Apparatus and method for low complexity combinatorial coding of signals

• US 9,256,579 B2
• Filed: 05/15/2013
• Issued: 02/09/2016
• Est. Priority Date: 09/12/2006
• Status: Active Grant

• Current Assignee: Google Technology Holdings LLC (Alphabet Inc.)
• Original Assignee: Google Technology Holdings LLC (Alphabet Inc.)
• Inventors: Mittal, Udar, Ashley, James P., Cruz-Zeno, Edgardo M.
• Primary Examiner(s): Yaary, Michael D
• Application Number:
  US13/894,557
• Publication Number:
  US 20130254249A1
• Time in Patent Office: 1,000 Days
• Field of Search: None
• US Class Current: 1/1
• CPC Class Codes: G06F 17/17 Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method G06F17/18 takes precedence ; interpolation for numerical control G05B19/18
• CPC Class Codes: G10L 19/0212 using orthogonal transformation
• CPC Class Codes: G10L 19/035 Scalar quantisation
• CPC Class Codes: H03M 7/14 Conversion to or from non-weighted codes

Abstract

The invention utilizes low complexity estimates of complex functions to perform combinatorial coding of signal vectors. The invention disregards the accuracy of such functions as long as certain sufficient properties are maintained. The invention in turn may reduce computational complexity of certain coding and decoding operations by two orders of magnitude or more for a given signal vector input.

Claims

1. A method for combinatorial coding and decoding, the method comprising the steps of:

receiving a vector comprising speech, audio, image, or video;

receiving a value n based on a number of positions in the vector;

receiving a value d based on a number of occupied positions within the vector;

generating a value F′

(n,d) based on a logarithmic approximation of the combinatorial function of F(n,d) and comprising generating a logarithmic approximation of a numerator of F(n,d) and generating a logarithmic approximation of a denominator by subtracting a combinatorial function Q′

(d) from the numerator; and

using the value F′

(n,d) to code or decode the vector to produce coded or decoded speech, audio, image, or video, wherein the step generating of the value F′

(n,d) comprises the step of generating a value F′

(n,d)=R′

(k), where R′

(k) is an approximation of the function a^k, and where a is a logarithm base,

wherein the step of generating a value F′

(n,d)=R′

(k) further comprises the steps of;

generating an integer component k_i and a fractional component k_f, based on a value k such that k=k_i+k_f;

generating a value K_f, wherein K_f is based on a low resolution Talyor series expansion of 2^kf;

producing the value R′

(k) based on K_f.

2. The method of claim 1 wherein Q′

(d) is an approximation of the function Q(d)=Σ

_j=1^d log_a(j), where a is a logarithm base.

3. The method of claim 1 wherein

4. The method of claim 3 wherein the summation is generated as

5. The method of claim 1 wherein the step of producing the value R′

(k) based on K_f further comprises generating;

R′

(k)=└

2<sup>ki−

l</sup>└

2^lK_f┘

┘

.

6. The method of claim 1 wherein the value F′

(n,d) such that

7. The method of claim 1 wherein the approximation of the function a^k is obtained using a Taylor series expansion method.

8. An apparatus comprising:

a vector generator receiving a vector comprising speech, audio, image, or video;

a combinatorial function generator receiving a value n based on a number of positions in the vector, receiving a value d based on a number of occupied positions within the vector, and generating a value F′

(n,d) based on a logarithmic approximation of the combinatorial function of F(n,d) and comprising generating a logarithmic approximation of a numerator of F(n,d) and generating a logarithmic approximation of a denominator by subtracting a combinatorial function Q′

(d) from the numerator; and

a coder/decoder using the value F′

(n,d) to code or decode the vector to produce coded or decoded speech, audio, image, or video,

said combinatorial function generator generating of the value F′

(n,d) including generating a value F′

(n,d)=R′

(k), where R′

(k) is an approximation of the function a^k, and where a is a logarithm base, generating an integer component k_i and a fractional component k_f, based on a value k such that k=k_i+k_f;

generating a value K_f, wherein K_f is based on a low resolution Talyor series expansion of 2^kf, and producing the value R′

(k) based on K_f.

9. The apparatus of claim 8 wherein Q′

(d) is an approximation of the function Q(d)=Σ

_j=1^d log_a(j) where a is a logarithm base.

10. The apparatus of claim 8 wherein