nd/or obtainable code rates. Concatenation to Overcome Error Floors What is meant by an "error floor" is that the error probability of a given code does not approach 0 as quickly for medium to high SNR as it does at low SNR. Such error floors pri- marily affect codes with low- (Hamming-) weight codewords, such as LDPC and Turbo codes. To lower the error floor, the LDPC (or Turbo) code can be concatenated with an outer code, such as a BCH code. Digital Video Broadcast (DVB) has chosen this method of FEC, using LDPC and BCH coding, for its new DVB-S2 standard. Chapter 4 Coding Lattice and Trellis Codes Although the Term trellis code is sometimes used to refer to convolutional codes in general, Trellis-Coded Modulation (TCM) is a combined modulation and coding scheme (Burr, 1993) invented by Ungerboeck (1982). In TCM each multibit data symbol is split into two groups of bits; one group from each symbol (group 1) is then fed into a convolutional encoder, whose output bits determine which of a number of signal constellations (sets of possible signal values) is used for that symbol. The other group of bits (group 2) selects which value from the constellation is transmitted. A very simple example would be that at each symbol time the choice of symbol is either between 1 and 3 or between 2 and 4. Based on the received values, a convolutional code decoder in the receiver estimates the sequence of constellations and, from that, the values of the group-1 bits. It then determines which of the constellation points was most probably transmitted and, hence, the values of the group-2 bits. If, for example, the decoder knows that the received value is either 2 or 4 at one particular symbol time, then it does not choose 3. The separation between the allowed possible symbol values at each symbol time is thereby increased, which gives rise to the performance gain of TCM. TCM is incorporated in the CCITT V.32 and V.32 modem standards. Lattice-coded modulation is the block code-based equivalent of TCM but is little used. Space-Time Co