## 4.2.11 2nd interleaving

25.2223GPPMultiplexing and channel coding (TDD)Release 17TS

The 2^{nd} interleaving is a block interleaver and consists of bits input to a matrix with padding, the inter-column permutation for the matrix and bits output from the matrix with pruning. The 2nd interleaving can be applied jointly to all data bits transmitted during one frame, or separately within each timeslot, on which the CCTrCH is mapped. The selection of the 2nd interleaving scheme is controlled by higher layer.

#### 4.2.11.1 Frame related 2nd interleaving

In case of frame related 2^{nd} interleaving, the bits input to the block interleaver are denoted by , where *U* is the total number of bits after TrCH multiplexing transmitted during the respective radio frame with .

The relation between *x _{k}* and the bits

*u*in the respective physical channels is given below:

_{p,k} *k = *1, 2 , …, *U _{1}*

_{} *k* = 1, 2 , …, *U*_{2}

…

*k* = 1, 2 , …, *U*_{P}

The following steps have to be performed once for each CCTrCH:

(1) Assign C2 = 30 to be the number of columns of the matrix. The columns of the matrix are numbered 0, 1, 2, …, C2 – 1 from left to right.

(2) Determine the number of rows of the matrix, R2, by finding minimum integer R2 such that:

*U* R2 X C2.

The rows of rectangular matrix are numbered 0, 1, 2, …, R2 – 1 from top to bottom.

(3) Write the input bit sequence into the R2 C2 matrix row by row starting with bit in column 0 of row 0:

where for *k* = 1, 2, …, *U* and if R2 C2 > *U*, the dummy bits are padded such that = 0 or 1 for *k* = *U* + 1, *U* + 2, …, R2 C2. These dummy bits are pruned away from the output of the matrix after the inter-column permutation.

(4) Perform the inter-column permutation for the matrix based on the pattern that is shown in table 7, where P_{2}(*j*) is the original column position of the *j*-th permuted column. After permutation of the columns, the bits are denoted by .

(5) The output of the block interleaver is the bit sequence read out column by column from the inter-column permuted R2 C2 matrix. The output is pruned by deleting dummy bits that were padded to the input of the matrix before the inter-column permutation, i.e. bits that corresponds to bits with *k* > *U* are removed from the output. The bits at the output of the block interleaver are denoted by , where *z*_{1} corresponds to the bit with smallest index *k* after pruning, *z*_{2} to the bit with second smallest index *k* after pruning, and so on.

The bits shall be segmented as follows:

*k = *1, 2 , …, *U _{1}*

*k = *1, 2 , …, *U _{2}*

…

*k = *1, 2 , …, *U _{P}*

The bits after frame related 2^{nd} interleaving are denoted by , where *t* refers to the timeslot sequence number and *U _{t} *is the number of bits transmitted in this timeslot during the respective radio frame.

Let *T* be the number of time slots in a CCTrCH during the respective radio frame (where for 1.28Mcps TDD, the respective radio frame includes subframes 1 and 2), and . The physical layer shall assign the time slot sequence number *t *in ascending order of the allocated time slots in the CCTrCH in the respective radio frame. In time slot *t, R _{t}* refers to the number of physical channels within the respective time slot and . The relation between

*r*and

*t*and the physical channel sequence number

*p*as detailed in 4.2.12.1 is given by:

Defining the relation* u _{t,r,k }*=

*u*

_{p,k}_{ }and denoting as the number of bits for physical channel

*r*in time slot

*t*, the relation between

*v*and

_{t,k}*u*

_{t,r,k}_{ }is given below:

*k = *1, 2 , …,

_{ }*k = *1, 2 , …,

…

*k = *1, 2 , …,

#### 4.2.11.2 Timeslot related 2^{nd} interleaving

In case of timeslot related 2^{nd} interleaving, the bits input to the block interleaver are denoted by , where *t* is the timeslot sequence number, and *U _{t}* is the number of bits transmitted in this timeslot during the respective radio frame.

Let *T* be the number of time slots in a CCTrCH during the respective radio frame (where for 1.28Mcps TDD, the respective radio frame includes subframes 1 and 2), and. The physical layer shall assign the time slot sequence number *t *in ascending order of the allocated time slots in the CCTrCH in the respective radio frame. In timeslot *t,* *R _{t}* refers to the number of physical channels within the respective timeslot and . The relation between

*r*and

*t*and the physical channel sequence number

*p*as detailed in 4.2.12.1 is given by:

_{ }Defining the relation *u _{t,r,k }*=

*u*

_{p,k}_{ }and denoting as the number of bits for physical channel

*r*in time slot

*t*, the relation between

*x*and

_{t,k}*u*is given below:

_{t,r,k} *k = *1, 2 , …,

_{ }*k = *1, 2 , …,

…

*k = *1, 2 , …,

The following steps have to be performed for each timeslot *t*, on which the respective CCTrCH is mapped:

(1) Assign C2 *= *30 to be the number of columns of the matrix. The columns of the matrix are numbered 0, 1, 2, …, C2 – 1 from left to right.

(2) Determine the number of rows of the matrix, R2, by finding minimum integer R2 such that:

*U _{t}* R2 C2.

The rows of rectangular matrix are numbered 0, 1, 2, …, R2 – 1 from top to bottom.

(3) Write the input bit sequence into the R2 C2 matrix row by row starting with bit in column 0 of row 0:

where for *k* = 1, 2, …, *U _{t}* and if R2 C2 >

*U*, the dummy bits are padded such that = 0 or 1 for

_{t}*k*=

*U*+ 1,

_{t}*U*+ 2, …, R2 C2. These dummy bits are pruned away from the output of the matrix after the inter-column permutation.

_{t}(4) Perform the inter-column permutation for the matrix based on the pattern that is shown in table 7, where P2(*j*) is the original column position of the *j*-th permuted column. After permutation of the columns, the bits are denoted by .

(5) The output of the block interleaver is the bit sequence read out column by column from the inter-column permuted R2 C2 matrix. The output is pruned by deleting dummy bits that were padded to the input of the matrix before the inter-column permutation, i.e. bits that corresponds to bits with *k* *>* *U _{t}* are removed from the output. The bits after time slot 2

^{nd}interleaving are denoted by , where

*v*

_{t,}_{1}corresponds to the bit with smallest index

*k*after pruning,

*v*

_{t,}_{2}to the bit with second smallest index

*k*after pruning, and so on.

Table 7 Inter-column permutation pattern for 2nd interleaving

Number of Columns C2 |
Inter-column permutation pattern < P2(0), P2(1), …, P2(C2-1) > |

30 |
<0, 20, 10, 5, 15, 25, 3, 13, 23, 8, 18, 28, 1, 11, 21, 6, 16, 26, 4, 14, 24, 19, 9, 29, 12, 2, 7, 22, 27, 17> |