Subpacket Generation (Channel Interleaver or Interleaver and Puncturing) [1]and Puncturing) [1]

The proposed FEC structure in IEEE 802.16e OFDMA punctures the mother codeword to generate a subpacket with various coding rates. The framework consists of the following:

• bit separation,

• subblock interleaving,

• bit grouping, and

• bit selection.

The subpacket is also used in HARQ packet transmission. Figure 2.3 shows the block diagram of subpacket generation. A rate-1/3 CTC encoded codeword goes through inter-leaving and puncturing. Figure 2.9 shows the block diagram of the interinter-leaving block. The puncturing is performed to select a consecutive interleaved bit sequence that starts at some point in the whole codeword.

For the first transmission, the subpacket is generated to select the consecutive interleaved bit sequence that starts from the first bit of the systematic part of the mother codeword. The length of the subpacket is chosen according to the needed coding rate reflecting the channel condition. The first subpacket can also be used as a codeword with the needed coding rate for a burst where HARQ is not applied.

Bit Separation

All of the encoded bits can be demultiplexed into six subblocks denoted A, B, Y 1, Y 2, W 1, and W 2. The encoder output bits are sequentially distributed into the six subblocks with the first N bits going to the A subblock, the second N to the B subblock, the third N to the Y 1 subblock, the fourth N to the Y 2 subblock, the fifth N to the W 1 subblock, and the sixth N to the W 2 subblock.

Subblock Interleaving

The six subblocks can be interleaved separately. The interleaving is performed in unit of bits. The sequence of interleaver output bits for each subblock can be generated by the procedure described below. The entire subblock of bits to be interleaved is written into an array at addresses from 0 to the number of the bits minus one (N − 1), and the interleaved bits are read out in a permuted order with the ith bit being read from the address AD_i (i = 0, . . . , N − 1), as follows:

1. Determine the subblock interleaver parameters, m and J. Table 2.3 gives these pa-rameters.

2. Initialize i and k to 0.

Table 2.3: Parameters for the Subblock Interleavers

3. Form a tentative output address T_k according to

T_k= 2^m(k mod J) + BRO_m(bk/Jc) (2.1) where BRO_m(y) indicates the bit-reversed m-bit value of y (e.g. BRO₃(6) = 3).

4. If T_k is less than N, AD_i = T_k and increment i and k by 1. Otherwise, discard T_k and increment k only.

5. Repeat steps 3 and 4 until all N interleaver output addresses are obtained.

Bit Grouping

The channel interleaver output sequence consists of the interleaved A and B subblock sequences, followed by a bit-by-bit multiplexed sequence of the interleaved Y 1 and Y 2 sub-block sequences, followed by a bit-by-bit multiplexed sequence of the interleaved W 1 and W 2 subblock sequences.

Figure 2.9: Block diagram of CTC channel interleaving scheme (from [1]).

The bit-by-bit multiplexed sequence of interleaved Y 1 and Y 2 subblock sequences con-sists of the first output bit from the Y 1 subblock interleaver, the first output bit from the Y 2 subblock interleaver, the second output bit from the Y 1 subblock interleaver, the second output bit from the Y 2 subblock interleaver, etc. The bit-by-bit multiplexed sequence of interleaved W 1 and W 2 subblock sequences consists of the first output bit from the W 1 sub-block interleaver, the first output bit from the W 2 subsub-block interleaver, the second output bit from the W 1 subblock interleaver, the second output bit from the W 2 subblock inter-leaver, etc. Figure 2.9 shows the interleaving scheme. The order of bit grouping sequence is as follows:

A⁰₀,A⁰₁,...,A⁰_{N −1},B₀⁰,B₁⁰,...,B_{N −1}⁰ , Y_1,0⁰ ,Y_2,0⁰ ,Y_1,1⁰ ,Y_2,1⁰ ,Y_1,2⁰ ,Y_2,2⁰ ,...,Y_{1,N −1}⁰ ,Y_{2,N −1}⁰ , W_1,0⁰ ,W_2,0⁰ ,W_1,1⁰ ,W_2,1⁰ ,W_1,2⁰ ,W_2,2⁰ ,...,W_{1,N −1}⁰ ,W_{2,N −1}⁰ .

Bit Selection

Lastly, bit selection is performed to generate the subpacket. The puncturing block is referred to as bit selection in the viewpoint of subpacket generation. The mother code is transmitted with one of the subpackets. The bits in a subpacket are formed by selecting specific sequences of bits from the interleaved CTC encoder output sequence. The resulting subpacket sequence is a binary sequence of bits for the modulator. The parameters for bit selection are listed below:

• k: the subpacket index when IR HARQ is enabled.

– When IR HARQ is not used, k=0 (for the first transmission and increases by one for the next subpacket).

– When there is more than one FEC block in a burst, the subpacket index for each FEC block shall be the same.

• N_EP: the number of bits in the encoder packet (before encoding).

• NSCHk: the number of concatenated slots for the subpacket, as defined in [1, Table 569] for the non-HARQ and Chase HARQ CTC schemes.

• m_k: the modulation order for the kth subpacket (m_k=2 for QPSK, 4 for 16-QAM, and 6 for 64QAM).

• SP ID_k: the subpacket ID for the kth subpacket (for the first subpacket, SP ID_k=0=0).

Also, let the scrambled and selected bits be numbered from zero with the 0th bit being the first bit in the sequence. Then, the index of the ith bit for the kth subpacket shall be

S_k,i= (F_k+ i)mod(3 · N_EP) (2.2)

where i = 0, . . . , Lk−1, Lk = 48·NSCHk·mk, and Fk= (SP IDk·Lk)mod(3·NEP). The NEP, NSCHk, mk , and SP ID values are determined by the base station (BS) and can be inferred by the subscriber station (SS) through the allocation size in the DL-MAP and UL-MAP.

The above bit selection makes the following possible.

• The first transmission includes the systematic part of the mother code. Thus it can be used as the codeword for a burst where the HARQ is not applied or when Chase HARQ is applied.

• The location of the subpacket can be determined by the SP ID without the knowledge of previous subpacket. This is a very important property for IR HARQ retransmission.

Note that the optional IR HARQ is not considered in our research, so we bypass a detailed introduction of the IR HARQ mechanism.

2.1.7 Modulation [1]

After bit interleaving, the data bits are entered serially to the constellation map-per. Gray-mapped QPSK and 16-QAM are supported, whereas the support of 64-QAM is optional. The constellations as shown in Fig. 2.10 shall be normalized by multiplying the constellation points with the indicated factor c to achieve equal average power. The constellation-mapped data shall be subsequently modulated onto the allocated data carriers.