In continuation to an earlier work, where error exponents of typical random codes were studied in the context of general block coding, with no underlying structure, here we carry out a parallel study on typical random, time–varying trellis codes, focusing on a certain range of low rates. By analyzing an upper bound to the error probability of the typical random trellis code, using the method of types, we first derive a Csiszár–style error exponent formula (with respect to the constraint length), which allows to characterize properties of good codes and dominant error events. We also derive a Gallager–style form, which turns out to be related to the expurgated error exponent. The main result is further extended to channels with memory and mismatch.

中文翻译：

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典型随机网格码的误差指数

在之前的工作中，在没有底层结构的一般分组编码的背景下研究了典型随机码的误差指数，这里我们对典型的随机、时变格状码进行了并行研究，重点是特定的低利率范围。通过分析典型随机网格码错误概率的上限，使用类型方法，我们首先推导出 Csiszár 式错误指数公式（关于约束长度），它允许表征良好代码的特性和显性错误事件。我们还推导出了一个 Gallager 风格的形式，结果证明它与去除的误差指数有关。主要结果进一步扩展到具有记忆和失配的通道。