  The performance of ``typical set (pairs) decoding'' for ensembles of
Gallager's linear code is investigated using statistical physics. In this
decoding, error happens when the information transmission is corrupted by an
untypical noise or two or more typical sequences satisfy the parity check
equation provided by the received codeword for which a typical noise is added.
We show that the average error rate for the latter case over a given code
ensemble can be tightly evaluated using the replica method, including the
sensitivity to the message length. Our approach generally improves the existing
analysis known in information theory community, which was reintroduced by
MacKay (1999) and believed as most accurate to date.
