This paper proposes a low-complexity data-driven multi-user detector for grant-free non-orthogonal multiple access (GF-NOMA), which has gained significant interest in Internet of Things (IoT). IoT traffic is predominantly sporadic, where devices become active whenever they have data to transmit. The conventional grant-access procedure for requesting a transmission slot every time results in significant signaling overhead and latency. In power domain GF-NOMA, multiple devices can be preallocated the same channel resource, but different power levels. Whenever a device has data, it starts transmission directly using the allocated power level without any grant request. While this significantly reduces the signaling overhead, the access point has to perform the complex task of identifying the active devices and decoding their data. Conventional receivers for power domain NOMA fail in such GF scenarios and the typical solution is to limit transmissions to be packet-synchronized and add carefully chosen pilots in every packet to facilitate activity detection. However, in fairly static IoT networks with low-complexity devices and small packet sizes, this represents a significant overhead and reduces efficiency. In this work we solve the GF-NOMA detection problem without these constraints, by analyzing the boundaries of the received constellation points in power domain GF-NOMA for all activation combinations at once. A low-complexity decision tree-based receiver is proposed, which performs as well as the maximum likelihood-based benchmark receiver, and better than traditional data-driven detectors for GF-NOMA. Comprehensive simulation results demonstrate the performance of the proposed detector in terms of its detection efficiency and parameter learning with minimal training data.

In this article, we consider a federated learning (FL) problem over wireless channel that takes into account the coding rate and packet transmission errors. Communication channels are modeled as packet erasure channels (PECs), where the probability of erasure is determined by block length, code rate, and signal-to-noise ratio (SNR). In spite of fluctuations in instantaneous loss of FL, we prove that the expectation of loss converges even in the presence of packet erasure. To mitigate the impact of packet erasure on FL performance, we suggest a paradigm in which the central node (CN) makes use of memory. In particular, we propose two schemes in which, in the event of packet erasure, the CN retains either the most recent local updates or the most recent global parameters. We investigate the impact of coding rate, SNR, and the CN memory on the convergence of FL. For both short- and long-packet communications, we examine a realistic scenario of a massive IoT under the assumption of error-prone transmissions. Our simulation results demonstrate that even a single memory unit has a considerable effect on the FL’s efficiency in erroneous communication.

Information leakage to a guessing adversary in index coding is studied, where some messages in the system are sensitive and others are not. The non-sensitive messages can be used by the server like secret keys to mitigate leakage of the sensitive messages to the adversary. We construct a deterministic linear coding scheme, developed from the rank minimization method based on fitting matrices (Bar-Yossef et al. 2011). The linear scheme leads to a novel upper bound on the optimal information leakage rate, which is proved to be tight over all deterministic scalar linear codes. We also derive a converse result from a graph-theoretic perspective, which holds in general over all deterministic and stochastic coding schemes.

Two main privacy models for sanitising datasets are differential privacy (DP) and syntactic privacy. The former restricts individual values’ impact on the output based on the dataset while the latter restructures the dataset before publication to link any record to multiple sensitive data values. Besides both providing mechanisms to sanitise data, these models are often applied independently of each other and very little is known regarding how they relate. Knowing how privacy models are related can help us develop a deeper understanding of privacy and can inform how a single privacy mechanism can fulfil multiple privacy models. In this paper, we introduce a framework that determines if the privacy mechanisms of one privacy model can also guarantee privacy for another privacy model. We apply our framework to understand the relationship between DP and a form of syntactic privacy called t-closeness. We demonstrate, for the first time, how DP and t-closeness can be interpreted in terms of each other by introducing generalisations and extensions of both models to explain the transition from one model to the other. Finally, we show how applying one mechanism to guarantee multiple privacy models increases data utility compared to applying separate mechanisms for each privacy model.

We study the information leakage to a guessing adversary in zero-error source coding. The source coding problem is defined by a confusion graph capturing the distinguishability between source symbols. The information leakage is measured by the ratio of the adversary's successful guessing probability after and before eavesdropping the codeword, maximized over all possible source distributions. Such measurement under the basic adversarial model where the adversary makes a single guess and the guess is regarded successful if and only if the estimator sequence equals to the true source sequence is known as the maximum min-entropy leakage or the maximal leakage in the literature. We develop a single-letter characterization of the optimal normalized leakage under the basic adversarial model, together with an optimum-achieving memoryless stochastic mapping scheme. An interesting observation is that the optimal normalized leakage is equal to the optimal compression rate with fixed-length source codes, both of which can be simultaneously achieved by some deterministic coding schemes. We then extend the leakage measurement to generalized adversarial models where the adversary makes multiple guesses and allows a certain level of distortion, for which we derive single-letter lower and upper bounds.

We study the information leakage to a guessing adversary in index coding with a general message distribution. Under both vanishing-error and zero-error decoding assumptions, we develop lower and upper bounds on the optimal leakage rate, which are based on the broadcast rate of the subproblem induced by the set of messages the adversary tries to guess. When the messages are independent and uniformly distributed, the lower and upper bounds match, establishing an equivalence between the two rates.

We consider a Multi-Sender Unicast Index-Coding (MSUIC) problem, where in a broadcast network, multiple senders collaboratively send distinct messages to multiple receivers, each having some subset of the messages a priori. The aim is to find the shortest index code that minimizes the total number of coded bits sent by the senders. In this paper, built on the classic single-sender minrank concept, we develop a new rank-minimization framework for MSUIC that explicitly takes into account the sender message constraints and minimizes the sum of the ranks of encoding matrices subject to the receiver decoding requirements. This framework provides a systematic way to construct multi-sender linear index codes and to study their capability in achieving the shortest index codelength per message length (i.e., the optimal broadcast rate). In particular, we establish the optimal broadcast rate for all critical MSUIC instances with up to four receivers and show that a binary linear index code is optimal for all, except 15 instances with four receivers. We also propose a heuristic algorithm (in lieu of exhaustive search) to solve the rank-minimization problem. The effectiveness of the algorithm is validated by numerical studies of MSUIC instances with four or more receivers.

In this paper, we propose a new coding scheme and establish new bounds on the capacity region for the multi-sender unicast index-coding problem. We revisit existing partitioned distributed composite coding (DCC) proposed by Sadeghi et al. and identify its limitations in the implementation of multi-sender composite coding and in the strategy of sender partitioning. We then propose two new coding components to overcome these limitations and develop a multi-sender cooperative composite coding (CCC). We show that CCC can strictly improve upon partitioned DCC, and is the key to achieve optimality for a number of index-coding instances. The usefulness of CCC and its special cases is illuminated via non-trivial examples, and the capacity region is established for each example. Comparisons between CCC and other non-cooperative schemes in recent works are also provided to further demonstrate the advantage of CCC.

We address a centralized caching problem with unequal cache sizes. We consider a system with a server of files connected via a shared error-free link to a group of cache-enabled users, where one subgroup has a larger cache size than the other, and the number of files in the server is at least as large as the number of users. We propose a caching scheme for the considered system aimed at minimizing the load of worst-case demands over the shared link. Numerical evaluations show that our scheme improves upon the best existing explicit scheme by having a lower worst-case load, and performs within a multiplicative factor of 1.11 from the optimal scheme with uncoded placement and linear coded delivery. Unlike the optimal scheme-for which the placement, the delivery, and the load can be obtained by solving an optimisation problem, and become intractable as the number of users grows-our proposed scheme is an explicit scheme.

We provide a correction to[1]in response to an error reported by Vaddi and Rajan[2]. To this effect, we add one extra condition for the definition of an$\mathsf {IC}$structure on page 3696.

We establish new capacity bounds for the multi-sender unicast index-coding problem. We first revisit existing bounds proposed by Sadeghi et al. and identify the suboptimality of their inner bounds in general. We then present a simplified version of the existing multi-sender maximal-acyclic-induced-subgraph outer bound. For the inner bound, we propose joint link-and-sender partitioning to replace sender partitioning in partitioned Distributed Composite Coding (DCC). This leads to a modified DCC (mDCC) that outperforms partitioned DCC and suffices to achieve optimality for some index-coding instances. We also propose cooperative compression of composite messages in composite coding to exploit messages common to different senders to support larger composite rates than those by point-to-point compression in the existing schemes. We then develop a new multi-sender Cooperative Composite Coding (CCC) scheme. CCC further improves upon mDCC in general, and is instrumental to achieve optimality for a number of index-coding instances.

This study considers the optimisation of multi‐edge type low‐density parity‐check (MET‐LDPC) codes to maximise the decoding threshold. The authors propose an algorithm to jointly optimise the node degree distribution and the multi‐edge structure of MET‐LDPC codes for given values of the maximum number of edge‐types and maximum node degrees. This joint optimisation is particularly important for MET‐LDPC codes as it is not clear a priori which structures will be good. Using several examples, they demonstrate that the MET‐LDPC codes designed by the proposed joint optimisation algorithm exhibit improved decoding thresholds compared with previously reported MET‐LDPC codes.

Machine-to-machine (M2M) constitutes the communication paradigm at the basis of Internet of Things vision. M2M solutions allow billions of multi-role devices to communicate with each other or with the underlying data transport infrastructure without, or with minimal, human intervention. Current solutions for wireless transmissions originally designed for human-based applications thus require a substantial shift to cope with the capacity issues in managing a huge amount of M2M devices. In this paper, we consider the multiple access techniques as promising solutions to support a large number of devices in cellular systems with limited radio resources. We focus on non-orthogonal multiple access (NOMA) where, with the aim to increase the channel efficiency, the devices share the same radio resources for their data transmission. This has been shown to provide optimal throughput from an information theoretic point of view. We consider a realistic system model and characterize the system performance in terms of throughput and energy efficiency in an NOMA scenario with a random packet arrival model, where we also derive the stability condition for the system to guarantee the performance.

We consider the three-receiver Gaussian multiple-input multiple-output broadcast channel with an arbitrary number of antennas at the transmitter and the receivers. We investigate the degrees-of-freedom (DoF) region of the channel when each receiver requests a private message, and may know some of the messages requested by the other receivers as receiver message side information (RMSI). We establish the DoF region of the channel for all 16 possible non-isomorphic RMSI configurations by deriving tight inner and outer bounds on the region. To derive the inner bounds, we first propose a scheme for each RMSI configuration, which exploits both the null space and the side information of the receivers. We then use these schemes in conjunction with time sharing for 15 RMSI configurations, and with time sharing and two-symbol extension for the remaining one. To derive the outer bounds, we construct enhanced versions of the channel for each RMSI configuration, and upper bound their DoF region. After establishing the DoF region, in the case where all the nodes have the same number of antennas, we introduce some common properties of the DoF region, and the capacity region of the index coding problem.

The focus of this paper is on the analysis and design of Raptor codes using a multi-edge framework. In this regard, we first represent Raptor codes as multi-edge type (MET) low-density parity-check codes. This MET representation gives a general framework to analyze and design Raptor codes over a binary input additive white Gaussian noise channel using MET density evolution (MET-DE). We then consider a joint decoding scheme based on the belief propagation (BP) decoding for Raptor codes in the multi-edge framework, and analyze the convergence behavior of the BP decoder using MET-DE. In joint decoding of Raptor codes, the component codes corresponding to the inner code and the precode are decoded in parallel and provide information to each other. We also derive an exact expression for the stability of Raptor codes with joint decoding. We then propose an efficient Raptor code design method using the multi-edge framework, where we simultaneously optimize the inner code and the precode. Through density evolution analysis we show that the designed Raptor codes using the multi-edge framework outperform the existing Raptor codes in literature in terms of realized rates.

We consider a graphical approach to index coding. As cycles have been shown to provide coding gain, cycles and cliques (a specific type of overlapping cycles) have been exploited in an existing literature. In this paper, we define a more general form of overlapping cycles, called the interlinked-cycle (IC) structure, that generalizes cycles and cliques. We propose a scheme, called the interlinked-cycle-cover (ICC) scheme, that leverages IC structures in digraphs to construct scalar linear index codes. We characterize a class of infinitely many digraphs where our proposed scheme is optimal over all linear and nonlinear index codes. Consequently, for this class of digraphs, we indirectly prove that scalar linear index codes are optimal. Furthermore, we show that the ICC scheme can outperform all the existing graph-based schemes (including partial-clique-cover and fractional-local-chromatic number schemes), and a random coding scheme (namely, composite coding) for certain graphs.

Machine-to-machine (M2M) wireless systems aim to provide ubiquitous connectivity between machine-type communication (MTC) devices without any human intervention. Given the exponential growth of MTC traffic, it is of utmost importance to ensure that future wireless standards are capable of handling this traffic. In this paper, we focus on the design of a very efficient massive access strategy for highly dense cellular networks with M2M communications. Several MTC devices are allowed to simultaneously transmit in the same resource block by incorporating Raptor codes and a simple modulation scheme. This significantly reduces the access delay and improves the achievable system throughput. A simple yet efficient random access strategy is proposed to not only detect the selected preambles, but also estimate the number of devices which have chosen them. No device identification is needed in the random access phase which significantly reduces the signaling overhead. The proposed scheme is analyzed and the maximum number of MTC devices that can be supported in a resource block is characterized as a function of the message length, number of available resources, and the number of preambles. Simulation results show that the proposed scheme can effectively support a massive number of MTC devices for a limited number of available resources, when the message size is small.

The focus of this work is on the design of Raptor codes for continuous variable Quantum key distribution (CV-QKD) systems. We design a highly efficient Raptor code for very low signal to noise ratios (SNRs), which enables CV-QKD systems to operate over long distances with a significantly higher secret key rate compared to conventional fixed rate codes. The degree distribution design of Raptor codes in the low SNR regime is formulated as a linear program, where a set of optimized degree distributions are also obtained through linear programming. Simulation results show that the designed code achieves efficiencies higher than 94% for SNRs as low as −20 dB and −30 dB. We further propose a new error reconciliation protocol for CV-QKD systems by using Raptor codes and show that it can achieve higher secret key rates over long distances compared to existing protocols.

We consider the two-receiver memoryless broadcast channel with states where each receiver requests both common and private messages, and may know part of the private message requested by the other receiver as receiver message side information (RMSI). We address two categories of the channel (i) channel with states known causally to the transmitter, and (ii) channel with states known non-causally to the transmitter. Starting with the channel without RMSI, we first propose a transmission scheme and derive an inner bound for the causal category. We then unify our inner bound for the causal category and the best-known inner bound for the non-causal category, although their transmission schemes are different. Moving on to the channel with RMSI, we first apply a pre-coding to the transmission schemes of the causal and non-causal categories without RMSI. We then derive a unified inner bound as a result of having a unified inner bound when there is no RMSI, and applying the same pre-coding to both categories. We show that our inner bound is tight for some new cases as well as the cases whose capacity region was known previously.

We propose a capacity approaching coding strategy for additive white Gaussian noise (AWGN) channels by using multi-layer Raptor codes and superposition modulation. Each AWGN channel is divided into several binary-input AWGN (BI-AWGN) channels at a very low signal to noise ratio (SNR), where a capacity approaching Raptor code can be used to encode the message over each layer. A single capacity approaching degree distribution is then used for the Raptor codes over all the layers. A well-known multi-stage decoder is used for successive interference cancellation and decoding the multi-layer Raptor code, where each decoding stage is modeled by a BI-AWGN channel of a fixed SNR. This allows the development of a capacity approaching code for an AWGN channel at every SNR by using a single Raptor code with a fixed degree distribution as the component code.

This paper considers density evolution for low-density parity-check (LDPC) and multi-edge type LDPC (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three single-parameter Gaussian approximations for density evolution and discuss their accuracy under several conditions, namely, at low rates, with punctured and degree-one variable nodes. We observe that the assumption of symmetric Gaussian distribution for the density-evolution messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Thus, single-parameter Gaussian approximation methods produce very poor results in these cases. Based on these observations, we then introduce a new density evolution approximation algorithm for LDPC and MET-LDPC codes. Our method is a combination of full density evolution and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after density-evolution messages closely follow a symmetric Gaussian distribution. Our method significantly improves the accuracy of the code threshold estimation. Additionally, the proposed method significantly reduces the computational time of evaluating the code threshold compared with full density evolution thereby making it more suitable for code design.

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum output node degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.

This paper investigates the capacity regions of two-receiver broadcast channels where each receiver (i) has both common and private-message requests, and (ii) knows part of the private message requested by the other receiver as side information. We first propose a transmission scheme and derive an inner bound for the two-receiver memoryless broadcast channel. We next prove that this inner bound is tight for the deterministic channel and the more capable channel, thereby establishing their capacity regions.We show that this inner bound is also tight for all classes of two-receiver broadcast channels whose capacity regions were known prior to this work. Our proposed scheme is consequently a unified capacity-achieving scheme for these classes of broadcast channels.

We study the index coding problem in the unicast message setting, i.e., where each message is requested by one unique receiver. This problem can be modeled by a directed graph. We propose a new scheme called interlinked cycle cover, which exploits interlinked cycles in the directed graph, for designing index codes. This new scheme generalizes the existing clique cover and cycle cover schemes. We prove that for a class of infinitely many digraphs with messages of any length, interlinked cycle cover provides an optimal index code. Furthermore, the index code is linear with linear time encoding complexity.

This paper investigates the capacity region of the three-receiver AWGN broadcast channel where the receivers: 1) have private-message requests and 2) may know some of the messages requested by other receivers as side information. We first classify all 64 possible side information configurations into eight groups, each consisting of eight members. We next construct transmission schemes, and derive new inner and outer bounds for the groups. This establishes the capacity region for 52 out of 64 possible side information configurations. For six groups (i.e., groups 1, 2, 3, 5, 6, and 8 in our terminology), we establish the capacity region for all their members, and show that it tightens both the best-known inner and outer bounds. For group 4, our inner and outer bounds tighten the best-known inner bound and/or outer bound for all the group members. Moreover, our bounds coincide at certain regions, which can be characterized by two thresholds. For group 7, our inner and outer bounds coincide for four members, and thereby establishing the capacity region. For the remaining four members, our bounds tighten both the best-known inner and outer bounds.

This paper considers the finite-field multi-way relay channel with pairwise message sharing, where multiple users exchange messages through a single relay and where the users may share parts of their source messages (meaning that some message parts are known/common to more than one user). In this paper, we design an optimal functional-decode-forward coding scheme that takes the shared messages into account. More specifically, we design an optimal function for the relay to decode (from the users on the uplink) and forward (back to the users on the downlink). We then show that this proposed function-decode-forward coding scheme can achieve the capacity region of the finite-field multi-way relay channel with pairwise message sharing. This paper generalizes our previous result for the case of three users to any number of users.

This paper investigates the capacity region of three-receiver AWGN broadcast channels where the receivers (i) have private-message requests and (ii) know the messages requested by some other receivers as side information. We classify these channels based on their side information into eight groups, and construct different transmission schemes for the groups. For six groups, we characterize the capacity region, and show that it improves both the best known inner and outer bounds. For the remaining two groups, we improve the best known inner bound by using side information during channel decoding at the receivers.

Abstract—This paper considers the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) know some of the messages requested by other receivers as side information. For this setup, all possible side information configurations have been recently classified into eight groups and the capacity of the channel has been established for six groups (Asadi et al., ISIT 2014). We propose inner and outer bounds for the two remaining groups, groups 4 and 7. A distinguishing feature of these two groups is that the weakest receiver knows the requested message of the strongest receiver as side information while the in-between receiver does not. For group 4, the inner and outer bounds coincide at certain regions. For group 7, the inner and outer bounds coincide, thereby establishing the capacity, for four members out of all eight members of the group; for the remaining four members, the proposed bounds reduce the gap between the best known inner and outer bounds. I.

A low-density parity-check (LDPC) code is a linear block code described by a sparse parity-check matrix, which can be efficiently represented by a bipartite Tanner graph. The standard iterative decoding algorithm, known as belief propagation, passes messages along the edges of this Tanner graph. Density evolution is an efficient method to analyze the performance of the belief propagation decoding algorithm for a particular LDPC code ensemble, enabling the determination of a decoding threshold. The basic problem addressed in this work is how to optimize the Tanner graph so that the decoding threshold is as large as possible. We introduce a new code optimization technique which involves the search space range which can be thought of as minimizing randomness in differential evolution or limiting the search range in exhaustive search. This technique is applied to the design of good irregular LDPC codes and multi-edge type LDPC codes.

The authors propose the construction of spatially coupled low‐density parity‐check (SC‐LDPC) codes using a periodic time‐variant quasi‐cyclic (QC) algorithm. The QC‐based approach is optimised to obtain memory efficiency in storing the parity‐check matrix in the decoders. A hardware model of the parity‐check storage units has been designed for a Xilinx field‐programmable gate array (FPGA), to compare the logic and memory requirements for various approaches. It is shown that the proposed QC SC‐LDPC code (with optimisation) can be stored with reasonable logic resources and without the need of block memory in the FPGA. In addition, a significant improvement in the processing speed is also achieved. This study also proposes a new QC algorithm for constructing spatially coupled repeat‐accumulate (SC‐RA) codes. The proposed construction reduces the implementation complexity of the encoder and subsequently saves significant computational resources required for storing and accessing the circulants in the decoder. The performance of the proposed code is also compared with the standard RA codes through simulations.

This paper studies the three-user finite-field multi-way relay channel, where the users exchange messages via a relay. The messages are arbitrarily correlated, and the finite-field channel is linear and is subject to additive noise of arbitrary distribution. The problem is to determine the minimum achievable source-channel rate, defined as channel uses per source symbol needed for reliable communication. We combine Slepian-Wolf source coding and functional-decode-forward channel coding to obtain the solution for two classes of source and channel combinations. Furthermore, for correlated sources that have their common information equal their mutual information, we propose a new coding scheme to achieve the minimum source-channel rate.

We consider a multi-way relay network with an orthogonal uplink and correlated sources, and we characterise reliable communication (in the usual Shannon sense) with a single-letter expression. The characterisation is obtained using a joint source-channel random-coding argument, which is based on a combination of Wyner et al.'s Cascaded Slepian-Wolf Source Coding and Tuncel's Slepian-Wolf Coding over Broadcast Channels. We prove a separation theorem for the special case of two nodes; that is, we show that a modular code architecture with separate source and channel coding functions is (asymptotically) optimal. Finally, we propose a practical coding scheme based on low-density parity-check codes, and we analyse its performance using multi-edge density evolution.

This paper considers the multi-way relay channel (MWRC) where multiple users exchange messages via a single relay. The capacity region is derived for a special class of MWRCs where (i) the uplink and the downlink are separated in the sense that there is no direct user-to-user links, (ii) the channel is restricted in the sense that each user's transmitted channel symbols can depend on only its own message, but not on its received channel symbols, and (iii) the uplink is any deterministic function.

The multi-way relay channel (MWRC) models cooperative communication networks in which many users exchange messages via a relay. In this paper, we consider the finite field MWRC with correlated messages. The problem is to find all achievable rates, defined as the number of channel uses required per reliable exchange of message tuple. For the case of three users, we have previously established that for a special class of source distributions, the set of all achievable rates can be found [Ong et al., ISIT 2010]. The class is specified by an almost balanced conditional mutual information (ABCMI) condition. In this paper, we first generalize the ABCMI condition to the case of more than three users. We then show that if the sources satisfy the ABCMI condition, then the set of all achievable rates is found and can be attained using a separate source-channel coding architecture.

This paper compares the partial-decode-forward and the complete-decode-forward coding strategies for the half-duplex Gaussian single-relay channel. We analytically show that the rate achievable by partial-decode-forward outperforms that of the more straightforward complete-decode-forward by at most 12.5%. Furthermore, in the following asymptotic cases, the gap between the partial-decode-forward and the complete-decode-forward rates diminishes: (i) when the relay is close to the source, (ii) when the relay is close to the destination, and (iii) when the SNR is low. In addition, when the SNR increases, this gap, when normalized to the complete-decode-forward rate, also diminishes. Consequently, significant performance improvements are not achieved by optimizing the fraction of data the relay should decode and forward, over simply decoding the entire source message.

The$L$-user additive white Gaussian noise multiway relay channel is investigated, where$L$users exchange information at the same rate through a single relay. A new achievable rate region, based on the functional-decode-forward coding strategy, is derived. For the case where there are three or more users, and all nodes transmit at the same power, the capacity is obtained. For the case where the relay power scales with the number of users, it is shown that both compress-forward and functional-decode-forward achieve rates within a constant number of bits of the capacity at all SNR levels; in addition, functional-decode-forward outperforms compress-forward and complete-decode-forward at high SNR levels.

We study the half-duplex multiple-relay channel (HD-MRC) where every node can either transmit or listen but cannot do both at the same time. We obtain a capacity upper bound based on a max-flow min-cut argument and achievable transmission rates based on the decode-forward (DF) coding strategy, for both the discrete memoryless HD-MRC and the phase-fading HD-MRC. We discover that both the upper bound and the achievable rates are functions of the transmit/listen state (a description of which nodes transmit and which receive). More precisely, they are functions of the time fraction of the different states, which we term a schedule. We formulate the optimal scheduling problem to find an optimal schedule that maximizes the DF rate. The optimal scheduling problem turns out to be a maximin optimization, for which we propose an algorithmic solution. We demonstrate our approach on a four-node multiple-relay channel, obtaining closed-form solutions in certain scenarios. Furthermore, we show that for the received signal-to-noise ratio degraded phase-fading HD-MRC, the optimal scheduling problem can be simplified to a max optimization.

This paper investigates the additive white Gaussian noise two-way relay channel, where two users exchange messages through a relay. Asymmetrical channels are considered where the users can transmit data at different rates and at different power levels. We modify and improve existing coding schemes to obtain three new achievable rate regions. Comparing four downlink-optimal coding schemes, we show that the scheme that gives the best sum-rate performance is (i) complete-decode-forward, when both users transmit at low signal-to-noise ratio (SNR); (ii) functional-decode-forward with nested lattice codes, when both users transmit at high SNR; (iii) functional-decode-forward with rate splitting and time-division multiplexing, when one user transmits at low SNR and another user at medium-high SNR.

The three-user finite field multi-way relay channel with correlated sources is considered. The three users generate possibly correlated messages, and each user is to transmit its message to the two other users reliably in the Shannon sense. As there is no direct link among the users, communication is carried out via a relay, and the link from the users to the relay and those from the relay to the users are finite field adder channels with additive noise of arbitrary distribution. The problem is to determine the set of all possible achievable rates, defined as channel uses per source symbol for reliable communication. For two classes of source/channel combinations, the solution is obtained using Slepian-Wolf source coding combined with functional-decode-forward channel coding.

The multiway relay channel is a multicast network whereLusers exchange data through a relay. In this paper, the capacity region of a class of multiway relay channels is derived, where the channel inputs and outputs take values over finite fields. The cut-set upper bound to the capacity region is derived and is shown to be achievable by our proposed functional-decode-forward coding strategy. More specifically, for the general case where the users can transmit at possibly different rates, functional-decode-forward, combined with rate splitting and joint source-channel decoding, is proved to achieve the capacity region; while for the case where all users transmit at a common rate, rate splitting and joint source-channel decoding are not required to achieve the capacity. That the capacity-achieving coding strategies do not utilize the users' received signals in the users' encoding functions implies that feedback does not increase the capacity region of this class of multiway relay channels.

We present capacity results of the binary-symmetric parallel-relay network, where there is one source, one destination, and K relays in parallel. We show that forwarding relays, where the relays merely transmit their received signals, achieve the capacity in two ways: with coded transmission at the source and a finite number of relays, or uncoded transmission at the source and a sufficiently large number of relays. On the other hand, decoding relays, where the relays decode the source message, re-encode, and forward it to the destination, achieve the capacity when the number of relays is small.

The L-user additive white Gaussian noise multi-way relay channel is considered, where multiple users exchange information through a single relay at a common rate. Existing coding strategies, i.e., complete-decode-forward and compress-forward are shown to be bounded away from the cut-set upper bound at high signal-to-noise ratios (SNR). It is known that the gap between the compress-forward rate and the capacity upper bound is a constant at high SNR, and that between the complete-decode-forward rate and the upper bound increases with SNR at high SNR. In this paper, a functional-decode-forward coding strategy is proposed. It is shown that for L ≥ 3, complete-decode-forward achieves the capacity when SNR ≤ 0 dB, and functional-decode-forward achieves the capacity when SNR ≥ 0 dB. For L = 2, functional-decode-forward achieves the capacity asymptotically as SNR increases.

In this paper, we present a new class of iteratively decoded error correction codes. These codes, which are a modification of irregular repeat-accumulate (IRA) codes, are termed generalized IRA (GIRA) codes, and are designed for improved error floor performance. GIRA codes are systematic, easily encodable, and are decoded with the sum-product algorithm. In this paper we present a density evolution algorithm to compute the threshold of GIRA codes, and find GIRA degree distributions which produce codes with good thresholds. We then propose inner code designs and show using simulation results that they improve upon the error floor performance of IRA codes.

In this paper, we extend our previous work on the half duplex multiple-relay channel (MRC). A capacity upper bound based on the max-flow min-cut argument and achievable transmission rates based on the decode-forward coding strategy (DF) for the half duplex MRC have been shown to be functions of the schedule of the network, which is defined as the probability mass function of the transmit state vector (a description of which nodes transmit and which receive). Finding the optimal (rate-maximizing) schedule for DF can be formulated as a maximin optimization problem which is not easily solved in general. In our recent paper, we presented a technique to find optimal schedules for the 4-node MRC based on minimax hypothesis testing. Closed-form solutions were obtained for certain channel topologies. In this paper, we extend the technique to solve for optimal schedules for the general D-node half duplex MRC, where D ges 3.

In this paper low-density parity-check (LDPC) codes are designed for burst erasure channels. Firstly, lower bounds for the maximum length erasure burst that can always be corrected with message-passing decoding are derived as a function of the parity-check matrix properties. We then show how parity-check matrices for burst erasure correcting LDPC codes can be constructed using superposition, where the burst erasure correcting performance of the resulting codes is derived as a property of the stopping set size of the base matrices and the choice of permutation matrices for the superposition. This result is then used to design both single burst erasure correcting LDPC codes which are also resilient to the presence of random erasures in the received bits and LDPC codes which can correct multiple erasure bursts in the same codeword.

In this paper we design practical interleavers for regular, systematic repeat-accumulate (RA) codes. The new interleavers, which we call L-type and modified L-type interleavers, are deterministic, described by a single parameter, and straightforward to implement. Despite their simple description, the new interleavers are shown to perform equally as well as, or better than, traditional interleavers over a wide range of code lengths and rates.

This paper considers the performance, on the binary erasure channel, of low-density parity-check (LDPC) codes without repeated edges in their Tanner graphs. A modification to existing finite-length analysis algorithms is presented for these codes.

This paper proposes novel interleaver and accumulator structures for systematic, regular repeat-accumulate (RA) codes. It is well known that such codes are amenable to iterative (sum-product) decoding on the Tanner graph of the code, yet are as readily encodable as turbo codes. In this paper, interleavers for RA codes are designed using combinatorial techniques as a basis for deterministic interleaver constructions, yielding RA codes whose Tanner graphs are free of 4-cycles. Further, a generalized RA code accumulator structure is proposed, leading to codes, termed w3RA codes, whose parity-check matrices have many fewer weight-2 columns than conventional RA codes. The w3RA codes retain the low-complexity encoding of conventional RA codes and exhibit improved error-floor performance.

In this paper we design deterministic interleavers for systematic repeat-accumulate (RA) codes. Despite their simple description the new interleavers are shown to outperform traditional interleavers over a wide range of code lengths and rates

Recent promising theoretical results for irregular repeat-accumulate (IRA) codes, together with their extremely simple encoding, motivates this investigation into the design and implementation of finite-length IRA codes. In this paper interleavers for RA codes are designed using combinatorial techniques to produce RA codes with Tanner graphs suitable for sum-product decoding. Further, a modified RA code accumulator is used to construct new IRA codes with columns of weight 3 in the accumulator. These new codes, called w3IRA codes, can be designed with flexible degree distributions and retain the simple encoding of traditional IRA codes

The effect of channel gain quantization on the information capacity of unknown time varying flat fading channels is investigated. The phase and/or amplitude of the flat fading channel gain is modelled as a finite state Markov (FSM) process and the information capacity of the FSM channel is calculated numerically as a measure for choosing the number of channel quantization levels, as well as quantization thresholds. The results indicate that for binary signalling, the capacity is saturated beyond 8 to 16 levels of phase and 8 to 16 levels of amplitude quantization.

This paper develops codes suitable for iterative decoding using the sum-product algorithm. By considering a large class of combinatorial structures, known as partial geometries, we are able to define classes of low-density parity-check (LDPC) codes, which include several previously known families of codes as special cases. The existing range of algebraic LDPC codes is limited, so the new families of codes obtained by generalizing to partial geometries significantly increase the range of choice of available code lengths and rates. We derive bounds on minimum distance, rank, and girth for all the codes from partial geometries, and present constructions and performance results for the classes of partial geometries which have not previously been proposed for use with iterative decoding. We show that these new codes can achieve improved error-correction performance over randomly constructed LDPC codes and, in some cases, achieve this with a significant decrease in decoding complexity.

The paper presents a construction of very high-rate low-density parity-check (LDPC) codes based on incidence matrices of unital designs. Like the projective geometry and oval designs, unital designs exist with incidence matrices which are significantly rank deficient. Thus high-rate LDPC codes with a large number of linearly dependent parity-check equations can be constructed. The LDPC codes from unitals have Tanner graphs free of 4-cycles and perform well with iterative decoding, offering new LDPC codes at rates and lengths not available with existing algebraic LDPC codes.

This paper extends the class of low-density parity-check (LDPC) codes that can be algebraically constructed. We present regular LDPC codes based on resolvable Steiner 2-designs which have Tanner graphs free of four-cycles. The resulting codes are (3, /spl rho/)-regular or (4, /spl rho/)-regular for any value of /spl rho/ and for a flexible choice of code lengths.

Gallager introduced low-density parity-check (LDPC) codes in 1962, presenting a construction method to randomly allocate bits in the parity-check matrix subject to certain structural constraints. Since then improvements have been made to Gallager's construction method and some analytic constructions for LDPC codes have been presented. However analytically constructed LDPC codes comprise only a very small subset of possible codes and as a result LDPC codes are still, for the most part, constructed randomly. This paper extends the class of LDPC codes that can be systematically generated by presenting a construction method for regular LDPC codes based on combinatorial designs known as Kirkman triple systems. That is, we construct (3, /spl rho/)-regular codes whose Tanner (1981) graph is free of 4-cycles for any integer /spl rho/.

Analytically constructed LDPC codes comprise only a very small subset of possible codes and as a result LDPC codes are still, for the most part, constructed randomly. This paper extends the class of LDPC codes that can be systematically generated by presenting a construction method for regular LDPC codes based on combinatorial designs known as Kirkman triple systems. We construct (3, /spl rho/)-regular codes whose Tanner graph is free of 4-cycles for any integer /spl rho/, and examine girth and minimum distance properties of several classes of LDPC codes obtained from combinatorial designs.