Correct and clarify the P1 usage and construction.

pull/73/head
Rob Riggs 2021-08-22 18:48:26 -05:00
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@ -208,7 +208,7 @@ Two different puncturing schemes are used in M17 stream mode:
#. :math:`P_1` leaving 46 from 61 encoded bits
#. :math:`P_2` leaving 11 from 12 encoded bits
Scheme :math:`P_1` is used for the initial LICH link setup info, taking 488
Scheme :math:`P_1` is used for the *link setup frame*, taking 488
bits of encoded data and selecting 368 bits. The :math:`gcd(368, 488)`
is 8 which, when used to divide, leaves 46 and 61 bits. However, a full puncture
pattern requires the puncturing matrix entries count to be divisible by the number of encoding
@ -220,14 +220,17 @@ The construction of the partial puncturing pattern :math:`P_1` is as follows:
:nowrap:
\begin{align}
\mathbb{M} = & \begin{bmatrix}
1 & 0 & 1 & 1
\end{bmatrix} \\
P_1 = & \begin{bmatrix}
1 & r & \vdots & r
1 & \mathbb{M}_{1} & \cdots & \mathbb{M}_{15}
\end{bmatrix}
\end{align}
In which :math:`r=[1, 0, 1, 1]` and is used 15 times to form an array of length 61.
The *r* matrix is actually a 2/3 rate puncturer. It can be used, because after subtracting
1 bit from 61, multiplying this amount by 3/4 gives 45 bits.
In which :math:`\mathbb{M}` is a standard 2/3 rate puncture matrix and is used 15 times,
along with a leading `1` to form an array of length 61.
The first pass of the partial puncturer discards :math:`G_1` bits only, second pass discards
:math:`G_2`, third - :math:`G_1` again, and so on. This ensures that both bits are punctured out evenly.