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An Efficient Algorithmic Lower Bound for the Error Rate of Linear Block Codes

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3 Author(s)
Behnamfar, F. ; Nortel Networks, Ottawa ; Alajaji, F. ; Linder, T.

We present an efficient algorithmic lower bound for the block error rate of linear binary block codes under soft maximum-likelihood decoding over binary phase-shift keying modulated additive white Gaussian noise channels. We cast the problem of finding a lower bound on the probability of a union as an optimization problem that seeks to find the subset that maximizes a recent lower bound - due to Kuai, Alajaji, and Takahara - that we will refer to as the KAT bound. The improved bound, which is denoted by LB-s, is asymptotically tight [as the signal-to-noise 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 LB-s lower bound not only significantly reduces computational complexity, but also tightens the bound specially at low SNRs. Numerical results for binary block codes indicate that at high SNRs, the LB-s bound is tighter than other recent lower bounds in the literature, which comprise the lower bound due to Seguin, the KAT bound (evaluated on the entire codebook), and the dot-product and norm bounds due to Cohen and Merhav.

Published in:

Communications, IEEE Transactions on  (Volume:55 ,  Issue: 6 )