Set of uniquely decodable codes for overloaded synchronous CDMA. Issue 10 (1st July 2016)

• Record Type: Journal Article
• Authors: Singh, Amiya; Amini, Arash; Singh, Poonam; Marvasti, Farokh
• Is Part Of: IET communications. Volume 10:Issue 10(2016)
• Page Start: 1236
• Page End: 1245
• Publication Date: 2016-07-01
• Subjects: codes -- code division multiple access -- iterative methods -- matrix algebra -- correlation methods -- set theory -- matched filters -- filtering theory -- maximum likelihood decoding -- error statistics -- radiofrequency interference; uniquely decodable codes -- overloaded synchronous CDMA -- uncoded synchronous overloaded code division multiple access -- code length -- recursive method -- k orthogonal subsets -- binary Hadamard -- twin tree structured cross‐correlation hierarchy -- auto cross‐correlation -- intergroup cross‐correlation -- multistage detector -- noiseless transmission -- matched filtering -- optimum maximum likelihood decoder -- average bit error rate -- subset cardinality -- interference net level; Telecommunication systems -- Periodicals; Speech processing systems -- Periodicals; 621.38205
• DOI: 10.1049/iet-com.2015.0819
• Languages: English
• ISSNs: 1751-8628

Abstract

Abstract : In this study, the authors consider the designing of a new set of uniquely decodable codes for uncoded synchronous overloaded code division multiple access for the number of codes exceeding the assigned code length. For the construction, the proposed recursive method at iteration‐ k generates a matrix that can be classified into k orthogonal subsets of different dimensions. Out of them, all besides the largest (binary Hadamard) one are ternary in nature. There resides an inbuilt twin tree structured cross‐correlation hierarchy that facilitates an advantageous balance between the auto and intergroup cross‐correlation for the signatures in a subset. This opportunity is further leveraged by the proposed multi‐stage detector to maintain the uniquely decodable (errorless) nature of the matrices for noiseless transmission. The simple logic of matched filtering serving as the basic designing block of the decoder provides an enormous saving over the complexity of optimum maximum likelihood decoder. For the noisy channel, the authors derive the theoretical expression of the average bit error rate for the individual subset. Moreover, the authors explain the role of the two factors (cardinality of the subset, and net level of interference) in being responsible for the non‐uniformity in the order of their error performance.