Reorder input symbols using algebraically derived permutation table
Block sublibrary of Interleaving
The Algebraic Interleaver block rearranges the elements of its input vector using a permutation that is algebraically derived. The Number of elements parameter, N, indicates how many numbers are in the input vector. This block accepts a column vector input signal.
The block accepts the following data types:
fixed-point. The output signal inherits its data type from the input
The Type parameter indicates the algebraic method
that the block uses to generate the appropriate permutation table.
Welch-Costas. Each of these
methods has parameters and restrictions that are specific to
If you set Type to
Welch-Costas, then N + 1 must be prime. The Primitive element parameter is an integer, A, between 1 and N that represents a primitive element of the finite field GF(N + 1). This means that every nonzero element of GF(N + 1) can be expressed as A raised to some integer power.
In a Welch-Costas interleaver, the permutation maps the integer k to mod(Ak,N + 1) - 1.
If you set Type to
Takeshita-Costello, then N must be 2m for some integer m. The Multiplicative factor parameter, k, must be an odd integer less than N. The Cyclic shift parameter, h, must be a nonnegative integer less than N.
A Takeshita-Costello interleaver uses a length-N cycle vector whose nth element is
for integers n between 1 and N. The intermediate permutation function is obtained by using the following relationship:
The interleaver's actual permutation vector is the result of cyclically shifting the elements of the permutation vector, π, by the Cyclic shift parameter, h.
The type of permutation table that the block uses for interleaving.
- Number of elements
The number of elements, N, in the input vector.
- Multiplicative factor
The factor used to compute the interleaver's cycle vector. This field appears only if Type is set to
- Cyclic shift
The amount by which the block shifts indices when creating the permutation table. This field appears only if Type is set to
- Primitive element
An element of order N in the finite field GF(N+1). This field appears only if Type is set to
 Heegard, Chris and Stephen B. Wicker. Turbo Coding. Boston: Kluwer Academic Publishers, 1999.
 Takeshita, O. Y. and D. J. Costello, Jr. "New Classes Of Algebraic Interleavers for Turbo-Codes." Proc. 1998 IEEE International Symposium on Information Theory, Boston, Aug. 16-21, 1998. 419.