Sharper Upper Bounds for Unbalanced Uniquely Decodable Code Pairs

Two sets $A, B \subseteq \{0, 1\}^n$ form a Uniquely Decodable Code Pair (UDCP) if every pair $a \in A$, $b \in B$ yields a distinct sum $a+b$, where the addition is over $\mathbb{Z}^n$. We show that every UDCP $A, B$, with $|A| = 2^{(1-\epsilon)n}$ and $|B| = 2^{\beta n}$, satisfies $\beta \leq 0.4228 +\sqrt{\epsilon}$. For sufficiently small $\epsilon$, this bound significantly improves previous bounds by Urbanke and Li~[Information Theory Workshop '98] and Ordentlich and Shayevitz~[2014, arXiv:1412.8415], which upper bound $\beta$ by $0.4921$ and $0.4798$, respectively, as $\epsilon$ approaches $0$.Comment: 11 pages; to appear at ISIT 201

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

Quickest Sequence Phase Detection

A phase detection sequence is a length-$n$ cyclic sequence, such that the location of any length-$k$ contiguous subsequence can be determined from a noisy observation of that subsequence. In this paper, we derive bounds on the minimal possible $k$ in the limit of $n\to\infty$, and describe some sequence constructions. We further consider multiple phase detection sequences, where the location of any length-$k$ contiguous subsequence of each sequence can be determined simultaneously from a noisy mixture of those subsequences. We study the optimal trade-offs between the lengths of the sequences, and describe some sequence constructions. We compare these phase detection problems to their natural channel coding counterparts, and show a strict separation between the fundamental limits in the multiple sequence case. Both adversarial and probabilistic noise models are addressed.Comment: To appear in the IEEE Transactions on Information Theor

High Capacity CDMA and Collaborative Techniques

The thesis investigates new approaches to increase the user capacity and improve the error performance of Code Division Multiple Access (CDMA) by employing adaptive interference cancellation and collaborative spreading and space diversity techniques. Collaborative Coding Multiple Access (CCMA) is also investigated as a separate technique and combined with CDMA. The advantages and shortcomings of CDMA and CCMA are analysed and new techniques for both the uplink and downlink are proposed and evaluated. Multiple access interference (MAI) problem in the uplink of CDMA is investigated first. The practical issues of multiuser detection (MUD) techniques are reviewed and a novel blind adaptive approach to interference cancellation (IC) is proposed. It exploits the constant modulus (CM) property of digital signals to blindly suppress interference during the despreading process and obtain amplitude estimation with minimum mean squared error for use in cancellation stages. Two new blind adaptive receiver designs employing successive and parallel interference cancellation architectures using the CM algorithm (CMA) referred to as ‘CMA-SIC’ and ‘BA-PIC’, respectively, are presented. These techniques have shown to offer near single user performance for large number of users. It is shown to increase the user capacity by approximately two fold compared with conventional IC receivers. The spectral efficiency analysis of the techniques based on output signal-to interference-and-noise ratio (SINR) also shows significant gain in data rate. Furthermore, an effective and low complexity blind adaptive subcarrier combining (BASC) technique using a simple gradient descent based algorithm is proposed for Multicarrier-CDMA. It suppresses MAI without any knowledge of channel amplitudes and allows large number of users compared with equal gain and maximum ratio combining techniques normally used in practice. New user collaborative schemes are proposed and analysed theoretically and by simulations in different channel conditions to achieve spatial diversity for uplink of CCMA and CDMA. First, a simple transmitter diversity and its equivalent user collaborative diversity techniques for CCMA are designed and analysed. Next, a new user collaborative scheme with successive interference cancellation for uplink of CDMA referred to as collaborative SIC (C-SIC) is investigated to reduce MAI and achieve improved diversity. To further improve the performance of C-SIC under high system loading conditions, Collaborative Blind Adaptive SIC (C-BASIC) scheme is proposed. It is shown to minimize the residual MAI, leading to improved user capacity and a more robust system. It is known that collaborative diversity schemes incur loss in throughput due to the need of orthogonal time/frequency slots for relaying source’s data. To address this problem, finally a novel near-unity-rate scheme also referred to as bandwidth efficient collaborative diversity (BECD) is proposed and evaluated for CDMA. Under this scheme, pairs of users share a single spreading sequence to exchange and forward their data employing a simple superposition or space-time encoding methods. At the receiver collaborative joint detection is performed to separate each paired users’ data. It is shown that the scheme can achieve full diversity gain at no extra bandwidth as inter-user channel SNR becomes high. A novel approach of ‘User Collaboration’ is introduced to increase the user capacity of CDMA for both the downlink and uplink. First, collaborative group spreading technique for the downlink of overloaded CDMA system is introduced. It allows the sharing of the same single spreading sequence for more than one user belonging to the same group. This technique is referred to as Collaborative Spreading CDMA downlink (CS-CDMA-DL). In this technique T-user collaborative coding is used for each group to form a composite codeword signal of the users and then a single orthogonal sequence is used for the group. At each user’s receiver, decoding of composite codeword is carried out to extract the user’s own information while maintaining a high SINR performance. To improve the bit error performance of CS-CDMA-DL in Rayleigh fading conditions, Collaborative Space-time Spreading (C-STS) technique is proposed by combining the collaborative coding multiple access and space-time coding principles. A new scheme for uplink of CDMA using the ‘User Collaboration’ approach, referred to as CS-CDMA-UL is presented next. When users’ channels are independent (uncorrelated), significantly higher user capacity can be achieved by grouping multiple users to share the same spreading sequence and performing MUD on per group basis followed by a low complexity ML decoding at the receiver. This approach has shown to support much higher number of users than the available sequences while also maintaining the low receiver complexity. For improved performance under highly correlated channel conditions, T-user collaborative coding is also investigated within the CS-CDMA-UL system

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