Uniquely Decodable Codes with Fast Decoder for Overloaded 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: Simulation Resultsmentioning

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

“…It is worth noting that in order to calculate the first term of (8), one has to average overall possible M |J |NM c input symbols (up to M KNM c for sum-rate) according to (9). However, when M c and/or N are too large, this task becomes intractable due to prohibitive computational complexity.…”

Section: Finite Constellation Inputmentioning

confidence: 99%

“…For instance, if dim(S T ) < KNM, H is obviously singular when L = 1, while H can be still invertible when L > 1 since dim(S) is possible to be equal to KNM according to the channel selectivity and the potential offset in the multi-path environment 5 . This is particularly helpful in an overloaded CDMA system [8,21], where the number of users exceed the spreading factor.…”

Section: Proposition 2 the Asymptotic Sum-capacity Of The Frequency-mentioning

confidence: 99%

“…In the literature, most studies on fundamental limits of multiuser CDMA systems have been done under the assumptions of synchronous, time-invariant (each user uses the same spreading sequence for all data symbols), and/or random spreading sequences [6][7][8][9][10][11]. In [6][7][8], the optimal spreading sequences and capacity limits for synchronous CDMA have been studied with a discretetime signal model.…”

Section: Introductionmentioning

confidence: 99%

“…In [6][7][8], the optimal spreading sequences and capacity limits for synchronous CDMA have been studied with a discretetime signal model. A more theoretical approach on CDMA capacity analysis has been pursued in [9][10][11] by modeling the spreading sequences with random sequences.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Waveform domain framework for capacity analysis of uplink WCDMA systems

Tai

Kim

Oechtering

et al. 2015

J Wireless Com Network

This paper investigates the capacity limit of an uplink WCDMA system considering a continuous-time waveform signal. Various realistic assumptions are incorporated into the problem, which make the study valuable for performance assessment of real cellular networks to identify potentials for performance improvements in practical receiver designs. An equivalent discrete-time channel model is derived based on sufficient statistics for optimal decoding of the transmitted messages. The capacity regions are then characterized using the equivalent channel considering both finite constellation and Gaussian distributed input signals. The capacity with sampling at the receiver is also provided to exemplify the performance loss due to a typical post-processing at the receiver. Moreover, we analyze the asymptotic capacity when the signal-to-noise ratio goes to infinity. The conditions to simultaneously achieve the individual capacities are derived, which reveal the impacts of signature waveform space, channel frequency selectivity and signal constellation on the system performance.

Wirel. Commun. Mob. Comput.

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

Singh

Amini

et al. 2016

Self Cite

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.