Recursive Constructions of Detecting Matrices for Multiuser Coding: A Unifying Approach

• Published in: IEEE transactions on information theory Vol. 55; no. 1; pp. 93 - 98
• Main Author: Mow, Wai Ho
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Africa; Applied sciences; Binary adder channels; Binary system; Codes; Coding; Coding, codes; coin weighing; Combinatorial analysis; Construction; Councils; Decoding; detecting matrices; Equivalence; Exact sciences and technology; Information theory; Information, signal and communications theory; Materials science and technology; Mathematical analysis; Matrices; Matrix methods; Milling machines; multiuser codes; Recursive; Signal and communications theory; Telecommunications and information theory; unique decodability; multiuser codes; Multiple access; Binary channel; Combinatorial method; coin weighing; Coding; Recursive method; detecting matrices; Adder; unique decodability; Binary adder channels
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2008.2008139

Detecting matrices are a class of combinatorial objects originated from the coin weighing problem of Soderberg and Shapiro in the early 1960s. In this paper, various known recursive construction techniques for binary, bipolar, and ternary detecting matrices are reexamined in a unifying framework. New, general recursive constructions of detecting matrices, which include previous recursive constructions as special cases, are derived. Such matrices find applications in multiuser coding since they are equivalent to a certain class of uniquely decodable multiuser codes for the binary adder channel. Interestingly, it is found that among the three kinds of detecting matrices, ternary detecting matrices are of fundamental significance from the combinatorial theoretic, as well as from the multiuser coding application, point of view.