  We consider the Additive White Gaussian Noise channel with Binary Phase Shift
Keying modulation. Our aim is to enable an algebraic hard decision Bounded
Minimum Distance decoder for a binary block code to exploit soft information
obtained from the demodulator. This idea goes back to Forney and is based on
treating received symbols with low reliability as erasures. This erasing at the
decoder is done using a threshold, each received symbol with reliability
falling below the threshold is erased. Depending on the target overall
complexity of the decoder this pseudo-soft decision decoding can be extended
from one threshold T to z>1 thresholds T_1<...<T_z for erasing received symbols
with lowest reliability. The resulting technique is widely known as Generalized
Minimum Distance decoding. In this paper we provide a means for explicit
determination of the optimal threshold locations in terms of minimal decoding
error probability. We do this for the one and the general z>1 thresholds case,
starting with a geometric interpretation of the optimal threshold location
problem and using an approach from Zyablov.
