Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

180 Implementation Issues2.01.5OFDM (OFDMA, MC-TDMA)MC-CDMA, MLSE/MLSSEMC-CDMA, MMSE equalizerSNR gain in dB1.00.50.01001000 10000Turbo code interleaver sizeFigure 4-40 SNR gain with Turbo codes relative to convolutional codes versus Turbo code interleaversize I TCViterbi algorithm (SOVA) [31]. The Turbo code interleaver is implemented as a randominterleaver. Iterative Turbo decoding in the channel decoder uses 10 iterations. The SNRgain with Turbo codes relative to convolutional codes with R = 1/2andmemory6versusthe Turbo code interleaver size I TC is given in Figure 4-40 for the BER of 10 −3 .The results show that OFDMA and MC-TDMA systems benefit more from the applicationof Turbo codes than MC-CDMA systems. It can be observed that the improvementswith Turbo codes at interleaver sizes smaller than 1000 are small. Due to the largeinterleaver sizes required for convolutional Turbo codes, they are of special interest fornon-real-time applications.4.4.3.2 Block Turbo CodingThe idea of product block or block Turbo coding is to use the well-known product codeswith block codes as components for two-dimensional coding (or three dimensions) [71].The two-dimensional code is depicted in Figure 4-41. The k r information bits in the rowsare encoded into n r bits by using a binary block code C r (n r ,k r ). The redundancy of thecode is r r = n r − k r and d r the minimum distance. After encoding the rows, the columnsare encoded using another block code C c (n c ,k c ), where the check bits of the first codeare also encoded.The two-dimensional code has the following characteristics:– overall block size n = n r · n c ;– number of information bits k r · k c ;– code rate R = R r · R c ,whereR i = k i /n i ,i = c, r; and– minimum distance d min = d r · d c .