confidence level of 95 percent is sufficient. Different confidence levels lead to different measurement times. For more details, refer to this guide on how to measure BER. 

Importance of SER in PAM4 Context 

In this application note, the term SER corresponds to the PAM4 signaling, and not to be confused with the SER requirements stated to forward error correction (FEC) in the IEEE standard. 

In PAM4, each symbol represents 2 bits. However, when an error occurs, one symbol error could be either 1-bit error or a 2-bit error. 

Depending on the error, the BER and SER can be the same, or the BER can be half of the SER when each symbol error is only a 1-bit error. 

One of the popular ways of generating PAM4 includes its generation using two binary weighted NRZ streams which involves combining them using power combiner to generate PAM4 signal (discussed later). In this approach, however, problems with one of the NRZ transmitters such as slew rate, incorrect voltage level, and skew could result in errors that only appear on specific transitions (symbol errors) in the PAM4 output. Diagnosing the cause of these situations is possible through error analysis on specific transition types. 


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