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# Hierarchical Coded Modulation of Data with Fast Decaying Probability Distributions

IP.com Disclosure Number: IPCOM000110075D
Original Publication Date: 1992-Oct-01
Included in the Prior Art Database: 2005-Mar-25
Document File: 2 page(s) / 82K

IBM

Feig, E: AUTHOR

## Abstract

This invention is concerned with data with statistics described by a fast decaying probability distribution, and the transmission of such data. A motivating example is efficient transmission of image data, where we allow the data to be corrupted but in such a way that the received data yields a reconstructed image which is essentially visually indistinguishable from the original. One very popular method for achieving this is by first transforming the data to some other domain, usually one reflecting frequency, quantizing the transformed data, and then entropy coding the result with either a Huffman coder or an arithmetic coder. A most popular transform is the Discrete Cosine Transform (DCT), usually on blocks of 8 times 8 pixels.

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Hierarchical Coded Modulation of Data with Fast Decaying Probability Distributions

This invention is concerned with data with statistics
described by a fast decaying probability distribution, and the
transmission of such data.  A motivating example is efficient
transmission of image data, where we allow the data to be corrupted
but in such a way that the received data yields a reconstructed image
which is essentially visually indistinguishable from the original.
One very popular method for achieving this is by first transforming
the data to some other domain, usually one reflecting frequency,
quantizing the transformed data, and then entropy coding the result
with either a Huffman coder or an arithmetic coder. A most popular
transform is the Discrete Cosine Transform (DCT), usually on blocks
of 8 times 8 pixels.  The non-DC components of the quantized DCT
outputs each are well approximated as random data from an exponential
distribution.  The DC component is somewhat uniformly distributed,
but using DPCM (differential pulse code modulation) yields again an
exponential distribution.  That is, if we order the positions of the
DCT output from 0 to 63, and index them by j, and denote by pj
(k) the probability that k is the value of the quantized DCT output
at position j, then for some positive real numbers a, b, pj(k)

(Image Omitted)

Typical methods for encoding such data is to first entropy code
them into bit strings where each symbol is coded on average by

(Image Omitted)

bits.  These are then modulated using some QAM (quadrature amplitude
modulation) scheme, where 2 mj levels, equally spaced from  - (2 mj -
1) sj/2 to (2 mj - 1) sj/2 on each of the in phase and
quadrature channels, are used for encoding.  If only one channel is
used, the system is called PAM (pulse amplitude modulation).

The sj is chosen for some desired reliability criteria.  The
average power for transmission on each of the channels is

(Image Omitted)

If Ej bits are transmitted over K channels, then the average power to
...