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

Channel Coding and Decoding 179a (k)convolutionalencoderpuncturingb (k)interleaverconvolutionalencoderpuncturingFigure 4-38Convolutional Turbo encoderdeinterleaverinterleaverl (k)‘0’ insertionconvolutionaldecoderinterleaverconvolutionaldecoderdeinterleavera^(k)sign(.)‘0’ insertionFigure 4-39Convolutional Turbo decoderin the form of LLRs, improving the next decoding step. In the initial stage, the noninterleavedpart of the coded bits b (k) is decoded. Only the LLRs given by the vector l (k)at the input of the Turbo decoder are used. In the second stage, the interleaved part isdecoded. In addition to the LLRs given by l (k) , the decoder uses the output of the firstdecoding step as apriori information about the coded bits. This is possible due to theseparation of the two codes by the interleaver. In the next iteration cycle, this procedure isrepeated, but now the non-interleaved part can be decoded using the apriori informationdelivered by the last decoding step. Hence, this decoding run has a better performancethan the first one and the decoding improves. Since in each individual decoding step thedecoder combines soft information from different sources, the representation of the softinformation is crucial.It is shown in References [32] and [33] that the soft value at the decoder input shouldbe an LLR to guarantee that after combining the soft information at the input of thedecoder LLRs are available again. The size of the Turbo code interleaver and the numberof iterations essentially determine the performance of the Turbo coding scheme.The performance of Turbo codes as channel codes in different multi-carrier multipleaccess schemes is analyzed for the following Turbo coding scheme. The component codesof the Turbo code are recursive systematic punctured convolutional codes, each of rate2/3, resulting in an overall Turbo code rate of R = 1/2. Since the performance withTurbo codes in fading channels cannot be improved with a memory greater than 2 for aBER of 10 −3 [33], we consider a convolutional Turbo code with memory 2 in order tominimize the computational complexity. The component decoders exploit the soft output