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lecture12 - EE455/591 Digital Transm ission Digital Re...

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EE455/591 EE455/591 Digital Transmission Digital Transmission Reading: Section 7.1, 7.2 Reading: Section 7.1, 7.2 Review: Vector Quantizaton Review: Vector Quantizaton Topics: Topics: 1. Shannon Channel Capacity Formula 1. Shannon Channel Capacity Formula 2. Digital Multiplexing 2. Digital Multiplexing 3. Digital Communications System 3. Digital Communications System 4. PulseAmplitudeModulation (PAM) and PulsePosition Modulation (PPM) Modulation (PPM)
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Review: Vector Quantization Ex 2: (x 1 , x 2 ) is highly correlated: x 1 uniformin [-1,1] and x 2 = x 1 + u with u uniformin [-¼,¼] Wemay quantizex 1 and x 2 each by 2 bits. This is bad because wearequantizing a large box where most probability is located within theparallelogram shown Wemay also quantize x 1 and u separately, but sinceu has a smaller range, it should require fewer quantization levels, e.g. x 1 is quantized by 3 bits and u by 1 bit Thebetter way is to dividethethin parallelogram into 16 smaller parallelograms as shown below. x 1 x 2 1 -1 ¼ If wequantizeby 8 bits, i.e. dividing theparallelogram into 256 regions, then weshould use256 small squares or hexagons to dividetheparallelogram. At theboundary, thesesquares or hexagons may fall outside becausethey do not fit exactly theparallelogram.
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1. Shannon Channel Capacity Formula For channel of bandwidth W, and SNR S/N, error free transmission is possiblefor data rate R less than channel capacity C = W log 2 (1 + S/N) Noise power N=N 0 W where ½N 0 = ½kT is the spectral noise power.
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