Help Lloyds
3
Non Uniform Quantization Functions Optimal Output Alphabets and Levels LLOYD S: Optimize quantization para meter s using the Lloyd algorith m. [PART ITIO N, CODEBOOK] = LLOYDS(TRAINING _SET , INI_CODEBOOK) opti mizes the sca lar qua nti zation PAR TITION and COD EBO OK bas ed on the pro vided tra ini ng vec tor TRA INING_SET usi ng the Llo yd algori thm . The dat a in the var iable TRA NIN G_SET sho uld be typ ica l data for the mes sag e source to be qua nti zed . INI_CODEBOOK is the ini tia l gue ss of the codebook val ues. The opt imized CODEBOOK has the sam e vec tor siz e as INI_CODEBOOK. Whe n INI_CODEBOOK is a scalar int ege r instead of vec tor, it is the len gth of the des ired CODEBO OK vec tor . PAR TIT ION is a vec tor with the vec tor length bei ng the CODEBOOK vector length minus 1. The optimization will be terminated if the relative dis tortio n is less tha n 10^ (-7 ). [PART ITIO N, CODEBOOK] = LLOYDS(TRAINING _SET , INI_CODEBOOK, TOL) provi des the tole rance in the opti mizat ion. [PART ITIO N, CODEBOOK, DISTORTIO N] = LLOY DS(.. .) outpu ts the final disto rtio n valu e. [PART ITIO N, CODEBOOK, DISTORTION, REL_DISTO RTION ] = LLOYD S(... ) outputs the relative dis tor tion val ue in ter min ating the computation. See also QUANTIZ, DPCMOPT . Non-Uniform Quantization QUANTIZ: Pro duce a quantization index and a qua nti zed out put val ue. INDX = QUANTI Z(S IG, PAR TIT ION) produces a quantization index INDX of the input sig nal SIG based on the decision points PAR TIT ION. Eac h element in INDX is one of the N integers in range [0 : N-1]. PAR TITION is a strict asc end ing ord ered N-1 vec tor tha t spe cifies the boundaries. Elements of INDX = 0, 1, 2, ..., N-1 represent SIG in the range of (-In f, PARTI TION (1)], (PARTITI ON(1) , PART ITION (2)], (PART ITIO N(2), PARTI TION( 3)], ..., (PART ITION (N-1 ), Inf). [INDX , QUANT ] = QUAN TIZ(S IG, PARTI TION, CODEBOOK ) produces the output value of the quantiz er in QUANT. CODEBOO K is a length N vec tor tha t contains the out put set .
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Transcript of Help Lloyds
8/12/2019 Help Lloyds
http://slidepdf.com/reader/full/help-lloyds 1/3
Non Uniform Quantization Functions
Optimal Output Alphabets and Levels
LLOYDS: Optimize quantization parameters using the Lloyd algorithm.
[PARTITION, CODEBOOK] = LLOYDS(TRAINING_SET, INI_CODEBOOK) optimizes
the scalar quantization PARTITION and CODEBOOK based on the provided
training vector TRAINING_SET using the Lloyd algorithm. The data in
the variable TRANING_SET should be typical data for the message
source to be quantized. INI_CODEBOOK is the initial guess of the
codebook values. The optimized CODEBOOK has the same vector size as
INI_CODEBOOK. When INI_CODEBOOK is a scalar integer instead of
vector, it is the length of the desired CODEBOOK vector. PARTITIONis a vector with the vector length being the CODEBOOK vector length
minus 1. The optimization will be terminated if the relative
distortion is less than 10^(-7).
[PARTITION, CODEBOOK] = LLOYDS(TRAINING_SET, INI_CODEBOOK, TOL)
provides the tolerance in the optimization.
[PARTITION, CODEBOOK, DISTORTION] = LLOYDS(...) outputs the final
distortion value.
[PARTITION, CODEBOOK, DISTORTION, REL_DISTORTION] = LLOYDS(...)
outputs the relative distortion value in terminating thecomputation.
See also QUANTIZ, DPCMOPT.
Non-Uniform Quantization
QUANTIZ: Produce a quantization index and a quantized output value.
INDX = QUANTIZ(SIG, PARTITION) produces a quantization index INDX of
the input signal SIG based on the decision points PARTITION. Each
element in INDX is one of the N integers in range [0 : N-1].
PARTITION is a strict ascending ordered N-1 vector that specifies
the boundaries. Elements of INDX = 0, 1, 2, ..., N-1 represent SIGin the range of (-Inf, PARTITION(1)], (PARTITION(1), PARTITION(2)],
(PARTITION(2), PARTITION(3)], ..., (PARTITION(N-1), Inf).
[INDX, QUANT] = QUANTIZ(SIG, PARTITION, CODEBOOK) produces the
output value of the quantizer in QUANT. CODEBOOK is a length N
vector that contains the output set.
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[INDX, QUANT, DISTOR] = QUANTIZ(SIG, PARTITION, CODEBOOK) outputsDISTOR, the estimated distortion value of the quantization. There is
no decode quantizer function in this toolbox. The decode computation
can be done using the command Y = CODEBOOK(INDX+1).
See also LLOYDS, DPCMENCO, DPCMDECO.
8/12/2019 Help Lloyds
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TIME SAMPLES
R E A L I Z A T I O N
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LLOYD−MAX, GAUSSIAN PDF, N = 3000
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RANGE OF INPUT , x[n]
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LLOYD−MAX, GAUSSIAN PDF, N = 3000
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LLOYD−MAX, GAUSSIAN PDF, N = 3000, W = 8 bits, tol = 10−6
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Figure 1: Lloyd Max quantization: (a) sample realization of standard Gaus-sian distributed input, (b) histogram of Gaussian distributed input, and (c)
quantization error of the non uniform quantizer for a word-length of 8 bits.
