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1 Facuty of Electronics & Telecommunications, HCMUNS BÀI 3: Format (Channel coding) Facuty of Electronics & Telecommunications, HCMUNS Đặng Lê Khoa Email:danglekhoa@yahoo.com dlkhoa@fetel.hcmuns.edu.vn 2 Facuty of Electronics & Telecommunications, HCMUNS 2006-01-26 Lecture 2 3 Facuty of Electronics & Telecommunications, HCMUNS 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: 2 Sat 2 Lin 222 )()(})]({[ σσσ +==−= ∫ ∞ ∞− dxxpxexqx q E ll L l l qxp q )( 12 2 12/ 0 2 2 Lin ∑ − = = σ Uniform q. 12 2 2 Lin q = σ 2006-01-26 Lecture 2 4 Facuty of Electronics & Telecommunications, HCMUNS 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 2006-01-26 Lecture 2 5 Facuty of Electronics & Telecommunications, HCMUNS 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 )(ty )(tx )( ˆ ty )( ˆ tx x )( xCy = x ˆ y ˆ Compress Qauntize Channel Expand Transmitter Receiver 2006-01-26 Lecture 2 6 Facuty of Electronics & Telecommunications, HCMUNS Statistical of speech amplitudes • In speech, weak signals are more frequent than strong ones. • Using equal step sizes (uniform quantizer) gives low for weak signals and high for strong signals. – Adjusting the step size of the quantizer by taking into account the speech statistics improves the SNR for the input range. 0.0 1.0 0.5 1.0 2.0 3.0 Normalized magnitude of speech signal Probability density function q N S ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ q N S ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 2006-01-26 Lecture 2 7 Facuty of Electronics & Telecommunications, HCMUNS Baseband transmission • To transmit information through physical channels, PCM sequences (codewords) are transformed to pulses (waveforms). – Each waveform carries a symbol from a set of size M. – Each transmit symbol represents bits of the PCM words. – PCM waveforms (line codes) are used for binary symbols (M=2). – M-ary pulse modulation are used for non-binary symbols (M>2). Mk 2 log= 2006-01-26 Lecture 2 8 Facuty of Electronics & Telecommunications, HCMUNS PCM waveforms • PCM waveforms category:  Phase encoded  Multilevel binary  Nonreturn-to-zero (NRZ)  Return-to-zero (RZ) 1 0 1 1 0 0 T 2T 3T 4T 5T +V -V +V 0 +V 0 -V 1 0 1 1 0 0 T 2T 3T 4T 5T +V -V +V -V +V 0 -V NRZ-L Unipolar-RZ Bipolar-RZ Manchester Miller Dicode NRZ 2006-01-26 Lecture 2 9 Facuty of Electronics & Telecommunications, HCMUNS PCM waveforms … • Criteria for comparing and selecting PCM waveforms: – Spectral characteristics (power spectral density and bandwidth efficiency) – Bit synchronization capability – Error detection capability – Interference and noise immunity – Implementation cost and complexity 2006-01-26 Lecture 2 10 Facuty of Electronics & Telecommunications, HCMUNS Spectra of PCM waveforms