Fundamentals of Digital Communication

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

Sampling Time domain Frequency domain

Aliasing effect LP filter Nyquist rate aliasing

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.

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

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

Quantization example Quant. levels boundaries x(nTs): sampled values amplitude x(t) x(nTs): sampled values xq(nTs): quantized values boundaries Quant. levels 111 3.1867 110 2.2762 101 1.3657 100 0.4552 011 -0.4552 010 -1.3657 001 -2.2762 000 -3.1867 Ts: sampling time t PCM codeword 110 110 111 110 100 010 011 100 100 011 PCM sequence

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

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.

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

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

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

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

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

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

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)

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

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

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

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