 
Summary: IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 55, NO. 6, JUNE 2007 1093
Transactions Letters
An Efficient Algorithmic Lower Bound for the Error Rate of Linear Block Codes
Firouz Behnamfar, Member, IEEE, Fady Alajaji, Senior Member, IEEE, and Tamás Linder, Senior Member, IEEE
AbstractWe present an efficient algorithmic lower bound for
the block error rate of linear binary block codes under soft max
imumlikelihood decoding over binary phaseshift keying modu
lated additive white Gaussian noise channels. We cast the problem
of finding a lower bound on the probability of a union as an op
timization problem that seeks to find the subset that maximizes a
recent lower bounddue to Kuai, Alajaji, and Takaharathat we
will refer to as the KAT bound. The improved bound, which is de
noted by LBs, is asymptotically tight [as the signaltonoise ratio
(SNR) grows to infinity] and depends only on the code's weight
enumeration function for its calculation. The use of a subset of the
codebook to evaluate the LBs lower bound not only significantly
reduces computational complexity, but also tightens the bound spe
cially at low SNRs. Numerical results for binary block codes indi
cate that at high SNRs, the LBs bound is tighter than other recent
lower bounds in the literature, which comprise the lower bound
