Issue understanding matrix layout #17
Description
In WirehairCodec.h we find:
(1) Matrix Construction
A = Original data blocks, N blocks long.
D = Count of dense/heavy matrix rows (see below), chosen based on N.
E = N + D blocks = Count of recovery set blocks.
R = Recovery blocks, E blocks long.
C = Matrix, with E rows and E columns.
0 = Dense/heavy rows sum to zero.
+---------+-------+ +---+ +---+
| | | | | | |
| P | M | | | | A |
| | | | | | |
+---------+-----+-+ x | R | = +---+
| D | J |0| | | | 0 |
+---------+-+---+-+ | | +---+
| 0 | H | | | | 0 |
+-----------+-----+ +---+ +---+
A and B are Ex1 vectors of blocks.
A has N rows of the original data padded by H zeros.
R has E rows of encoded blocks.
C is the ExE hybrid matrix above:
P is the NxN peeling binary submatrix.
- Optimized for success of the peeling solver.
M is the NxD mixing binary submatrix.
- Used to mix the D dense/heavy rows into the peeling rows.
D is the DxN dense binary submatrix.
- Used to improve on recovery properties of peeling code.
J is a DxD random-looking invertible submatrix.
H is the 6x18 heavy GF(256) submatrix.
- Used to improve on recovery properties of dense code.
0 is a Dx6 zero submatrix.
My confusion lies in the M, D, J and 0 part. If M is NxD and D is DxN and J is DxD, then J exactly fills the corner between M and D and there should be no room for the 0 part. What gives?