Digital Signal Processing Reference
In-Depth Information
The high-dimension parity code has an n dimensional discrete cubical
structure in Figure 7-2. Each dimensional axis has a size of m, and the axis
consists of m code points. The code is denoted as nDm, where n is dimension
and m is size. For example, 3Dm5 means that dimension of the code is three
and size is five. Each axis has one single redundant digit and m-1 data digits,
which satisfies the even parity. There are n such independent parity axes,
which form code points. The nDm code has data digits, totaling
digits including parity redundant digits, and has a transmission rate of
On the decoding side, each digit is checked by n parity check lines
and is corrected when the number of failed parity check lines exceeds the
threshold value.
On these code points, the transmission order runs obliquely to form a
discrete torus knot similar to the number change in Figure 7-3. Therefore, the
errors that appear on the block are uniformly distributed on each code axis.
Figure 7-2.
Hi-dimension parity code, an example of 3Dm4.
3.
PERFORMANCE OF THE PROPOSED CODE
Figure 7-4 illustrates the results of the proposed code to the Reed-
Solomon code. Simulation conditions are summarized in Table 7-1.
Although the performance of the Reed-Solomon code is higher than the
proposed code in an area with few errors, but in an area with many errors, the
performance of the proposed code is higher than the Reed-Solomon code.
When the proposed code is constituted into the high dimension structure
as four dimensions, the number of uncorrectable patterns extremely
