  A counter braid (CB) is a novel counter architecture introduced by Lu et al.
in 2007 for per-flow measurements on high-speed links. CBs achieve an
asymptotic compression rate (under optimal decoding) that matches the entropy
lower bound of the flow size distribution. Spatially-coupled CBs (SC-CBs) have
recently been proposed. In this work, we further analyze single-layer CBs and
SC-CBs using an equivalent bipartite graph representation of CBs. On this
equivalent representation, we show that the potential and area thresholds are
equal. We also show that the area under the extended belief propagation (BP)
extrinsic information transfer curve (defined for the equivalent graph),
computed for the expected residual CB graph when a peeling decoder equivalent
to the BP decoder stops, is equal to zero precisely at the area threshold.
This, combined with simulations and an asymptotic analysis of the Maxwell
decoder, leads to the conjecture that the area threshold is in fact equal to
the Maxwell decoding threshold and hence a lower bound on the maximum a
posteriori (MAP) decoding threshold. Finally, we present some numerical results
and give some insight into the apparent gap of the BP decoding threshold of
SC-CBs to the conjectured lower bound on the MAP decoding threshold.
