An Upper Bound on the Sizes of Multiset-Union-Free Families

Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be two families of subsets of an $n$-element set. We say that $\mathcal{F}_1$ and $\mathcal{F}_2$ are multiset-union-free if for any $A,B\in \mathcal{F}_1$ and $C,D\in \mathcal{F}_2$ the multisets $A\uplus C$ and $B\uplus D$ are different, unless both $A = B$ and $C= D$. We derive a new upper bound on the maximal sizes of multiset-union-free pairs, improving a result of Urbanke and Li.Comment: A shorter ISIT conference version titled "VC-Dimension Based Outer Bound on the Zero-Error Capacity of the Binary Adder Channel" is availabl

Zero-error communication over adder MAC

Adder MAC is a simple noiseless multiple-access channel (MAC), where if users send messages $X_1,\ldots,X_h\in \{0,1\}^n$, then the receiver receives $Y = X_1+\cdots+X_h$ with addition over $\mathbb{Z}$. Communication over the noiseless adder MAC has been studied for more than fifty years. There are two models of particular interest: uniquely decodable code tuples, and $B_h$-codes. In spite of the similarities between these two models, lower bounds and upper bounds of the optimal sum rate of uniquely decodable code tuple asymptotically match as number of users goes to infinity, while there is a gap of factor two between lower bounds and upper bounds of the optimal rate of $B_h$-codes. The best currently known $B_h$-codes for $h\ge 3$ are constructed using random coding. In this work, we study variants of the random coding method and related problems, in hope of achieving $B_h$-codes with better rate. Our contribution include the following. (1) We prove that changing the underlying distribution used in random coding cannot improve the rate. (2) We determine the rate of a list-decoding version of $B_h$-codes achieved by the random coding method. (3) We study several related problems about R\'{e}nyi entropy.Comment: An updated version of author's master thesi

Finite Field Multiple Access

In the past several decades, various multiple-access (MA) techniques have been developed and used. These MA techniques are carried out in complex-field domain to separate the outputs of the users. It becomes problematic to find new resources from the physical world. It is desirable to find new resources, physical or virtual, to confront the fast development of MA systems. In this paper, an algebraic virtual resource is proposed to support multiuser transmission. For binary transmission systems, the algebraic virtual resource is based on assigning each user an element pair (EP) from a finite field GF($p^m$). The output bit from each user is mapped into an element in its assigned EP, called the output symbol. For a downlink MA system, the output symbols from the users are jointly multiplexed into a unique symbol in the same field GF($p^m$) for further physical-layer transmission. The EPs assigned to the users are said to form a multiuser algebraic uniquely decodable (UD) code. Using EPs over a finite field, a network, a downlink, and an uplink orthogonal/non-orthogonal MA systems are proposed, which are called finite-field MA (FFMA) systems. Methods for constructing algebraic UD codes for FFMA systems are presented. An FFMA system can be designed in conjunction with the classical complex-field MA techniques to provide more flexibility and varieties.Comment: 32 pages, 10 figure

High capacity multiuser multiantenna communication techniques

One of the main issues involved in the development of future wireless communication systems is the multiple access technique used to efficiently share the available spectrum among users. In rich multipath environment, spatial dimension can be exploited to meet the increasing number of users and their demands without consuming extra bandwidth and power. Therefore, it is utilized in the multiple-input multiple-output (MIMO) technology to increase the spectral efficiency significantly. However, multiuser MIMO (MU-MIMO) systems are still challenging to be widely adopted in next generation standards. In this thesis, new techniques are proposed to increase the channel and user capacity and improve the error performance of MU-MIMO over Rayleigh fading channel environment. For realistic system design and performance evaluation, channel correlation is considered as one of the main channel impurities due its severe influence on capacity and reliability. Two simple methods called generalized successive coloring technique (GSCT) and generalized iterative coloring technique (GICT) are proposed for accurate generation of correlated Rayleigh fading channels (CRFC). They are designed to overcome the shortcomings of existing methods by avoiding factorization of desired covariance matrix of the Gaussian samples. The superiority of these techniques is demonstrated by extensive simulations of different practical system scenarios. To mitigate the effects of channel correlations, a novel constellation constrained MU-MIMO (CC-MU-MIMO) scheme is proposed using transmit signal design and maximum likelihood joint detection (MLJD) at the receiver. It is designed to maximize the channel capacity and error performance based on principles of maximizing the minimum Euclidean distance (dmin) of composite received signals. Two signal design methods named as unequal power allocation (UPA) and rotation constellation (RC) are utilized to resolve the detection ambiguity caused by correlation. Extensive analysis and simulations demonstrate the effectiveness of considered scheme compared with conventional MU-MIMO. Furthermore, significant gain in SNR is achieved particularly in moderate to high correlations which have direct impact to maintain high user capacity. A new efficient receive antenna selection (RAS) technique referred to as phase difference based selection (PDBS) is proposed for single and multiuser MIMO systems to maximize the capacity over CRFC. It utilizes the received signal constellation to select the subset of antennas with highest (dmin) constellations due to its direct impact on the capacity and BER performance. A low complexity algorithm is designed by employing the Euclidean norm of channel matrix rows with their corresponding phase differences. Capacity analysis and simulation results show that PDBS outperforms norm based selection (NBS) and near to optimal selection (OS) for all correlation and SNR values. This technique provides fast RAS to capture most of the gains promised by multiantenna systems over different channel conditions. Finally, novel group layered MU-MIMO (GL-MU-MIMO) scheme is introduced to exploit the available spectrum for higher user capacity with affordable complexity. It takes the advantages of spatial difference among users and power control at base station to increase the number of users beyond the available number of RF chains. It is achieved by dividing the users into two groups according to their received power, high power group (HPG) and low power group (LPG). Different configurations of low complexity group layered multiuser detection (GL-MUD) and group power allocation ratio (η) are utilized to provide a valuable tradeoff between complexity and overall system performance. Furthermore, RAS diversity is incorporated by using NBS and a new selection algorithm called HPG-PDBS to increase the channel capacity and enhance the error performance. Extensive analysis and simulations demonstrate the superiority of proposed scheme compared with conventional MU-MIMO. By using appropriate value of (η), it shows higher sum rate capacity and substantial increase in the user capacity up to two-fold at target BER and SNR values