, one loop is spent since the testing requires computations.
Similarly, one loop will be spent even if and
is not true. Hence, when a new node with
is considered, the number of loops that will be spent on the
path construction equals the number of paths with distinct finite
field elements that have already been constructed. Therefore, the
less new paths with distinct field elements can be constructed
when each new node is considered, the more nodes will be involved
in the path construction in a given number of loops. In
the worst case, the first nodes with the smallest nonzero
LLRs are all in the stage of . For computation, there is
still only one constructed path, path 0, after loops are
spent in Algorithm B. When the nonzero-LLR node is considered,
one new path will be constructed, and it has different
field element from path 0. After that, if each new node considered
is in a different stage and none of the paths that can
be constructed has distinct field element, then two loops will
be spent in Algorithm B when each new node is considered.
Therefore, if the maximum loop number of Algorithm B is set
to , then the maximum number of nonzero-LLR nodes,
, that will be involved in the path construction should
satisfy . Accordingly,
at most v-to-c messages with the smallest nonzero
LLRs need to be sorted out for the path construction when the
maximum loop number in Algorithm B is set to .