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Achievable Rates for Channels With Deletions and Insertions

机译：具有删除和插入的通道可达到的速率

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摘要

This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability $d$, or an extra bit is added after it with probability $i$, or it is transmitted unmodified with probability $1-d-i$. A computable lower bound on the capacity of this channel is derived. The transformation of the input sequence by the channel may be viewed in terms of runs as follows: some runs of the input sequence get shorter/longer, some runs get deleted, and some new runs are added. It is difficult for the decoder to synchronize the channel output sequence to the transmitted codeword mainly due to deleted runs and new inserted runs. The main idea is a mutual information decomposition in terms of the rate achieved by a suboptimal decoder that determines the positions of the deleted and inserted runs in addition to decoding the transmitted codeword. The mutual information between the channel input and output sequences is expressed as the sum of the rate achieved by this decoder and the rate loss due to its suboptimality. Obtaining computable lower bounds on each of these quantities yields a lower bound on the capacity. The bounds proposed in this paper provide the first characterization of achievable rates for channels with general insertions, and for channels with both deletions and insertions. For the special case of the deletion channel, the proposed bound improves on the previous best lower bound for deletion probabilities up to 0.3.
机译：本文考虑了具有删除和插入的二进制通道，其中每个输入位都通过以下方式之一转换：以概率$ d $删除它，或者以概率$ i $添加一个额外的位，或者传输时未修改，概率为$ 1-di $。得出此通道容量的可计算下限。可以按运行方式查看通道对输入序列的转换，如下所示：输入序列的某些运行变短/变长，一些运行被删除，并且添加了一些新运行。解码器很难将信道输出序列与传输的码字同步，这主要是由于删除了游程和新插入了游程。主要思想是根据次优解码器实现的速率进行互信息分解，次优解码器除了对传输的码字进行解码之外，还确定删除和插入行的位置。通道输入和输出序列之间的相互信息表示为该解码器获得的速率与由于其次优性导致的速率损失之和。在这些数量中的每一个上获得可计算的下界，将在容量上产生下界。本文提出的边界为具有一般插入的通道以及具有删除和插入的通道可达到的速率提供了第一个特征。对于删除通道的特殊情况，建议的边界将删除概率的最高最佳下界提高到0.3。

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