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首页> 外文期刊>IEEE Transactions on Communications >An Efficient Algorithmic Lower Bound for the Error Rate of Linear Block Codes
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An Efficient Algorithmic Lower Bound for the Error Rate of Linear Block Codes

机译：线性分组码错误率的有效算法下界

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摘要

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 SÉguin, the KAT bound (evaluated on the entire codebook), and the dot-product and norm bounds due to Cohen and Merhav.
机译：我们提出了在二进制相移键控调制加性高斯白噪声信道的软最大似然解码下，线性二进制块码的块误码率的有效算法下限。我们将寻找联合概率下界的问题作为优化问题来寻求找到最大化最近下界的子集（归因于Kuai，Alajaji和Takahara），我们将其称为KAT界。改进的边界（用LB-s表示）渐近严格[随着信噪比（SNR）增长到无穷大]，并且仅依赖于代码的权重枚举函数进行计算。使用码本的子集来评估LB的下限不仅显着降低了计算复杂性，而且特别降低了低SNR时的界限。二进制块码的数值结果表明，在高SNR时，LB-s边界比文献中其他最近的下边界（包括Séguin，KAT边界（在整个密码本上评估））导致的下边界更严格。 Cohen和Merhav的点积和范数界。

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