Sequential Decoding of Lattice Codes

We consider lattice tree-codes based on a latt ice A having a finite trellis diagram T . Such codes are easy to encode and benefit f rom the structure of A. Sequential decoding of lattice tree-codes is studied, and the corresponding Fano metric is derived. A n upper bound on the running time of the sequential decoding algorithm is established, and found to resemble the Pareto distribution. O u r bound indicates that t h e order of label groups in T plays an important role in determining the complexity of sequential decoding. Furthermore, it is proved that lattice tree-codes of arbitrari ly high rate, based on A and T , can be sequentially decoded wi th the same complexity, and without a n y possibility of buffer overflow.