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

Channel Coding and Decoding 1754.4.1 Punctured Convolutional CodingA punctured convolutional code that provides from the mother code rate 1/2, memoryν (e.g. ν = 6 resulting in 64 states), a wide range of higher inner code rates R (e.g.R = 2/3, 3/4, 5/6, and 7/8) is usually applied, for instance, with a generator polynomialG 1 = 171 oct ,G 2 = 133 oct .The puncturing patterns of a convolutional code with 64 states for different inner coderates R are given in Table 4-2. In this table ‘0’ means that the coded bit is not transmitted(i.e. punctured or masked) and ‘1’ means that the coded bit is transmitted. It shouldbe noticed that each matrix has two rows and several columns, where the puncturingvector for each row corresponds to the outputs of the encoder X and Y respectively (seeFigures 4-34 and 4-35). For decoding the received data a soft input maximum likelihoodsequence estimator efficiently realized with the Viterbi algorithm can be employed [70].Deriving the soft values by taking the channel state information gives a high diversity fordecoding, resulting in high performance. The number of bits that could be used for softvalues is typically 3–4 bits.Table 4-3 shows the performance of punctured convolutional coding (CC) for differentmodulation schemes in AWGN, Rayleigh, and Ricean (10 dB Rice factor) fading channelswith perfect channel estimation.4.4.2 Concatenated Convolutional and Reed Solomon CodingCompared to a single code, the main advantage of concatenated coding schemes is toobtain much higher coding gains at low BERs with reduced complexity. For concatenatedcoding, usually as the outer code a shortened Reed Solomon code and as the innercode punctured convolutional codes are used (see Figures 4-36 and 4-37). An optionalinterleaving between these codes can be inserted. The role of this byte interleaving is toscatter the bursty errors at the output of the inner decoder, i.e the Viterbi decoder [70].Table 4-2Puncturing patterns of a 64-state convolutional code (X 1 is sent first)Inner code rate R Puncturing patterns Minimum distance d min Transmitted sequences(after P/S conversion)1/2 X: 1 10 X 1 Y 1Y: 12/3 X: 1 0 6 X 1 Y 1 Y 2Y: 1 13/4 X:101 5 X 1 Y 1 Y 2 X 3Y:1105/6 X:10101 4 X 1 Y 1 Y 2 X 3 Y 4 X 5Y:110107/8 X:1000101 3 X 1 Y 1 Y 2 Y 3 Y 4 X 5 Y 6 X 7Y:1111010