## Bounding Decoding Complexity

Figure 4 shows the results of applying Viterbi decoding constraints to -codes. Specifically, it shows the decoding complexity achieved under linear and quadratic decoding bounds. The degradation in code length compared to the standard lexicodes is modest for these examples.

Table: Parameters of d = 8 codes. We display the following parameters for lexicodes and trellis-oriented -codes: length, dimension, state complexity and Viterbi decoding complexity with the BCJR trellis.
 Dim- Standard Trellis- Standard Trellis- Standard Trellis- ension oriented oriented oriented Length Length States States 2| E| - | V| + 1 2| E| - | V| + 1 1 8 1 17 2 12 2 35 3 14 3 71 4 15 4 143 5 16 4 195 6 18 5 341 7 19 6 647 8 20 6 779 9 21 7 1,547 10 22 8 2,395 11 23 9 4,219 12 24 9 4,475 13 28 9 4,529 14 30 9 4,777 15 31 9 5,463 16 32 9 5,515 17 34 9 7,645 5,693 18 35 9 12,671 6,143 19 36 9 12,803 6,275 20 37 10 9 24,267 7,691 21 38 10 9 25,115 8,539 22 39 10 9 26,939 10,363 23 40 10 9 27,195 10,619 24 42 10 31,805 17,853 25 43 11 41,791 33,087 26 44 11 41,987 33,283 27 45 12 65,227 28 46 12 67,163 29 47 12 72,571 78,203 30 48 12 72,827 78,459 31 49 50 13 12 135,611 80,317 32 50 51 13 12 169,019 87,103 33 51 52 13 12 248,123 88,643 34 52 53 13 248,507 137,547 35 53 54 14 13 427,579 138,331 36 54 55 14 13 431,419 142,203 37 55 56 14 13 442,171 142,459 38 56 57 14 442,555 274,875 39 58 14 487,997 308,283 40 59 14 628,031 457,019 41 60 14 628,227 460,091 42 62 14 629,197 460,861 43 63 14 631,903 464,703 44 64 14 632,035 464,899 45 65 15 14 1,263,819 581,835 46 66 15 1,287,195 1,053,275