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

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

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

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

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

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

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

IVTW2017– Multibit Encoding | Chris Phillips

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

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

Tone IVTW2017– Multibit Encoding | Chris Phillips

Tone IVTW2017– Multibit Encoding | Chris Phillips

Tone IVTW2017– Multibit Encoding | Chris Phillips

SNR, weak(ish) tone IVTW2017– Multibit Encoding | Chris Phillips

Tone IVTW2017– Multibit Encoding | Chris Phillips

Tone IVTW2017– Multibit Encoding | Chris Phillips

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

2 Tone IVTW2017– Multibit Encoding | Chris Phillips

2 Tone IVTW2017– Multibit Encoding | Chris Phillips

2 Tone IVTW2017– Multibit Encoding | Chris Phillips

2 Tone IVTW2017– Multibit Encoding | Chris Phillips

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

Noise Correlation IVTW2017– Multibit Encoding | Chris Phillips

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

Noise + Tone Correlation IVTW2017– Multibit Encoding | Chris Phillips

Noise + Tone Correlation IVTW2017– Multibit Encoding | Chris Phillips

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

IVTW2017– Multibit Encoding | Chris Phillips

Intermodulation IVTW2017– Multibit Encoding | Chris Phillips

Intermodulation IVTW2017– Multibit Encoding | Chris Phillips

Intermodulation IVTW2017– Multibit Encoding | Chris Phillips

Intermodulation IVTW2017– Multibit Encoding | Chris Phillips

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

Thank you Chris Phillips LBA Lead Scientist t +61 2 9123 4567 e Chris.Phillips@csiro.au w www.atnf.csiro.au CSIRO Astronomy and space science

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 http://johngustafson.net/publications.html IVTW2017– Multibit Encoding | Chris Phillips

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