DSL modem utilizing low density parity check codes

DETAILED DESCRIPTION It is therefore an object of the invention to provide simple methods of generating reproducible H matrices.
It is another object of the invention to provide DSL modems which utilize simply generated reproducible H matrices.
In accord with these objects which will be discussed in detail below, the DSL modem of the invention generally includes a receiver and a transmitter with the transmitter including a substantially deterministic LDPC encoder.
The encoder is a function of a substantially deterministic H matrix (H=A.
vertline.
B) which is determined according to the steps and rules set forth below.
More particularly, the encoder takes a block of bits and utilizes a generation matrix G=A.
sup.
-1 B which is derived from (i.
e.
, is a function of) the H matrix in order to generate redundant parity bits.
The redundant bits are appended to the original block of bits to generate a word.
The substantially deterministic H matrix is determined as follows.
First, the "ones" of a first column N are assigned randomly or deterministically.
Preferably, the ones are distributed evenly within the first column with the first "1" in the first row of the first column according to the algorithm: H(r,1)=1, where r=1+(i-1)*integer (M.
sub.
j /N.
sub.
j); i=1,2, .
.
.
N.
sub.
j (2) Then, beginning with the second column, assignment of "ones" is carried out deterministically with each "1" in a previous (ancestor) column generating a "1" in the next (descendant) column based on the rule that a descendant is placed one position below or one position above an ancestor (it being determined in advance by convention whether the position below is used or the position above is used).
As a result, a descending diagonal or an ascending diagonal is generated.
Where a descending diagonal is used and the ancestor is in the lowest row of the matrix, the descendant may take any position in the next column, although it is preferable to place the descendant in the highest free position.
When distributing "ones" in any given column, each new descendant should be checked to ensure that no rectangles are generated in conjunction with other "ones" in the current column and previous columns