It is a specific combination of a fixed number of bits. The rule is used in DAB and DAB+ for time interleaving of the CIFS (Common Interleave Frames) in the MSC (Main Service Channel). It recombines 4 bits or 16 numbers (0 to 15).
A permutation is a specific combination of several possible combinations. And the reverse bit law is nothing but an algorithm that results in one specific combination. Or a permutation of the 16 digits (0 to 15).
It is simple to understand because the binary number corresponding to its number in the inverse bit law permutation is the inverse bit number.
Example:
In binary, the number 12 corresponds to 1100. The inverse of 1100 is 0011 and corresponds to 3 (the inverse is rearranging the order of bits from the least significant to the most significant bit).
For each number from 0 to 15, we find the corresponding number by using the binary value and reverse it.
So, if you want to scramble bits by using the reverse bit law, the sequence of numbers 0 to 15 can be permuted as follows.
Reverse bit law results in the following permutation table:
Remark that some bit combinations, such as 0, 6, 9 and 15, don’t change in case of bit reversal.
Another way to present the above scrambling is the following table.
Understanding the “Inverse Bit Law” principle to understand “time Interleaving” is essential.