This paper studies two problems that are motivated by combining two novel approaches, namely DNA composite and rank modulation. The recent approach of composite DNA takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm, every composite symbols does not store a single nucleotide but a mixture of the four DNA nucleotides. Instead of considering all the possible composite symbols we are interested only in the rank of the motifs in the symbol. The first problem in this paper addresses the capacity of a channel that uses such symbols, while in the second, bounds and construction of such codes are studied.

翻译：本文研究了将两种新颖方法（即DNA复合编码与等级调制）相结合所引发的两个问题。复合DNA方法利用了DNA合成特性，该特性可为每条合成链产生大量副本。在该范式下，每个复合符号存储的并非单个核苷酸，而是四种DNA核苷酸的混合物。我们并不考虑所有可能的复合符号，而仅关注符号中基序的等级。本文的第一个问题探讨了采用此类符号的信道的容量，第二个问题则研究了此类编码的界限与构造方法。