A new approach to the design of codes for synchronous-CDMA systems

D’Amours

2018 IEEE 29th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

2018

In this paper, we consider the problem of recursively designing uniquely decodable ternary code sets for highly overloaded synchronous code-division multipleaccess (CDMA) systems. The proposed code set achieves larger number of users K < K t max than any other known state-of-the-art ternary codes that offer low-complexity decoders in the noisy transmission. Moreover, we propose a simple decoder that uses only a few comparisons and can allow the user to uniquely recover the information bits. Compared to maximum likelihood (ML) decoder, which has a high computational complexity for even moderate code length, the proposed decoder has much lower computational complexity. We also derived the computational complexity of the proposed recursive decoder analytically. Simulation results show that the performance of the proposed decoder is almost as good as the ML decoder. * where γ(n) function is the number of ones in the binary expansion of all positive integers less than n.

Section: The Proposed Fast Decodermentioning

confidence: 99%

Uniquely Decodable Ternary Codes for Synchronous CDMA Systems

D’Amours

2018 IEEE 29th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

2018

“…For example, Martirossian and Khachatrian in [32] presented a linear decoder for their explicit construction of binary code sets in the noiseless transmission channel. The linear decoders corresponding to their explicit construction with K max of antipodal and ternary code sets can be found in [33] - [35] and [25] - [27], respectively. Although such overloaded UD code sets theoretically facilitate a large capacity, their decoding for noisy transmission has always been a greater challenge to deal with.…”

Section: Introductionmentioning

confidence: 99%

Fast Decoder for Overloaded Uniquely Decodable Synchronous Optical CDMA

2019 IEEE Wireless Communications and Networking Conference (WCNC)

D’Amours

et al. 2019

In this paper, we propose a fast decoder algorithm for uniquely decodable (errorless) code sets for overloaded synchronous optical code-division multiple-access (O-CDMA) systems. The proposed decoder is designed in a such a way that the users can uniquely recover the information bits with a very simple decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML) decoder, which has a high computational complexity for even moderate code lengths, the proposed decoder has much lower computational complexity. Simulation results in terms of bit error rate (BER) demonstrate that the performance of the proposed decoder for a given BER requires only 1 − 2 dB higher signal-to-noise ratio (SNR) than the ML decoder.

Wirel. Commun. Mob. Comput.

“…The concept of overloading in CDMA as a solution to the strict capacity limit of its conventional counterpart has drawn frequent interest of the researchers in the past and continuously evolved though several phases. The existing research in the field can be broadly classified into problems like the following: (i) designing of the signature matrices (uniquely decodable (UD) and non‐UD ); (ii) development of reusing techniques for the existing non‐overloaded matrices; (iii) designing of multi user detectors (MUD) ; (iv) adding system level improvisations for improved error performance ; and (v) study of capacity and performance under different channel and input conditions , for synchronous or asynchronous transmission. For matrix C being considered as UD over x , the inequality C x 1 ≠ C x 2 is true for x 1 and x 2 denoting two different input vectors, whereas its major applications in literature are recorded in the field of multiuser encoding for physical layer network coding , overloaded CDMA , and T‐user channels .…”

Section: Introductionmentioning

confidence: 99%

“…The concept of UD‐based construction in the context of multi‐user communication is no more new to literature, and exist in the form of several recursive and non‐group based architecture. However, most of them are hardly accompanied by an efficient decoder (both in complexity and error performance) for noisy transmission.…”

Section: Introductionmentioning

confidence: 99%

Twin tree hierarchy: a regularized approach to construction of signature matrices for overloaded CDMA

Singh

Amini

et al. 2016

Overloaded code division multiple access being the only means of the capacity extension for conventional code division multiple access accommodates more number of signatures than the spreading gain. Recently, ternary Signature Matrices with Orthogonal Subsets (SMOS) has been proposed, where the capacity maximization is 200%. The proposed multi-user detector using matched filter exploits the twin tree hierarchy of correlation among the subsets to guarantee the errorless recovery. In this paper, we feature the non-ternary version of SMOS (i.e., 2k-ary SMOS) of same capacity, where the binary alphabets in all the k constituent (orthogonal) subsets are unique. Unlike ternary, the tree hierarchy for 2k-ary SMOS is non-uniform. However, the errorless detection of the multi-user detector remains undeviated. For noisy transmission, simulation results show the error performance of the right child for each subset of 2k-ary to be significantly improved over the left. The optimality of the right child of the largest (Hadamard) subset is also discovered. At higher loading, for larger and smaller subsets the superiority is reported for the 2k-ary and ternary, respectively, and the counter-intuitive deviations observed for the lower loading scenarios are logically explained. For the overall capacity maximization being 150%, superiority is featured by the 2k-ary, but beyond, it becomes a conditional entity.where y and r D CAx are the noisy and noiseless received vector for C D OEc 1 , c 2 , c 3 , , c M being a N M matrix representing M signatures of length N, x D OEx 1 , x 2 , x 3 , , x M T represents the input data vector corresponding to all M users or signatures, A D I M M = Identity matrix with diagonal elements representing the amplitudes assuming the system to be perfectly power controlled, and n denotes zero mean Additive white Gaussian noise vector. While for conventional (underloaded) CDMA the maximum achievable value of M is N (i.e., M Ä N), this capacity limit can be maximized beyond N (i.e., M > N) using the feature of overloaded CDMA, which subsequently leads to the significant rise in the loading (overloading) factorˇD . M =N/.Over a decade, the popularity of CDMA besides the military applications can be well-speculated from its growing commercialization of the wireless communication systems like Third Generation cellular architecture using wideband CDMA (WCDMA). Although for the Fourth Generation architecture, the scope of participation of CDMA has been fully obliterated, its further advancement in terms of sparse coded multiple access [1] using low density signature [2] has regained its priority and been prospectively provisioned for the Fifth Generation [3] cellular architecture.