Practical considerations

In practice, computing the G-construction using Algorithm [*] is only feasible for high-rate codes, because the algorithm needs to maintain a list of coset leaders at each iteration. In theory, it might be possible to use approximation techniques to store only ``important'' coset leaders, but we leave this as an open problem.

Another problem with the G-construction is that it is theoretically possible for bounding to be so severe as to halt the construction when, for example, $f(\ensuremath{\mathbb{C}})$ does not return a vector for a particular code $ \mathbb {C}$. Though we have not seen this with trellis state bounding (i.e. using the mapping $\ensuremath{f_{\mbox{\small state}}}$), we have seen indications that this can occur with $\ensuremath{f_{\mbox{\small decoding}}}$. Of course, certain constraints will simply not correspond to any existing linear code, so this problem is inherent to code design.