# 5-PAM - 5-PAM

PAM-5 is a pulse amplitude - modulation method with five amplitude levels . It is used with Fast Ethernet according to 100BASE-T2 and Gigabit Ethernet according to 1000BASE-T on copper cables.

One of five possible states, also referred to as a symbol , is transmitted per transmission step (cycle) . From the five states results in an information content of$\log _{2}5$ ≈ 2.32 bits. With Ethernet, 2 bits per symbol are used as user data, the rest is used to protect against transmission errors.

## Use case Ethernet

With Fast Ethernet according to 100BASE-T2, a two-dimensional 5-PAM is used (also referred to as PAM-5x5 in the standard ): With the symbol rate of 25 Msymbols / s used on each of the two pairs and the user data portion of 2 bits per symbol, the result is Usable bit rate of
${\rm {25{\tfrac {\;MSymbole}{s}}\cdot 2\cdot {\tfrac {2\;Bit}{Symbol}}=100\;{\tfrac {Mbit}{s}}}}$ . This means that exactly 4 bits of user data are transmitted in each cycle.

With Gigabit Ethernet 1000BASE-T according to the IEEE Standard 802.3, a four-dimensional 5-PAM is used via Cat-5 cable ( also referred to as 4D-PAM5 in the standard   ): at the symbol rate of 125 M symbols / s on each of the four wire pairs and the useful data portion of 2 bits per symbol results in the useful bit rate of
${\rm {125{\tfrac {\;MSymbole}{s}}\cdot 4\cdot {\tfrac {2\;Bit}{Symbol}}=1000\;{\tfrac {Mbit}{s}}}}$ . Exactly 8 bits of user data are transmitted in each cycle.

With the four-dimensional 5-PAM, 5 4 = 625 symbols are available per step (→$\log _{2}625$ ≈ 9.29 bit). Of this, 4 * 2 = 8 bits = 1 byte are used as user data (→ 2 8 = 256 symbols). The rest of the symbols are used for forward error correction (FEC).

With Gigabit Ethernet, a byte is first divided into four groups of 2 bits each. Each group of 2 bits is expanded to 3 bits using trellis code modulation (TCM). The additional bit per group introduced by the convolutional code of the TCM is not trivially dependent on the other bits and represents the error correction information required for forward error correction. Taking into account the additional bits introduced per group, the combined bit rate of user data and redundancy information is for forward error correction
${\rm {125{\tfrac {\;MSymbole}{s}}\cdot 4\cdot {\tfrac {3\;Bit}{Symbol}}=1500\;{\tfrac {Mbit}{s}}}}$ .
User data and forward error correction therefore require a total of 9 bits (→ 2 9 = 512 symbols); the remaining 113 symbols provided by PAM-5 are partly used for control information.

A similar procedure is used for Fast Ethernet according to 100BASE-T2, except that two groups of 2 bits each are formed and the trellis code modulation used has different parameters. 

An essential property of the TCM is not only an increase in redundancy due to the convolutional coding, but it also defines the assignment to the individual transmission symbols, in this case certain voltage levels on the line. With Gigabit Ethernet according to 1000BASE-T, the 3 bits of a group are assigned to the five different symbols (= voltage levels) of a wire pair. An essential property of the TCM is that this assignment is not carried out statically, but rather depends on the previous states, ie on the data that have already been transmitted. It is therefore not possible to specify a specific assignment table between user data bits and transmission symbol for a step of the transmission.

3 bit combination of a group Exemplary electrical voltage per pair
000 0 V
001 0.5 V
010 1 V
011 −0.5 V
100 0 V
101 0.5 V
110 −1 V
111 −0.5 V

## Individual evidence

1. IEEE 802.3-2008 Standard: Carrier sense multiple access with collision detection (CSMA/CD) access method and physical layer specification. ISBN 973-07381-5797-9.
2. IEEE 802.3-2002 standard. Older, freely available edition
3. Error Control Coding and Ethernet (PDF-Datei; 153 kB) Presentation Slides, IEEE 802.3 EFM Study Group, 2001.