In some telecommunication and magnetic/digital recording applications, bits/symbols tend to be lost in the transmission due to the interference. In this paper, we consider a segmented burst deletion channel where in a block of consecutive bits at most a single burst deletion of length up to bits exists. Existing synchronization approaches either provide a poor synchronization performance or suffer from a high computational complexity. For example, the reduced state Forward Backward Algorithm (FBA) incurs high time and space complexities, i.e., and , respectively, where denotes the sequence length. In this paper, we discover binary marker patterns which require the minimum bits redundancy to detect the burst deletion with the length up to bits for the segmented burst deletion channel, and propose an optimal algorithm to resynchronize the corrupted bit sequence that minimizes the expected bit error rate. As compared to the reduced state FBA, the time and space complexities of our proposed algorithm are reduced to and , respectively. Theoretical analysis and simulations verify the optimality of our proposed algorithm, and demonstrate that the expected bit error rate introduced in our proposed scheme is lower than that in the existing synchronization error detection schemes and that in the FBA under segmented burst deletion channels.

中文翻译：

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与分段突发删除错误的二进制标记的最佳同步

在一些电信和磁/数字记录应用中，由于干扰，比特/符号在传输中往往会丢失。在本文中，我们考虑分段突发删除通道，其中在连续比特块中最多存在长度达比特的单个突发删除。现有的同步方法要么提供较差的同步性能，要么遭受高计算复杂性的困扰。例如，简化状态前向后向算法（FBA）会产生高时间和空间复杂度，即分别为 和 ，其中 表示序列长度。在本文中，我们发现了需要最小比特冗余来检测分段突发删除通道的长度为比特的突发删除的二进制标记模式，并提出了一种重新同步损坏的比特序列的最佳算法，以最小化预期比特错误速度。与简化状态 FBA 相比，我们提出的算法的时间和空间复杂度分别降低为 和 。理论分析和仿真验证了我们提出的算法的最优性，并表明我们提出的方案中引入的预期误码率低于现有的同步错误检测方案和分段突发删除信道下的FBA中的预期误码率。