Data element: In data communications, our goal is to send data elements, like a passengers.

Signal element: the shortest unit of a digital signal, it is the carrier, like the vehicle.

The relation between data element and signal element can be 1 to 1, 1 to multiple, multiple to 1.

Data rate: the number of data elements(bits) sent in 1 second, unit is bits per second(bps).

Signal rate: number of signal elements sent in 1 second, unit is baud. Sometimes signal rate is called the pulse rate, the modulation rate or the baud rate.

The relationship between data rate and signal rate is :

S=c x N x 1/r

  • S is the number of signal elements
  • c is the case factor, the best , worst or average.The average is 1/2.
  • N is the data rate.
  • r is the previously defined factor, for a signal with L levels, r=log2L.

Just like the actual number of vehicles affects the traffic. The signal rate affects the bandwidth.

So, if we have minimum Bandwidth  Bmin=c x N x 1/r.   Then we can have the maximum data rate: Nmax=1/c x Bmin x r

Line coding schemes

Unipolar scheme:

  • NRZ( non-return to zero)non-return-to-zero_unipolar

The energy is concentrated

Polar schemes:

  • NRZ:
    • NRZ-L( NRZ-level): the level of the voltage determins the value of the bit.NRZ-L
    • NRZ-I( NRZ-Invert): the change lr lack of change in the level of the voltage determins the value of the bit. If there is no change the bit is 0, or else the bit is 1.NRZ-I


Baseline wandering is a problem for both schemes. NRZ-L: If there is a long sequence of 0s or 1s in NRZ-L, the receiver have difficulty discerning the bit value. NRZ-I: If a long sequence of 0s, we have the same problems as NRZ-L.

Synchronization: Receiver doe not know which bit has ended and the next is starting. exist in both NRZ-L and NRZ-I, but more serious in NRZ-L.

Sundden change of polarity in the system. If the polarity changes, NRZ-I does not have a problem; but NRZ-L will interpret 1s as 0s and 0s as 1s.

  • RZ( return to zero)RZ

The synchronization problem has been solved.

There are some other problems: Sudden change of polarity problem exists, three level of voltage, more complex to create and discern.

  • Biphase schemes: Manchester and Differential Manchester. See here.

Problems: need twice bandwidth as the NRZ.

  • Bipolar schemes: AMI( alternate mark inversion), In this code, a binary 0 is encoded as zero volts, as in unipolar encoding, whereas a binary 1 is encoded alternately as a positive voltage or a negative voltage.Means 1st one is positive, then 2nd one is negative, then 3rd one is positive. The name arose because, in the context of a T-carrier, a binary ‘1’ is referred to as a “mark”, while a binary ‘0’ is called a “space”. This is used in long distance communication.