Determining the exact decoding error probability of linear block codes is an interesting problem. For binary BCH codes, McEliece derived methods to estimate the error probability of a simple bounded distance decoding (BDD) for BCH codes. However, BDD falls short in many applications. In this work, we consider error-and-erasure decoding and its improved variants. We derive closed-form expressions for their error probabilities and validate them through simulations. Then, we illustrate their use in assessing concatenated coding schemes.

翻译：确定线性分组码的精确解码错误概率是一个有趣的问题。对于二进制BCH码，McEliece提出了估计BCH码在简单有界距离解码（BDD）下错误概率的方法。然而，BDD在许多应用中存在不足。本文研究错误与擦除解码及其改进变体。我们推导了其错误概率的闭式表达式，并通过仿真验证了其有效性。最后，我们展示了该方法在评估级联编码方案中的应用。