1. Fundamentals of Digital Communication

2. Digital communication system
Input
Signal
Analog/
Digital
Low
Pass
Filter
Sampler
Quantizer
Source
Encoder
Channel
Encoder
Multiplexer
Carrier
Modulator
Pulse
Shaping
Filters
Line
Encoder
To Channel
De-
Modulator
Receiver
Filter
Detector
From Channel
Carrier Ref.
Signal
at the
user end
Digital-to-Analog
Converter
Channel
Decoder
De-
Multiplexer

3. Sampling
Time domain
Frequency domain

4. Aliasing effect
LP filter
Nyquist rate
aliasing

5. modulated (PAM) signal
Sampling theorem
Sampling
process
Analog
signal
Pulse amplitude
modulated (PAM) signal
Sampling theorem: A bandlimited signal with no spectral components beyond , can be uniquely determined by values sampled at uniform intervals of
The sampling rate,
is called Nyquist rate.

6. Quantization
Amplitude quantizing: Mapping samples of a continuous amplitude waveform to a finite set of amplitudes. In
Out
Quantized
values
Average quantization noise power
Signal peak power
Signal power to average quantization noise power

7. Encoding (PCM)
Pulse code modulation (PCM): Encoding the quantized signals into a digital word (PCM word or codeword).
Each quantized sample is digitally encoded into an l bits codeword where L in the number of quantization levels and

8. Quantization example Quant. levels boundaries x(nTs): sampled values
amplitude
x(t)
x(nTs): sampled values
xq(nTs): quantized values
boundaries
Quant. levels
Ts: sampling time t
PCM
codeword
PCM sequence

9. Quantization error
Quantizing error: The difference between the input and output of a quantizer +
AGC
Qauntizer
Process of quantizing noise
Model of quantizing noise

10. Quantization error … Quantizing error:
Granular or linear errors happen for inputs within the dynamic range of quantizer
Saturation errors happen for inputs outside the dynamic range of quantizer
Saturation errors are larger than linear errors
Saturation errors can be avoided by proper tuning of AGC
Quantization noise variance:
Uniform q.

11. Uniform and non-uniform quant.
Uniform (linear) quantizing:
No assumption about amplitude statistics and correlation properties of the input.
Not using the user-related specifications
Robust to small changes in input statistic by not finely tuned to a specific set of input parameters
Simply implemented
Application of linear quantizer:
Signal processing, graphic and display applications, process control applications
Non-uniform quantizing:
Using the input statistics to tune quantizer parameters
Larger SNR than uniform quantizing with same number of levels
Non-uniform intervals in the dynamic range with same quantization noise variance
Application of non-uniform quantizer:
Commonly used for speech

12. Non-uniform quantization
It is done by uniformly quantizing the “compressed” signal.
At the receiver, an inverse compression characteristic, called “expansion” is employed to avoid signal distortion.
compression+expansion companding
Compress
Quantize
Expand
Channel
Transmitter
Receiver

13. Digital Signals Transmitting Analog Data with
To convert analog data into a digital signal, there are two basic techniques:
Pulse code modulation (used by telephone systems)
Delta modulation

14. Pulse Code Modulation Analog waveform is sampled at specific intervals
“Snapshots” are converted to binary values

15. Pulse Code Modulation (continued)
Binary values are later converted to an analog signal
Waveform similar to original results

16. Pulse Code Modulation (continued)
The more snapshots taken in the same amount of time, or the more quantization levels, the better the resolution

17. Pulse Code Modulation (continued)
Because the human voice has a fairly narrow bandwidth
Telephone systems digitize voice into either 128 levels or 256 levels
Called quantization levels
If 128 levels, then each sample is 7 bits (2 ^ 7 = 128)
If 256 levels, then each sample is 8 bits (2 ^ 8 = 256)

18. Pulse Code Modulation (continued)
How fast do you have to sample an input source to get a fairly accurate representation?
Nyquist says 2 times the bandwidth
Thus, if you want to digitize voice (4000 Hz), you need to sample at 8000 samples per second

19. Delta Modulation
An analog waveform is tracked using a binary 1 to represent a rise in voltage and a 0 to represent a drop

20. Source Coding To eliminate redundancy
Huffman Coding
Shannon-Fano Coding
To maximize information rate in a transmission
What is Information Rate ?
Information per bit  Entropy

21. Channel Coding Error Control Coding
To reduce the impact of channel errors by controlled introduction of redundancy
Decrease in effective data rate
Increased coding gain
Forward Error Correcting Codes
Linear Block Codes
Convolutional Codes
ARQ methods