TY - JOUR
T1 - Lower Bounds on the Error Probability of Block Codes Based on Improvements on de Caen's Inequality
AU - Cohen, Asaf
AU - Merhav, Neri
N1 - Funding Information:
1Work at the Lawrence Berkeley National Laboratory was sponsored by the US Department of Energy (DOE) Mathematical, Information, and Computing Sciences Division Contract DE-AC03-76SF00098, and a DOE LDRD award to GM. Other work was supported by a subcontract from the California Institute of Technology Center for the Simulation of Dynamic Response in Materials, which in turn is supported by the Academic Strategic Alliances Program of the Accelerated Strategic Computing Initiative (ASCI/ASAP) under DOE Contract B341492. Development of the PPM implementation presented here was supported in part by the ASCI/ASAP Center for Astrophysical Thermonuclear Flashes at the University of Chicago under DOE Contract B341495.
PY - 2004/2/1
Y1 - 2004/2/1
N2 - New lower bounds on the error probability of block codes with maximum-likelihood decoding are proposed. The bounds are obtained by applying a new lower bound on the probability of a union of events, derived by improving on de Caen's lower bound. The new bound includes an arbitrary function to be optimized in order to achieve the tightest results. Since the optimal choice of this function is known, but leads to a trivial and useless identity, we find several useful approximations for it, each resulting in a new lower bound. For the additive white Gaussian noise (AWGN) channel and the binary-symmetric channel (BSC), the optimal choice of the optimization function is stated and several approximations are proposed. When the bounds are further specialized to linear codes, the only knowledge on the code used is its weight enumeration. The results are shown to be tighter than the latest bounds in the current literature, such as those by Seguin and by Keren and Litsyn. Moreover, for the BSC, the new bounds widen the range of rates for which the union bound analysis applies, thus improving on the bound to the error exponent compared with the de Caen-based bounds.
AB - New lower bounds on the error probability of block codes with maximum-likelihood decoding are proposed. The bounds are obtained by applying a new lower bound on the probability of a union of events, derived by improving on de Caen's lower bound. The new bound includes an arbitrary function to be optimized in order to achieve the tightest results. Since the optimal choice of this function is known, but leads to a trivial and useless identity, we find several useful approximations for it, each resulting in a new lower bound. For the additive white Gaussian noise (AWGN) channel and the binary-symmetric channel (BSC), the optimal choice of the optimization function is stated and several approximations are proposed. When the bounds are further specialized to linear codes, the only knowledge on the code used is its weight enumeration. The results are shown to be tighter than the latest bounds in the current literature, such as those by Seguin and by Keren and Litsyn. Moreover, for the BSC, the new bounds widen the range of rates for which the union bound analysis applies, thus improving on the bound to the error exponent compared with the de Caen-based bounds.
KW - Binary-symmetric channel (BSC)
KW - Error exponent
KW - Gaussian channel
KW - Maximum-likelihood decoding
KW - Probability of a union
KW - Probability of error
UR - http://www.scopus.com/inward/record.url?scp=1442337676&partnerID=8YFLogxK
U2 - 10.1109/TIT.2003.822577
DO - 10.1109/TIT.2003.822577
M3 - Article
AN - SCOPUS:1442337676
SN - 0018-9448
VL - 50
SP - 290
EP - 310
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 2
ER -