In this paper, we consider the so-called uniquely decodable one-to-one code (UDOOC) that is formed by inserting a "comma" indicator, termed the unique word (UW), between consecutive one-to-one codewords for separation. Along this research direction, we first investigate several general combinatorial properties of UDOOCs, in particular the enumeration of the number of UDOOC codewords for any (finite) codeword length. Based on the obtained formula on the number of length-n codewords for a given UW, the per-letter average codeword length of UDOOC for the optimal compression of a given source statistics can be computed. Several upper bounds on the average codeword length of such UDOOCs are next established. The analysis on the bounds of average codeword length then leads to two asymptotic bounds for sources having infinitely many alphabets, one of which is achievable and hence tight for a certain source statistics and UW, and the other of which proves the achievability of source entropy rate of UDOOCs when both the block size of source letters for UDOOC compression and UW length go to infinity. Efficient encoding and decoding algorithms for UDOOCs are also given in this paper. Numerical results show that the proposed UDOOCs can potentially result in comparable compression rate to the Huffman code under similar decoding complexity and yield a smaller average codeword length than that of the Lempel-Ziv code, thereby confirming the practicability of UDOOCs.
Local List Recovery of High-rate Tensor Codes and Applications
在这项工作中，我们给出了第一个高速率的本地列表可恢复代码的建设。列表恢复一直是编码理论中非常有用的构建块，我们的动机是使用这些代码作为这样的构建块。特别是，我们的建设给出了第一个容量实现本地列表可解码的代码（在恒定大小的字母表）;第一个容量实现全局列表可解码的代码与近线性时间列表解码算法（再一次，在恒定大小的字母表）;和Gilbert-Varshamov界上的二进制码的随机化结构，可以在近线性时间内唯一解码，具有比以前已知的更高的速率。我们的技术实际上非常简单，并且受到Gopalan，Guruswami和Raghavendra（Siam Journal on Computing，2011）用于列表解码张量代码的方法的启发。我们表明，张量的权力（全球）列表可恢复的代码是“近似”本地列表可恢复的，和“近似”的修改器可以通过预编码的消息与合适的本地可解码的代码被删除。用高速率全局列表可恢复代码和高速率局部可解码代码的已知构造来实例化该构造完成该构造。
Correcting Contextual Deletions in DNA Nanopore Readouts
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；Instituto de Telecomunicações（电信研究所）
