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Trellis coding is a source coding technique that has resulted in numerous publications and some very effective source codes. Unfortunately, the computational burden of these codes is tremendous and grows exponentially with the encoding rate. A trellis is a transition diagram, that takes time into account, for a finite state machine. Populating a trellis means specifying output symbols for each branch, specifying an initial state yields a set of allowable output sequences. A trellis coder is defined as follows: given a trellis populated with symbols from an output alphabet and an input sequence x of length n, a trellis coder outputs the sequence of bits corresponding to the output sequence x that maximises the SNR of the encoding.