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Ultra-fast and Efficient Data Compression

Published PONS Papers

Flow diagram

 

Audio Files:

Original standard sample
(tchai.wav)

1-bit standard sample
(tchai-1bit.wav)

4-bit standard sample
(tchai-4bit.wav)

16-bit standard sample
(tchai-16bit.wav)

PONS 1-bit resampling
(tchai-pons-1bit.wav)

PONS 2-bit resampling
(tchai-pons-2bit.wav)

PONS 4-bit resampling
(tchai-pons-4bit.wav)

PONS 6-bit resampling
(tchai-pons-6bit.wav)

 

 

 

 

 

 

The audio files on this page are examples of compression using the real-time energy spreading transform known as PONS. Many details are in US patent number 5913186, 1999, "Discrete One Dimensional Signal Processing Method and Apparatus Using Energy Spreading Coding" (Byrnes, Ramalho, Ostheimer, Gertner).

The patent abstract is at the end of this page. Recent improvements in the implementation were done by Prometheus Principal Scientist Jerry Kautsky.

The purpose of this demonstration is for the reader to compare the difference between uniformly rounding an audio signal to a small number of bits per sample and doing the same thing on a signal transformed by the PONS system. Similar results would be obtained if the same technique were applied to any digital signal. The energy spreading feature of PONS allows the PONS encoder to dispense completely with time-varying bit allocation. This, plus the fact that the PONS coder requires almost exclusively integer arithmetic, makes PONS extremely fast and efficient. In addition, the PONS coder is in-place, thereby minimizing computer storage requirements during encoding and decoding. Finally, the PONS transform matrix is symmetric, which further reduces the computation requirement.

The sample audio file which we have chosen to illustrate these features of PONS is the beginning of the Tchaikovsky Piano Concerto. The 4-bit standard sample 1-bit standard sample are the results of uniformly quantizing the 16-bits per sample digitized version of the original sample to 4 and 1 bits per sample respectively. i.e., to get 4-bit standard sample from the 16-bits per sample digitized version of the original standard sample we simply discard the bottom 12 bits of each sample. 16-bit standard sample is the full 16-bits per sample digitized version of the original standard sample.

The files pons-xbit, where x = 1, 2, 4 or 6, are gotten by first applying the PONS transform to the 16-bits per sample digitized version of the original standard sample, which yields 16-bit coefficients. Then the bottom 16-x bits of each coefficient are dropped and Huffman coding is applied to what remains. Finally, the inverse PONS transform (which is the same as the forward transform because the PONS matrix is symmetric) is applied to the result and the PONS x-bit resampling file is created from this, yielding an approximation to the original standard sample. To play any of these .wav files simply double click on the name.

The reader will judge how good this approximation is, partially by comparing PONS 1-bit resampling with 1-bit standard sample and PONS 4-bit resampling with 4-bit standard sample. It should be mentioned that there are a few additional details to the PONS coding and decoding, such as blocking the original signal and other "bookkeeping", but these barely affect the processing, which is real-time and in-place in both the compression and decompression stages. The basic processing is illustrated in the flow diagram.

The sizes of the files that are created (in real-time) by applying the PONS algorithm, which are the files that would need to be stored or transmitted before the .wav files are constructed (again, in real-time), are: tchai-pons-6bit.mat, 442906 bytes tchai-pons-4bit.mat, 289749 bytes tchai-pons-2bit.mat, 126590 bytes tchai-pons-1bit.mat, 63693 bytes

Note, for example, that tchai-pons-1bit.wav requires a file to be stored or transmitted that is less than 3.9% of the size of tchai.wav (1638188 bytes). The corresponding statement is true for the other (more audibly pleasing) choices of x (2, 4, 6), and would also hold for any other choices of x (from 3 to 16 in this case) as well as for any other audio signals that one chose to process. It is also worth mentioning that a simple but effective encryption step may be added with virtually no effect upon the encoding or decoding speed or complexity. This would be accomplished by permuting the elements of the PONS basis. While such an encryption technique is well known to be relatively insecure, in the real-time communications environment envisioned it should prove to be completely adequate. Combined with the fact that the PONS transform representation of a signal inherently resembles white noise, the technology described herein should prove particularly advantageous in an environment where secure, real-time, computationally simple communications are required.

Patent abstract: PONS comprises a transform coder and decoder for discrete time electrical signals, in particular acoustic signals. The PONS coder utilizes an integer coefficient transform coder which is not frequency based, which requires almost exclusively fast integer arithmetic, and which spreads incoming signal energy nearly as evenly as possible among coefficients in the transform domain. The PONS coder also has the property that the magnitudes of transform domain coefficients vary by less than about an order of magnitude, so that the PONS coder dispenses completely with time-varying bit allocation. PONS uses only the quantization step to achieve significant compression. Energy spreading also permits reasonably accurate signal reconstruction even when significant numbers of transform coefficients are lost or corrupted.

 

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