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

176 Implementation IssuesDataMotherconvolutionalcode, R = 1/2XYPuncturingwith serialoutputto mappingEncoderDataMotherML Viterbidecoder, R = 1/2DecoderDe-puncturingSoft valuesfrom demappingFigure 4-34Punctured convolutional codingModulo-2 addition+X Output(Gen: 171 Octal)Input1 bitregister1 bitregister1 bitregister1 bitregister1 bitregister1 bitregister+Modulo-2 addition(Gen: 133 Octal)Y OutputFigure 4-35 Example of inner mother convolutional code of rate 1/2 with memory 6This type of coding scheme is quite flexible, providing different outer and inner coderates.The outer shortened Reed Solomon RS(K + 2t,K,t) code can transmit up to K bytes.This code can be derived, for instance, from the original systematic Reed SolomonRS(255, 239, t = 8) code, able to correct up to t = 8 byte errors. As the field generatorpolynomial for Reed Solomon codes over Galois field GF(256), the generator polynomialP(x) = x 8 + x 4 + x 3 + x 2 + 1 can be employed. As the inner code, the same convolutionalcoding as described in Section 4.4.1 can be used.Shortened RS codes together with convolutional coding can easily be adapted for thedownlink and uplink packet transmission:– One or several MAC packets can be mapped to the information part (K bytes of theouter code).