What is baud rate and how is it different from bit rate?

This post briefly describes the concept of baud and bit rates.

As seen from previous posts, multi-level line encoding techniques like QAM-8, QAM-16, QAM-64 etc. use multiple values of amplitudes and phases to form multiple symbol values or signalling levels. The number of different symbol values/signalling levels in a line encoding technique decides the number of binary bits (0 and 1) that can be represented by each symbol.

For e.g.

QAM-8 uses two different Amplitudes and four phases thereby giving eight different  symbols. Since there are 8 different symbols, each symbol could be used to represent 3 binary digits (for e.g. symbol1 represents 000, symbol2 represents 001, … symbol8 represents 111), thereby giving a data rate that is 3 times that of the symbol rate.

QAM-16 uses four amplitudes and four phases, therey giving sixteen different symbols. Since there are 16 different symbols, each symbol could be used to represent 4 binary digits (for e.g. symbol1 represents 000, symbol2 represents 001, …. symbol16 represents 1111). Hence the data rate of QAM-16 is four times that of the symbol rate.

Baud rate or symbol rate is the number of symbols that can be sent on the telecommunication link per second. It is also known as the signalling speed or the number of signal value changes per second. The baud rate mainly depends on the transmission capacity and noise tolerance level of the channel/link. Additionally, the sender and the receiver needs to have the processing capability to encode and decode symbols at the baud rate.

Bit rate or data rate is the number of bits that can be transmitted on the link per second.

The relationship between bit rate and baud rate is given below:

Let “M” denote the number of signalling levels or the number of symbols. For e.g. M = 8 for QAM-8 and M=16 for QAM-16.

•   Baud Rate = No: of symbol changes per second

•   Bit rate= (Baud rate) * log (M) ,   where log is to the base 2.

For a baud rate of 100 symbols per second, the table below gives the bit rate for three different line encoding methods.

Bit Rates for different encoding methods

 Thus, it is seen that  for the same baud rate, a change in the line encoding technique results in different bit rates.

Basic Analog Line Coding techniques used in Computer Communication

This post briefly outlines basic line coding techniques used during analog transmission. The focus is mainly on encoding digital data into analog signals (see diagram below), as this is widely used in computer communication. The other combination of analog data getting converted directly into analog signals is primarily used in radio and TV transmission networks.

The diagram given below illustrates a typical encoding process of converting digital data into analog signals, using a digital modem.

Digital data to Analog Signal conversion process

The primary three base methods used for encoding digital data into analog signals are Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK) and Phase Shift Keying (PSK). All the three techniques rely on modulating a high frequency carrier wave based on the binary data that is to be encoded.

• In ASK, the amplitude of the carrier wave  is changed instantly based on  the digital data, without changing the frequency and phase of the carrier wave.
• In FSK, the frequency of the carrier wave is alone changed based on the instantaneous value of the digital data, keeping the amplitude and phase constant.
• In PSK, the phase of the carrier wave is changed based on the digital data that is to be encoded, without changing the amplitude and carrier.

To understand these modulation techniques, let us take the very basic version of these techniques, namely Binary-ASK, Binary-FSK and Binary-PSK or BPSK. Since there are only two different types of symbols in binary data, namely 0 and 1, the encoded analog signal would either have two different amplitudes (ASK) or two different frequencies (FSK) or two different phases (PSK). The diagram given below illustrates the three digital modulation techniques for encoding the same digital data pattern (1010).

Example for Binary-ASK, Binary-FSK and Binary-PSK

In the diagram, for encoding the same digital binary stream 1010,

a) BASK uses two different amplitudes, namely A1 for encoding  a binary 1 and A2 for encoding a binary 0, without changing the carrier wave’s frequency and phase.

b) BFSK uses two different frequencies (number of cycles per second), for representing binary 1 and binary 0, without changing the carrier wave’s amplitude and phase. While a binary 1 is represented by a single cycle of the wave in one bit interval, a binary 0 is represented by a wave with two cycles in one bit interval. The amplitude and phase of the carrier wave is unchanged.

c) BPSK uses two different phases for representing binary 1 and binary 0, without chaning the carrier wave’s amplitude and frequency. While a binary 1 is represented by a normal sine wave, a binary 0 is represented by a similar sine wave shifted in phase by 180 degree.

Multi-Level ASKs, FSKs, PSKS

Generalizing the above line encoding techniques, by having multiple signalling levels/values (instead of two in binary), it is possible to have different line coding techniques. For example, 2-level, 4-level, 16-level ASKs, FSKs or PSKs etc. The diagram given below illustrates a 4-level PSK.

4-level PSK

The above diagram format is named as constellation diagram. It is similar to the polar coordinate system, where the angle of a vector represents the phase and the length of the vector represents the amplitude. Each dot represents a specific value of the signal or it represents a unique symbol.  In this example of 4-level PSK, there are 4 different symbols, each represented by dots. The 4 symbols have different phase values, while having the same amplitude. As seen from the above diagram, in this particular example of 4-level PSK, a sine wave with 4 different phases, namely with degrees 45, 135, 225 and 315 are used to represent four different symbols. If data  encoded is to be binary, then these 4 symbols could be 00, 01, 10 and 11. Thus using one signal value (or symbol), two binary digits could be encoded in this scheme. Therefore, in 4-level PSK, data rate (number of bits per second) that can be sent is double when compared to BPSK, for the same symbol rate.

Combining ASK and PSK (QAM)

Another common approach to increase the bit rate is to simultaneously use both ASK (different amplitudes) and PSK (different phases), without changing the frequency of the carrier wave. Such techniques are referred to as QAM (Quardature Amplitude Modulation). The figures given below illustrate two such examples of combining ASK and PSK.

QAM-8

QAM-16

As shown in the above diagram,

 QAM-8 uses two different Amplitudes and four phases thereby giving eight different  symbols. Since there are 8 different symbols, each symbol could be used to represent 3 binary digits (for e.g. symbol1 represents 000, symbol2 represents 001, … symbol8 represents 111), thereby giving a data rate that is 3 times that of the symbol rate.

QAM-16 uses four amplitudes and four phases, therey giving sixteen different symbols. Using a similar logic, QAM-16 can represent 4 binary digits per symbol and hence the data rate of QAM-16 is four times that of the symbol rate.

Using similar techniques with more values of amplitudes and phases, higher data rates can be achieved.

One thing to be noted is that more number of symbols means the overall complexity of processing increases at the sender and receivere. Especially, the complexity is more at the receiver as it does not know the incoming symbols and hence needs the capability to instantaneously decode between different symbols that are coming at  line rate.

Another approach that is commonly used is to combine these modulation techniques with channel multiplexing techniques like FDM, TDM etc. to achieve even more higher data rates.

Bit and Baud Rates

In general, for multi-level modulation techniques, if there are “N” number of symbols and if the symbol rate (number of symbols that can be transmitted on the link per second) is S, then the data rate (D)(number of bits per second that can be transmitted on the link) is D= S * log N, where the base of the log is 2.

While the symbol rate is generally known as the baud rate, the data rate is known as the bit rate.