Exponential Error Bounds and Decoding Complexity for Block Codes Constructed by Unit Memory Trellis Codes of Branch Length Two

Performance of block codes constructed by unit memory (UM) trellis codes is discussed from random coding arguments. There are three methods to obtain block codes from trellis codes, i.e., those of (a) Tail Termination (TT), (b) Direct Truncation (DT), and (c) Tail Biting (TB). In this paper, we derive exponential error bounds and decoding complexity for block codes constructed by the UM trellis codes of branch length two based on the above three methods to uniformly discuss their performance. For the UM trellis codes of branch length two, the error exponent of the tail biting unit memory (TB-UM) trellis codes is shown to be larger than or equal to those of the ordinary block codes, the tail termination unit memory (TT-UM) and the direct truncation unit memory (DT-UM) trellis codes for all rates less than the capacity. Decoding complexity for the TB-UM trellis codes of branch length two exhibits interesting property since their trellis diagrams become simple. Taking into account of the asymptotic decoding complexity, the TB-UM trellis codes are also shown to have a smaller upper bound on the probability of decoding error compared to the ordinary block codes for the same rate with the same decoding complexity.