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1 Introduction and Scanning Strategy

The PLANCK satellite (formerly COBRAS/SAMBA, Bersanelli et al. 1996), which is planned to be launched in 2007, will produce full sky CMB maps with high accuracy and resolution over a wide range of frequencies (Mandolesi et al. 1998; Puget et al. 1998). Table 1 summarizes the basic properties of LFI aboard PLANCK. The reported sensitivities per resolution element - i.e. a squared pixel with side equal to the Full Width at Half Maximum (FWHM) extent of the beam -, in terms of antenna temperature, represents the goals of LFI for 14 months of routine scientific operations as recently revised by the LFI Consortium (Mandolesi et al. 1999).

The limited bandwidth reserved to the downlink of scientific data calls for huge lossless compression, theoretical upper limit being about four (Maris et al. 1999). Careful simulations are demanded to quantify the capability of true compressors for "realistic'' synthetic data and improve the theoretical analysis, including CMB signal (monopole, dipole and anisotropies), foregrounds and instrumental noise.

During the data acquisition phase the PLANCK satellite will rotate at a rate of one circle per minute around a given spin axis that changes its direction every hour (of 2.5' on the ecliptic plane in the case of simple scanning strategy), thus observing the same circle on the sky for 60 consecutive times (Mandolesi et al. 1998; Mandolesi et al. 2000). LFI will produce continuous data streams of temperature differences between the microwave sky and a set of on-board reference sources; both differential measurements and reference source temperatures must be recorded.

The LFI Proposal assumes a sampling time $\tau_{{\rm s}} \sim
7$ msec for each detector (Mandolesi et al. 1998, Bersanelli et al. 2000), thus calling for a typical data rate of $\sim 260$ Kb/sec, while the allocated bandwidth to download PLANCK data to ground is in total $\sim 60$ Kb/sec. Assuming the total bandwidth to be equally split between instruments, $\approx 30$ Kb/sec on the average would be assigned to LFI asking for a compression of about a factor 8.4. Data have to be downloaded without information losses and by minimizing scientific processing on board.

A possible solution would be to adapt the sampling rate to the angular resolution specific for each frequency. This should allow to save about up to a factor $\approx 9$ for the 30 GHz channel, but since only $\approx 7\%$ of the samples come from such channel (see Table 1) the overall reduction in the final data rate would be $\approx 17\%$.

On the other hand, it is unlikely that the bandwidth for the downlink channel may be enhanced to solve the bandwidth problem, since the ground facilities are shared between different missions and there is the need to minimize possible cross-talks between the instrument and the communication system.

With the aim of optimizing of the transmission bandwidth dedicated to the downlink of LFI data from the PLANCK spacecraft to the FIRST/ PLANCK Ground Segment, we analyze in detail the role that can be played by lossless compression of LFI data before they are sent to Earth.

We apply different compression algorithms to suitable sets of PLANCK-LFI simulated data streams generated by considering different combinations of astrophysical and instrumental signals and for different instrumental characteristics and detection electronics.

The first considered contribution is that introduced by receiver noise: we consider here the case of pure white noise and of white noise coupled to 1/f noise with different knee frequencies. The reference load temperature is assumed to be 20 K for present tests; because of the strong dependence of the 1/f noise on the load temperature, this can be considered a worst case, since the actual baseline reference load is of 4 K.

Different sky signal sources are subsequently added to the receiver noise: CMB fluctuations, CMB dipole, Galaxy emission and extragalactic point sources. The signal from the different sky components is convolved with the corresponding antenna pattern shapes, assumed to be symmetric and Gaussian with the FWHM reported in Table 1.


Table 1: Summary of LFI characteristics as recently revised by the LFI Consortium (Mandolesi et al. 1999). Data rates are tabulated for the case of a sampling rate equal to 8640 samples per circle and constant time and frequency
Center frequency $\nu$ [GHz] 30 44 70 100
Number of detectors $n_{{\rm dtc},\nu}$ 8 12 24 68
Angular resolutions, FWHM ['] 33.6 22.9 14.4 10.0
Bandwidth [ $\Delta \nu / \nu$] 0.2 0.2 0.2 0.2
$10^6 \Delta T / T$ 1.6 2.4 3.6 4.3
$\Delta T_{\rm ant}$ [ $\mu{\rm K}$] 5.1 7.8 10.6 12.4
$\Delta T_{\rm ant}$ [${\rm mK}$] per sampling and receiver 2.06 2.61 3.16 4.36
Number of samples for beam 13.4 9.2 5.8 4.0
Data rate per Detector [Kb/sec] 2.3 2.3 2.3 2.3
Data rate per Frequency Channel [Kb/sec] 18.4 27.6 55.3 156.7
Uncompressed data rate partition function $f_\nu$ [$\%$] 7.14 10.71 21.43 60.71

We generate simulated data streams at the two extreme frequency channels, 30 GHz and 100 GHz and consider data streams with different time lengths. We explore also different signal offset and scaling. The large number of above combinations was systematically explored using an automated program generator as described by Maris et al. (1998).

In Sect. 2 we characterize quantitatively the LFI signal component by component. In Sect. 3 we discuss how the acquisition chain is modeled to perform compression simulations. A theoretical analysis of the compression efficiency is presented in Sect. 4. While Sect. 5 is devoted to the analysis of the signal statistics. The subject of quantization error is illustrated in Sect. 6. The experimental protocol and results about compression are reported in Sect. 7. Further constraints on the on-board data compression are reported in Sect. 8. A proposal for an alternative coding method is made in Sect. 9. The overall compression rate is estimated in Sect. 10. Conclusions are in Sect. 11. Appendix A is included to further illustrate the estimation of the overall compression rate.

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