Superimposed codes for the multiaccess binary adder channel

Abstract

AbsiractSuperimposed codes for multiple-access communication in a binary adder channel are analyzed. The superposition mechanism used in this correspondence is ordinary addition. Each user is assigned a codeword frow a Superimposed code. It is proved that every constantweight code C of weight w and maximal correlation c corresponds to a subclass of a disjunctive code D of order m < w/c. Therefore, any m or less codewords in C which are used at the same time yield a uniquely decodable code combination at the output of the adder channel. In the noisy case, for each subset A C of size IAl 5 m << T the receiver is able to determine the number of active users and to distinguish between the active users if the weight of the error pattern e satisfies W t (e) < min{w-cJAJ, w/2}. Decoding algorithms for both the noiseless and the noisy cases are proposed.

Semiquantitative Group Testing

“…of S i used in the k th test 5 . Note that the symbol 0 indicates that S i is not present in the test.…”

“…In its full generality, GT may be viewed as the problem of inferring the state of a system from the superposition of the state vectors of a subset of the system's elements. As such, GT has found many applications in communication theory [2]- [5], signal processing [6]- [8], computer science [9]- [11], and mathematics [12]. Some examples of these applications include error-correcting coding [4], [13], [14], identifying users accessing a multiple access channel (MAC) [15], [16], reconstructing sparse signals from low-dimensional projections [6], [7], and many others.…”

Error-correcting signature code for multiple-access adder channel

“…The signature code is also different from the works [7] [20] for synchronous-CDMA systems, where each user is assigned to a spreading sequence with components from 1 or −1. On the other hand, the proposed signature code is related to superimposed codes [8] [9], as well as codes for M active users out of T potential users [1] [17] [18].…”

Wireless Multiple Access Communications Using Collision Frequency Shift Keying

“…in the CFSK system. In [39], example of the application of KS code based on Reed-Solomon code over GF{7) is discussed. This provides us a clue for applying the Reed-Soloman codes in CFSK system for signal mapping.…”

“…To solve the problem, uniquely decodable block codes with large codeword numbers are useful. The KS code given by [37] and [39] provides us some inspiration for using the Reed-Solomon code to construct the uniquely decodable block code set. Also, researches of other nonbinary superimposed codes [37] We may also avoid generating the codes randomly.…”