bb==0100 bibo=110 b3b2bb==0110 b3b2bb==1111 b3b2bb==0111 y=1/42 b5b4b3b2b.bo 111011 = 011011 111010 b5b4b3b2b1bo = 011010 111000 b5b4b3b2b1bo = 011000 111001 babbb = 011001 111101 = 011101 111011 b5b4b3b2b.bo = 011011 111110 b5b4b3b2b1bo = 011110 bbbbbb 111111 = 011111 110111 000111 b5bbbbbb =100111 b5b4b3b2bb 010111 FIGURE 9-49 QPSK, 16 QAM, and 64 QAM constellations [1] CHAPTER 9 The IEEE 802. 16m Physical Layer (Part I) Input Bits FIGURE 9-50 The structure of a TBCC encoder with minimum code rate of 1/5 [2] interleaving is performed in the unit of bits. The output of the sub-block interleaver z'[k] with j = A,B,C,D,E, and k = 0, L - 1 corresponds to the input sequence y [k] and can be expressed as z'[k] = [IIk] where IIk is the interleaver index. The maximum value of parameter L is 128. The output sequence of sub-block interleaver consists of the interleaved A, B, C, D, and E sub-blocks. Let w[i] denote the bit grouping output with i = 0, 5L - 1. It can be shown that w[k] = A[k], w[k zB[k], w[k + 2L] = z°[k], + 3L] = zP[kk, and w[k + 4L] = 2E[k] with k = 0, ..., L - 1. Suppose the desired number of the output bits is M. The output sequence c[n] can be expressed as c[n] = w[n mod Kbuffer-size], n = 0, 1, M - 1 where Kbuffer-size 5L is the size of buffer that is used for repetition. The performance of an example tail-biting convolution coder with a minimum rate of 1/2 in the AWGN channel with different modulation orders, coding rates, and data frame sizes using Viterbi decoder has been evaluated and is shown in Figure 9-51, where the wrap depth is a predetermined number of trellis stages used as a parameter in the figure. One way to estimate the required wrap depth for MAP decoding of a tail-biting convolutional code is to conduct hardware or software experi- mentations, requiring a circular MAP decoder with a variable wrap depth to be implemented and to measure the decoded bit error rate versus Eb/No for successively increasing wrap depths. The minimum decoder wrap depth that provides the minimum probability of