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

Channel Coding and Decoding 181n rk rn ck cData bitsParitybitsParity bitsFigure 4-41Two-dimensional product code matrixTable 4-4 Generator polynomials of Hammingcodes as block Turbo code componentsn i k i Generator7 4 x 3 + x + 115 11 x 4 + x + 131 26 x 5 + x 2 + 163 57 x 6 + x + 1127 120 x 7 + x 3 + 1The binary block codes employed for rows and columns can be systematic BCH (Bose–Chaudhuri–Hocquenghem) or Hamming codes [51]. Furthermore, the constituent codesof rows or columns can be extended with an extra parity bit to obtain extended BCH orHamming codes. Table 4-4 gives the generator polynomials of the Hamming codes usedin block Turbo codes.The main advantage of block Turbo codes is in their application for packet transmission,where an interleaver, as it is used in convolutional Turbo coding, is not necessary.Furthermore, as typical for block codes, block Turbo codes are efficient at high code rates.To match packet sizes, a product code can be shortened by removing symbols. In thetwo-dimensional case, either rows or columns can be removed until the appropriate sizeis reached. Unlike one-dimensional codes (such as Reed Solomon codes), parity bits areremoved as part of the shortening process, helping to keep the code rate high.The decoding of block Turbo codes is done in an iterative way [71], as in the caseof convolutional Turbo codes. First, all of the horizontal received blocks are decodedand then all of the vertical received blocks are decoded (or vice versa). The decodingprocedure is iterated several times to maximize the decoder performance. The core ofthe decoding process is the soft-in/soft-out (SISO) constituent code decoder. High performanceiterative decoding requires the constituent code decoders to not only determine atransmitted sequence but also to yield a soft decision metric (i.e. LLR), which is a measureof the likelihood or confidence of each bit in that sequence. Since most algebraic block