  The paper is focused on the tradeoff between performance and decoding
complexity per iteration for LDPC codes in terms of their gap (in rate) to
capacity. The study of this tradeoff is done via information-theoretic bounds
which also enable to get an indication on the sub-optimality of message-passing
iterative decoding algorithms (as compared to optimal ML decoding). The bounds
are generalized for parallel channels, and are applied to ensembles of
punctured LDPC codes where both intentional and random puncturing are
addressed. This work suggests an improvement in the tightness of some
information-theoretic bounds which were previously derived by Burshtein et al.
and by Sason and Urbanke.
