The Hadamard transform-a tool for index assignment

We show that the channel distortion for maximum-entropy encoders, due to noise on a binary-symmetric channel, is minimized if the vector quantizer can be expressed as a linear transform of a hypercube. The index assignment problem is regarded as a problem of linearizing the vector quantizer. We define classes of index assignments with related properties, within which the best index assignment is found by sorting, not searching. Two powerful algorithms for assigning indices to the codevectors of nonredundant coding systems are presented. One algorithm finds the optimal solution in terms of linearity, whereas the other finds a very good, but suboptimal, solution in a very short time.

[1]  Kenneth Zeger,et al.  Asymptotic bounds on optimal noisy channel optimization via random coding , 1994, IEEE Trans. Inf. Theory.

[2]  Petter Knagenhjelm,et al.  How good is your index assignment? , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[3]  C. M. Rader,et al.  Efficient coding of vocoder channel signals using linear transformation , 1966 .

[4]  Roar Hagen,et al.  Robust vector quantization in spectral coding , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[5]  Kuldip K. Paliwal,et al.  Speech Coding and Synthesis , 1995 .

[6]  Hai-Shan Wu,et al.  Index allocation in vector quantisation for noisy channels , 1993 .

[7]  David L. Neuhoff,et al.  The Optimality of the Natural Binary Code , 1992, Coding And Quantization.

[8]  H. Andrews,et al.  Hadamard transform image coding , 1969 .

[9]  Lee C. Potter,et al.  Minimax non-redundant channel coding for vector quantization , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Nariman Farvardin,et al.  A study of vector quantization for noisy channels , 1990, IEEE Trans. Inf. Theory.

[11]  Robert M. Gray,et al.  An Algorithm for Vector Quantizer Design , 1980, IEEE Trans. Commun..

[12]  N. Rydbeck,et al.  Analysis of Digital Errors in Nonlinear PCM Systems , 1976, IEEE Trans. Commun..

[13]  Mikael Skoglund,et al.  Theory for transmission of vector quantization data , 1995 .

[14]  Lee C. Potter,et al.  Minimax nonredundant channel coding , 1995, IEEE Trans. Commun..

[15]  David G. Messerschmitt,et al.  Nonlinear Echo Cancellation of Data Signals , 1982, IEEE Trans. Commun..

[16]  David L. Neuhoff,et al.  Optimal binary index assignments for a class of equiprobable scalar and vector quantizers , 1995, IEEE Trans. Inf. Theory.

[17]  K. Zeger,et al.  Zero redundancy channel coding in vector quantisation , 1987 .

[18]  George C. Clark,et al.  Reconstruction error in waveform transmission (Corresp.) , 1967, IEEE Trans. Inf. Theory.

[19]  N.-J. Cheng,et al.  Robust zero-redundancy vector quantization for noisy channels , 1989, IEEE International Conference on Communications, World Prosperity Through Communications,.

[20]  Allen Gersho,et al.  Pseudo-Gray coding , 1990, IEEE Trans. Commun..

[21]  Mikael Skoglund,et al.  Vector quantization for speech transmission , 1995 .