1. Testing Multibit Encoding Schemes
Chris Phillips
11 October 2017
Astronomy and space science

2. Why more bits - Efficiency?
# of Levels
# Bits
Efficiency 3 2
80.983% 4
88.115% 8
96.256% 9
96.930% 16
98.846% 32 5
99.651%
256
99.991%
Traditionally don’t go past 2 bits with VLBI as bits are expensive
This analysis considers weak signals only and no RFI
All schemes (except 2 bit) use linear translation of sample voltage to bit value.
TMS 3rd Edition, Table 8.2
IVTW2017– Multibit Encoding | Chris Phillips

3. Why more bits – Dynamic Range!
Need additional bits for dynamic range
Cope with (possibly transient) RFI much stronger than astronomical signal and system noise
Avoid non-linear effects
Every stage of digital filtering requires additional bits to preserve full dynamic range
Traditionally the disadvantage of FX correlators
Current CASS instruments (ASKAP, Parkes UWB) use 16 bit samples after coarse filterbanks
This is expensive to receive for software backends
Traditionally don’t go past 2 bits with VLBI as bits are expensive
This analysis considers weak signals only and no RFI
All schemes (except 2 bit) use linear translation of sample voltage to bit value.
IVTW2017– Multibit Encoding | Chris Phillips

4. Multibit considerations
Need to set voltage separation between levels
Enough bits for the “noise”, retain dynamic range
Compromise between most efficient sampling and large dynamic range
Is there a way to optimize both?
Do we really need the same amount of precision for all voltage levels?
Does 16bit sampling really give significantly better results that 8bit if “real world” situatons?
IVTW2017– Multibit Encoding | Chris Phillips

5. How many bits do we need?
What do we loose if we drop from 16 to 8 bits?
Specifically in a world of increasing RFI
How can we quantitatively measure different bit depths/encoding schemes?
Are non-linear sampling schemes suitable?
* Surely we should be able to justify multibit systems better than “better dynamic range”
IVTW2017– Multibit Encoding | Chris Phillips

6. 8 bit floats 8 bit floating point proposed by Dr John Bunton (CSIRO)
1 sign bit
4 bit mantissa (0..15)
3 bit unsigned exponent
Exponent 0, mantissa just 4bit quantity (0..15)
Exponent 1-7, val = (M+15)*2^(Exponent-1)
±0..32,34,36..64,68,72…1920,1984
Sign
Mantissa
Exponent
Encode integers only – no need to encode teeny tiny numbers
64 “linear” samples – efficiency as should be > 99.5%
IVTW2017– Multibit Encoding | Chris Phillips

7. Testing Create “fake” voltage data
Gaussian Noise
Optional correlated Gaussian noise (ie common seed)
Optional 1 – 2 tones
Optional FIR filter to give bandpass shape
Concern FIR filter ripple artificially increasing measured RMS
Quantize as 2bit, 8bit or 16 bit integer, 8 bit float or 32 bit IEEE float
Raw voltage format to allow exotic encoding
Compute auto or ”zero delay” cross correlation
Also can channelize/filter data for separate investigation
IVTW2017– Multibit Encoding | Chris Phillips

8. IVTW2017– Multibit Encoding | Chris Phillips

9. Things to remember Uncorrelated noise generated with RMS of 1.0
95% of samples will be within ±2σ
Data later multiplied by 10 before quantizing
Except 2 bit data scaled to achieve 17.3/32.7/32.7/17.3%
8 bit tones will clip when amplitude of Sine > 12.7
Power 161
Float8 clips at 198.4, non-linear from 3.4
Clip at power ~40,000
Data created as voltage, displayed as power ( 𝑉 2 )
IVTW2017– Multibit Encoding | Chris Phillips

10. Noise + Tone Gaussian noise voltage Single tone at middle of band
Increase power linearly from weak to very strong
Calculate autocorrelation of 1 second of data
Measure peak of tone & SNR of tone to amplitude RMS on autocorrelation
IVTW2017– Multibit Encoding | Chris Phillips

11. Tone
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12. Tone
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13. Tone
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14. SNR, weak(ish) tone
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15. Tone
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16. Tone
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17. 2 Tone Gaussian noise plus 2 tones Increase power of one tone linearly
15 and 49 MHz in 64 MHz band
Increase power of one tone linearly
Calculate autocorrelation of voltages
IVTW2017– Multibit Encoding | Chris Phillips

18. 2 Tone
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19. 2 Tone
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20. 2 Tone
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21. 2 Tone
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22. Noise Correlation Create 2 voltage data sets
Uncorrelated Gaussian noise plus common (same seed) Gaussian noise
Cross correlate both sets and compute power
(FFT voltages and sum)
Inverse FFT cross correlation spectrum and calculate lag spectrum
IVTW2017– Multibit Encoding | Chris Phillips

23. Noise Correlation
IVTW2017– Multibit Encoding | Chris Phillips

24. Noise + Tone Correlation
Create 2 voltage data sets
Uncorrelated Gaussian noise plus common (same seed) Gaussian noise plus tone
Increase power of Tone
Cross correlate both sets and compute power
(FFT voltages and sum)
Inverse FFT cross correlation spectrum and calculate lag spectrum
IVTW2017– Multibit Encoding | Chris Phillips

25. Noise + Tone Correlation
IVTW2017– Multibit Encoding | Chris Phillips

26. Noise + Tone Correlation
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27. Intermodulation
Common problem is intermodulation between strong RFI tones
With numerous tones, intermodulation products fill spectrum
Worse with less bits
IVTW2017– Multibit Encoding | Chris Phillips

28. IVTW2017– Multibit Encoding | Chris Phillips

29. Intermodulation
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30. Intermodulation
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31. Intermodulation
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32. Intermodulation
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33. Conclusion
Better tests are needed to quantitatively compare different encoding approaches
“Float8” shows some promise, but possible issues
Need to investigate effect with adaptive RFI mitigation
Increase mantissa, reduced exponent?
Presentation title | Presenter name

34. Thank you Chris Phillips LBA Lead Scientist t +61 2 9123 4567e w
CSIRO Astronomy and space science

35. Aside - Unums Dr. John L. Gustafson
Proposes replacing IEEE Floating point with Unums
Claims all sorts of improvements
Can beat IEEE 32bit floats wrt precision on matrix operations with 16bit Unum
Has initial hardware developed with silicon implementation of Unum
Potentially really useful for astronomy
Replace 32 floats with 16 bit Unum for
Spectral line data
Image cubes
Visibility data etc
64 pJ multiply and add
4200 pJ Read 64bit float from memory
IVTW2017– Multibit Encoding | Chris Phillips

36. Aside – Intel Performance Primitives
Ignoring initialization, just 6 IPP calls needed ippsRandGauss_32f ippsTone_32f / ippsTone_32fc ippsAdd_32f_I ippsFIRSR_32f / ippsFIRSR_32fc ippsMulC_32f_I ippsMeanStdDev_32f
IVTW2017– Multibit Encoding | Chris Phillips