Distance and distortion estimation method and apparatus in channel optimized vector quantization

A distortion estimation method in channel optimized vector quantization, comprising the steps of:

• forming a sample vector x by sampling an input signal;
• weighting the sample vector x by a first weighting matrix A;
• weighting a set of code book vectors ĉr by a second weighting matrix B different from said first weighting matrix A;
• forming a set of distance measures dw(Ax,Bĉr) representing the distance between said weighted sample vector Ax and each weighted code book vector Bĉr;
• forming a distortion measure αi(x) by multiplying each distance measure by a predetermined channel transition probability pr|i that an index r has been received at a decoder when an index i has been sent from an encoder and adding together said multiplied distance measures for each possible index r.

A channel optimized vector quantization method, comprising the steps of:

• forming a sample vector x by sampling an input signal;
• weighting the sample vector x by a first weighting matrix A;
• weighting a set of code book vectors ĉr by a second weighting matrix B different from said first weighting matrix A;
• forming a set of distance measures dw(Ax,Bĉr) representing the distance between said weighted sample vector Ax and each weighted code book vector Bĉr;
• forming a set of distortion measures {αi(x)} by multiplying each distance measure by a predetermined channel transition probability pr|i that an index r has been received at a decoder when an index i has been sent from an encoder and adding together said multiplied distance measures for each possible index r;
• determining an index imin corresponding to the smallest distortion measure αi(x);
• and
• representing said sample vector by this index imin.

A channel optimized vector quantization method, comprising the steps of:

• forming a sample vector x by sampling an input signal;
• calculating a set of distortion measures {αi′(x)} in accordance with the expression
• αi′(x)=−2xTATB·μi+1T(φi{circle around (×)}(BTB))1
• where,
• A is a sample vector weighting matrix,
• B is a code book vector weighting matrix, at least one of said weighting matrices A, B being different from the identity matrix,
• μi is an expected i:th reconstruction vector,
• φi is a conditional i:th code book correlation matrix,
• T denotes transposition,
• 1 denotes a vector consisting of all ones, and
• {circle around (×)} denotes elementwise multiplication;
• determining an index imin corresponding to the smallest distortion measure αi′(x);
• and
• representing said sample vector by this index imin.

A distortion estimation method in channel optimized vector quantization, comprising the steps of:

• forming a sample vector x by sampling an input signal;
• calculating a distortion measure αi′(x) in accordance with the expression
• αi′(x)=−2xTATB·μi+1T(φi{circle around (×)}(BTB))1
• where
• A is a sample vector weighting matrix,
• B is a code book vector weighting matrix, at least one of said weighting matrices A, B being different from the identity matrix,
• μi is an expected i:th reconstruction vector,
• φi is a conditional i:th code book correlation matrix,
• T denotes transposition,
• 1 denotes a vector consisting of all ones, and
• {circle around (×)} denotes elementwise multiplication.

A distance estimation apparatus in channel optimized vector quantization, comprising:

• means for forming a sample vector x by sampling an input signal;
• means for weighting the sample vector x by a first weighting matrix A;
• means for weighting a code book vector ĉi by a second weighting matrix B different from said first weighting matrix A;
• and
• means for forming a distance measure dw (Ax,Bĉi) representing the distance between said weighted sample vector Ax and said weighted code book vector Bĉi.

A distortion estimation apparatus in channel optimized vector quantization, comprising:

• means for forming a sample vector x by sampling an input signal;
• means for weighting the sample vector x by a first weighting matrix A;
• means for weighting a set of code book vectors ĉr by a second weighting matrix B different from said first weighting matrix A;
• means for forming a set of distance measures dw (Ax,Bĉr) representing the distance between said weighted sample vector Ax and each weighted code book vector Bĉr;
• means for forming a distortion measure by multiplying each distance measure by a predetermined channel transition probability pr|i that an index r has been received at a decoder when an index i has been sent from an encoder and adding together said multiplied distance measures for each possible index r.

A channel optimized vector quantization apparatus, comprising:

• means for forming a sample vector x by sampling an input signal;
• means for weighting the sample vector x by a first weighting matrix A;
• means for weighting a set of code book vectors ĉr by a second weighting matrix B different from said first weighting matrix A;
• means for forming a set of distance measures {dw (Ax,Bĉr)} representing the distance between said weighted sample vector Ax and each weighted code book vector Bĉr;
• means for forming a set of distortion measures {αi(x)} by multiplying each distance measure by a predetermined channel transition probability Pr|i that an index r has been received at a decoder when an index i has been sent from an encoder and adding together said multiplied distance measures for each possible index r;
• means for determining an index imin corresponding to the smallest distortion measure αi(x) and representing said sample vector by this index imin.

A distortion estimation apparatus in channel optimized vector quantization, comprising:

• means for forming a sample vector x by sampling an input signal;
• and
• means for calculating a distortion measure αi′(x) in accordance with the expression
• αi′(x)=−2xTATB·μi+1T(φi{circle around (×)}(BTB))1
• where
• A is a sample vector weighting matrix,
• B is a code book vector weighting matrix, at least one of said weighting matrices
• A, B being different from the identity matrix,
• μi is an expected i:th reconstruction vector,
• φi is a conditional i:th code book correlation matrix,
• T denotes transposition,
• 1 denotes a vector consisting of all ones, and
• {circle around (×)}denotes elementwise multiplication.

A channel optimized vector quantization apparatus, comprising:

• means for forming a sample vector x by sampling an input signal;
• means for calculating a set of distortion measures {αi′(x)} in accordance with the expression
• αi′(x)=−2xTATB·μi+1T(φi{circle around (×)}(BTB))1
• where
• A is a sample vector weighting matrix,
• B is a code book vector weighting matrix, at least one of said weighting matrices A, B being different from the identity matrix,
• μi is an expected i:th reconstruction vector,
• φi is a conditional i:th code book correlation matrix,
• T denotes transposition,
• 1 denotes a vector consisting of all ones, and
• {circle around (×)} denotes elementwise multiplication;
• and
• means for determining an index imin corresponding to the smallest distortion measure αi′(x) and representing said sample vector by this index imin.