Yesterday, another signal was picked up for which both the "X" and the "Y" bit streams were generated by the same LFSR with polynomial [3,1,0] × [17,16,15,14,13,12,10,8,5,4,0] and period N= (2

^{3}-1)×(2

^{17}-1)=917,497. The cross-correlation between "X" and "Y" show that the "X" bit stream is offset w.r.t. "Y" bit stream by M=(N-1)/2=458,748 bits.

"X" and "Y" bit stream cross-correlations |

The data in the "X" channel can descrambled as follows

b(i) = XOR(~Y(M+i), X(i)),

and the auto-correlation of the descrambled bits b(i) has peaks at multiples of 48 bits:

Autocorrelation of the descrambled bit stream |

Descrambled bit stream in terms of 240-bit frames |

and in terms of 48-bit frames:

Descrambled bit stream in terms of 48-bit frames |

b(2i) = b(2i+1)

so there are 24 pairs of bits per 48-bit frame. These 24 bits are not independent: they are determined by 6 bits only:

1 ~3 4 6 13 ~202 9 ~15

5 18 -~21

7 8 11 16 19 -~23

10 17

12 14 -~22

where ~P denotes logical NOT of bit number P and -P denotes a bit at position P from the previous frame.

These 6 bits are likely not independent. Interpreting them as a 6-bit binary number, the histogram of these numbers shows that they are not equally probable:

These 6 bits are likely not independent. Interpreting them as a 6-bit binary number, the histogram of these numbers shows that they are not equally probable:

Histogram of 6-bit frame interpreted as 6-bit binary numbers |

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