Note: This page has been translated by MathWorks. Please click here

To view all translated materials including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materials including this page, select Japan from the country navigator on the bottom of this page.

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: `int8`

, `uint8`

, `int16`

, `uint16`

, `int32`

, `uint32`

, `boolean`

, `single`

, `double`

,
and fixed-point. The output signal inherits its data type from the
input signal.

The **Type** parameter indicates the algebraic
method that the block uses to generate the appropriate permutation
table. Choices are `Takeshita-Costello`

and `Welch-Costas`

.
Each of these methods has parameters and restrictions that are specific
to it:

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(*A*,^{k}*N*+ 1) - 1.If you set

**Type**to`Takeshita-Costello`

, then*N*must be 2^{m}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*n*^{th}element is$$c(n)=\mathrm{mod}\left(k\cdot \frac{n\cdot (n-1)}{2},N\right)+1,\text{\hspace{0.17em}}n$$

for integers n between 1 and N. The intermediate permutation function is obtained by using the following relationship:

$$\Pi \left(c\left(n\right)\right)=c\left(n+1\right)$$

where

$$n=1:N$$

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*.

**Type**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`Takeshita-Costello`

.**Cyclic shift**The amount by which the block shifts indices when creating the permutation table. This field appears only if

**Type**is set to`Takeshita-Costello`

.**Primitive element**An element of order

*N*in the finite field GF(N+1). This field appears only if**Type**is set to`Welch-Costas`

.

[1] Heegard, Chris and Stephen B. Wicker. *Turbo
Coding*. Boston: Kluwer Academic Publishers, 1999.

[2] 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.

Was this topic helpful?