It has been known for a long time that the mutual information between the input sequence and output of a binary symmetric channel (BSC) is upper bounded by the mutual information between the same input sequence and the output of a binary erasure channel (BEC) with the same capacity. Recently, Samorodintsky discovered that one may also lower bound the BSC mutual information in terms of the mutual information between the same input sequence and a more capable BEC. In this paper, we strengthen Samordnitsky's bound for the special case where the input to the channel is distributed uniformly over a linear code. Furthermore, for a general (not necessarily binary) input distribution $P_X$ and channel $W_{Y|X}$, we derive a new lower bound on the mutual information $I(X;Y^n)$ for $n$ transmissions of $X\sim P_X$ through the channel $W_{Y|X}$.

翻译：长期以来，人们已知二进制对称信道（BSC）输入序列与输出之间的互信息受相同输入序列与相同容量二进制擦除信道（BEC）输出之间互信息的上界约束。近期，Samorodintsky发现也可通过更优BEC的相同输入序列互信息来建立BSC互信息下界。本文针对输入均匀分布于线性码的特殊情形，强化了Samorodintsky的界。此外，对于一般（不必为二进制）输入分布$P_X$和信道$W_{Y|X}$，我们推导了在信道$W_{Y|X}$上经过$n$次传输$X\sim P_X$时互信息$I(X;Y^n)$的新下界。