Electronic – Infrared LED binary code

The answer is already present in the page whose link you posted:

From Technical Report TR-06-11, "B. Communication and Sensing", pg. 4

During any communication between robots, the receiving robot also measures the intensity of the incoming infrared light. This incoming light intensity is a monotonically de- creasing function of the distance between the transmitter and the receiver; therefore the distance to the transmitter can be calculated by the receiver. In practice, the incoming intensity of light is also affected by noise and manufacturing variances, which leads to sensing accuracy of ±2 mm, and precision under 1 mm.

(emphasis mine)

I suppose they experimentally found the relation between distance between Tx/Rx and received intensity (or have access to some characteristic graph from the manufacturer of the IR modules), and used that to base the distance calculations.

First of all, it's pretty clear that the "XX" bits are part of the channel designation, since that's the only thing they depend on. The "XX" bits may simply be a check on the "Ch" bits.

The check bits are a simple bitwise XOR of 24 of the 26 data bits: If you take the 6 Yaw bits, the 6 LSBs of the Throttle, the 6 Pitch bits, and the next 6 bits, and XOR these quantities together, you get the 6 check bits. It appears that the upper 2 bits of the Throttle do not affect the check bits at all.

The following Perl script verifies this.

#!/usr/bin/perl

# crc.pl - verify decoding of check bits

# On the lines starting with '1', just keep the '0's and '1's in an array. 
while (<>) {
    my @letters = split '', $_;
    next unless $letters[0] eq '1';
    @letters = grep /[01]/, @letters;
    @letters = @letters[1..32];
    $a = string2bin (@letters[0..5]);
    $b = string2bin (@letters[8..13]);
    $c = string2bin (@letters[14..19]);
    $d = string2bin (@letters[20..25]);
    $e = string2bin (@letters[26..31]);
    $f = $a ^ $b ^ $c ^ $d;
    printf "%02X %02X %02X %02X %02X %02X %s\n", $a, $b, $c, $d, $e, $f,
        $e == $f ? '-' : '###';
}

sub string2bin {
    my $temp = 0;
    for (@_) {
        $temp = ($temp << 1) + ($_ eq '1' ? 1 : 0);
    }
    $temp;
}