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

178 Implementation IssuesDatabytesTxShortenedRS codeInterleav.(optional)SerialoutputTailbitinsertionConvolutionalcodeXYPuncturingwith serialoutputTomapp.Figure 4-37Coding procedure for packet transmission– At the end of the each packet, tailbits (e.g. 6 bits for memory 6) can be inserted forinner code trellis termination purposes.– A block consisting of [(K + 16) ×8 + 6] bits is encoded by the inner convolutionalmother binary code of rate 1/2. After convolutional coding, the puncturing operationis applied following the used inner code rate R for the given packet. This results ina total of [(K + 16) ×8 + 6]/R bits. Finally, the punctured bits are serial-to-parallelconverted and submitted to the symbol mapper.If the BER before RS decoding is guaranteed to be about 2 × 10 −4 , then with sufficientinterleaving (e.g. eight RS code words) for the same SNR values given in Table 4-3, aquasi error-free (i.e. BER < 10 −12 ) transmission after RS decoding is guaranteed. However,if no interleaving is employed, depending on the inner coding rate, a loss of about1.5–2.5 dB has to be considered to achieve a quasi error-free transmission [22].4.4.3 Turbo CodingRecently, interest has focused on iterative decoding of parallel or serial concatenatedcodes using soft-in/soft-out (SISO) decoders with simple code components in an interleavedscheme [5, 31–33, 71]. These codes, after several iterations, provide near-Shannonperformance [32, 33]. We will consider two classes of codes with iterative decoding:convolutional and block Turbo codes. These codes have already been adopted in severalstandards.4.4.3.1 Convolutional Turbo CodingBy applying systematic recursive convolutional codes in an iterative scheme and by introducingan interleaver between the two parallel encoders, promising results can be obtainedwith so-called convolutional Turbo codes [5]. Convolutional Turbo codes are of greatinterest because of their good performance at low SNRs.Figure 4-38 shows the block diagram of a convolutional Turbo encoder. The codestructure consists of two parallel recursive systematic punctured convolutional codes. Ablock of encoded bits consists of three parts, the two parity bit parts and the systematicpart. The systematic part is the same in both code bit streams and, hence, has to betransmitted only once. The code bit sequence at the output of the Turbo encoder is givenby the vector b (k) .In the receiver, the decoding is performed iteratively. Figure 4-39 shows the blockdiagram of the convolutional Turbo decoder. The component decoders are soft outputdecoders providing log-likelihood ratios (LLRs) of the decoded bits (see Section 2.1.8).The basic idea of iterative decoding is to feed-forward/backward the soft decoder output