## 4.2.11 2^{nd} interleaving

25.2123GPPMultiplexing and channel coding (FDD)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 bits input to the block interleaver are denoted by , where *p* is PhCH number and *U* is the number of bits in one radio frame for one PhCH. The output bit sequence from the block interleaver is derived as follows:

(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 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 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* are removed from the output. The bits after 2^{nd} interleaving are denoted by , where *v _{p,}*

_{1}corresponds to the bit with smallest index

*k*after pruning,

*v*

_{p,}_{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> |

#### 4.2.11.1 2^{nd} interleaving for Secondary CCPCH with 16QAM

For MBSFN transmissions with 16QAM, the 2^{nd} interleaving for Secondary CCPCH is done as illustrated in figure 8a below. The basic block interleaver is as described in Clause 4.2.11. For 16QAM modulated bits, there are two identical basic block interleavers of size R2×30, where R2 is the minimum integer fulfilling

,

The output bits from the physical channel segmentation are divided two by two between the interleavers: bits *u _{p,k}* and u

_{p,k+1}go to the first interleaver and bits

*u*and

_{p,k+2}*u*go to the second interleaver. Bits are collected two by two from the interleavers: bits

_{p,k+3}*v*and

_{p,k}*v*are obtained from the first interleaver and bits

_{p,k+1}*v*and

_{p,k+2}*v*are obtained from the second interleaver, where k mod 4=1.

_{p,k+3}Figure 8a: Interleaver structure for Secondary CCPCH