In this paper, we derive the exact input/output transfer functions of the optimal a-posteriori probability channel detector for a general ISI channel with erasures. Considering three channel impulse responses of different memory as an example, we compute the BP and MAP thresholds for regular spatially coupled LDPC codes with joint iterative detection and decoding. When we compare the results with the thresholds of ISI channels with Gaussian noise we observe an apparent inconsistency, i.e., a channel which performs better with erasures performs worse with AWGN. We show that this anomaly can be resolved by looking at the thresholds from an entropy perspective. We finally show that with spatial coupling we can achieve the symmetric information rates of different ISI channels using the same code.

翻译：本文推导了在擦除情况下一般ISI信道的最优后验概率信道检测器的精确输入/输出传递函数。以三种不同记忆长度的信道冲激响应为例，计算了采用联合迭代检测与解码的规则空间耦合LDPC码的BP阈值和MAP阈值。当将这些结果与高斯噪声ISI信道的阈值进行比较时，观察到明显的不一致性——即在擦除情况下性能更好的信道却在加性高斯白噪声（AWGN）下表现更差。研究表明，这种异常现象可通过熵视角分析阈值得到解释。最终证明，利用空间耦合技术，使用同一编码即可达到不同ISI信道的对称信息速率。