We focus on the design of distributed Luby transform (DLT) codes for erasure networks with multiple sources and multiple relays, communicating to a single destination. The erasure-floor performance of DLT codes improves with the maximum degree of the relay-degree distribution. However, for conventional DLT codes, the maximum degree is upper-bounded by the number of sources. An additional constraint is that the sources are required to have the same information block length. We introduce a $D$-bit buffer for each source-relay link, which allows the relay to select multiple encoded bits from the same source for the relay-encoding process; thus, the number of sources no longer limits the maximum degree at the relay. Furthermore, the introduction of buffers facilitates the use of different information block sizes across sources. Based on density evolution we develop an asymptotic analytical framework for optimization of the relay-degree distribution. We further integrate techniques for unequal erasure protection into the optimization framework. The proposed codes are considered for both lossless and lossy source-relay links. Numerical examples show that there is no loss in erasure performance for transmission over lossy source-relay links as compared to lossless links. Additional delays, however, may occur. The design framework and our contributions are demonstrated by a number of illustrative examples, showing the improvements obtained by the proposed buffer-based DLT codes.
In this work, we propose a dynamic buffer-aided distributed space-time coding (DSTC) scheme for cooperative direct-sequence code-division multiple access systems. We first devise a relay selection algorithm that can automatically select the optimum set of relays among both the source-relay phase and the relay-destination phase for DSTC transmission according to the signal-to-interference-plus-noise ratio (SINR) criterion. Multiple relays equipped with dynamic buffers are introduced in the network, which allows the relays to store data received from the sources and wait until the most appropria…
This work proposes adaptive buffer-aided distributed space-time coding schemes and algorithms with feedback for wireless networks equipped with buffer-aided relays. The proposed schemes employ a maximum likelihood receiver at the destination and adjustable codes subject to a power constraint with an amplify-and-forward cooperative strategy at the relays. Each relay is equipped with a buffer and is capable of storing blocks of received symbols and forwarding the data to the destination if selected. Different antenna configurations and wireless channels, such as static block fading channels, are…
In this paper, link selection for half-duplex buffer-aided relay systems is revisited. A new fixed scheduling policy referred as alternate distributed beamforming (ADB) is proposed, in which the relays are divided into two groups, with one group receiving the same information broadcast from the source and the other group transmitting the common messages to the destination via distributed beamforming in each time slot. It is worth noting that the relays used for reception and transmission are determined without the need of instantaneous channel state information (CSI). Theoretical analysis of t…
In this work, we propose buffer-aided distributed space-time coding (DSTC) schemes and relay selection algorithms for cooperative direct-sequence code-division multiple access (DS-CDMA) systems. We first devise a relay pair selection algorithm that can form relay pairs and then select the optimum set of relays among both the source-relay phase and the relay-destination phase according to the signal-to-interference-plus-noise ratio (SINR) criterion. Multiple relays equipped with dynamic buffers are then introduced in the network, which allows the relays to store data received from the sources a…
In this paper, link selection is investigated in half-duplex (HD) dual-hop cooperative systems with multiple antennas at the relays. Alternate distributed beamforming (ADB) scheme is revisited for buffer-aided multi-antenna relay systems, in which the relays are divided into two groups, with one group receiving the same information broadcast from the source and the other group transmitting the common messages to the destination via distributed beamforming in each time slot. It is worth noting that the relays used for reception and transmission are determined without the need of instantaneous c…
In this work, we propose buffer-aided physical-layer network coding (PLNC) techniques for cooperative direct-sequence code-division multiple access systems. In the proposed buffer-aided PLNC schemes, a relay pair selection algorithm is employed to obtain the relay pair and the packets in the buffer entries with the best performance and the associated link combinations used for data transmission. We also devise PLNC schemes based on the design of linear network coding matrices using maximum likelihood and minimum mean-square error criteria to generate the network coded symbols that are sent to …
We present a closed-form expression for the minimal delay that is achievable in a setting that combines a buffer and an erasure code, used to mitigate the packet delay variance. The erasure code is modeled according to the recent information-theoretic results on finite block length codes. Evaluations reveal that accurate knowledge of the network parameters is essential for optimal operation. Moreover, it is shown that, when the network packet delay variance is large, the buffer delay becomes negligible. Therefore, in this case the delay budget should be spent mainly on the erasure code.
A practical rate-matching system for constructing rate-compatible polar codes is proposed. The proposed polar code circular buffer rate-matching is suitable for transmissions on communication channels that support hybrid automatic repeat request (HARQ) communications, as well as for flexible resource-element rate-matching on single transmission channels. Our proposed circular buffer rate matching scheme also incorporates a bit-mapping scheme for transmission on bit-interleaved coded modulation (BICM) channels using higher order modulations. An interleaver is derived from a puncturing order obt…
Exact queueing analysis of erasure networks with network coding in a finite buffer regime is an extremely hard problem due to the large number of states in the network. In such networks, packets are lost due to either link erasures or due to blocking due to full buffers. In this paper, a block-by-block random linear network coding scheme with feedback on the links is selected for reliability and more importantly guaranteed decoding of each block. We propose a novel method that iteratively estimates the performance parameters of the network and more importantly reduces the computational complex…
In this work we propose an adaptive buffer-aided space-time coding scheme for cooperative wireless networks. A maximum likelihood receiver and adjustable code vectors are considered subject to a power constraint with an amplify-and-forward cooperation strategy. Each multiple-antenna relay is equipped with a buffer and is capable of storing the received symbols before forwarding them to the destination. We also present an adaptive relay selection and optimization algorithm, in which the instantaneous signal to noise ratio in each link is calculated and compared at the destination. An adjustable…
We consider an additive White Gaussian channel where the transmitter is powered by an energy harvesting source. For such a system, we provide a lower bound on the maximal code book at finite code lengths that improves upon previously known bounds.
We consider a real-time streaming source coding system in which an encoder observes a sequence of randomly arriving symbols from an i.i.d. source, and feeds binary codewords to a FIFO buffer that outputs one bit per time unit to a decoder. Each source symbol represents a status update by the source, and the timeliness of the system is quantified by the age of information (AoI), defined as the time difference between the present time and the generation time of the most up-to-date symbol at the output of the decoder. When the FIFO buffer is allowed to be empty, we propose an optimal prefix-free …
Buffer aided relaying has recently attracted a lot of attention due to the improvement in the system throughput. However, a side effect usually deemed is that buffering at relay nodes results in the increase in packet delays. In this paper, we study the effect of buffering relays on the end-to-end delay of users' data, from the time they arrive at source until delivery to the destination. We use simple discussions to provide an insight on the overall waiting time of the packets in the system. By studying the Bernoulli distributed channel conditions, and using intuitive generalizations, we conc…
In this paper, throughput achieved in cognitive radio channels with finite blocklength codes under buffer limitations is studied. Cognitive users first determine the activity of the primary users' through channel sensing and then initiate data transmission at a power level that depends on the channel sensing decisions. It is assumed that finite blocklength codes are employed in the data transmission phase. Hence, errors can occur in reception and retransmissions can be required. Primary users' activities are modeled as a two-state Markov chain and an eight-state Markov chain is constructed in …
Hybrid radio frequency (RF)/free space optical (FSO) systems are among the candidate enabling technologies for the next generation of wireless networks since they benefit from both the high data rates of the FSO subsystem and the high reliability of the RF subsystem. In this paper, we focus on the problem of throughput maximization in the parallel hybrid RF/FSO relay channel. In the parallel hybrid RF/FSO relay channel, a source node sends its data to a destination node with the help of multiple relay nodes. Thereby, for a given relay, the source-relay and the relay-destination FSO links are o…
Flash memory is a non-volatile computer memory comprising blocks of cells, wherein each cell can take on q different values or levels. While increasing the cell level is easy, reducing the level of a cell can be accomplished only by erasing an entire block. Since block erasures are highly undesirable, coding schemes - known as floating codes (or flash codes) and buffer codes - have been designed in order to maximize the number of times that information stored in a flash memory can be written (and re-written) prior to incurring a block erasure. An (n,k,t)q flash code C is a coding scheme for st…
We derive closed-form expressions for the achievable rates of a buffer-aided full-duplex (FD) multiple-input multiple-output (MIMO) Gaussian relay channel. The FD relay still suffers from residual self-interference (RSI) after the application of self-interference mitigation techniques. We investigate both cases of a slow-RSI channel where the RSI is fixed over the entire codeword, and a fast-RSI channel where the RSI changes from one symbol duration to another within the codeword. We show that the RSI can be completely eliminated in the slow-RSI case when the FD relay is equipped with a buffer…
Understanding the real achievable performance of mobile ad hoc networks (MANETs) under practical network constraints is of great importance for their applications in future highly heterogeneous wireless network environments. This paper explores, for the first time, the performance modeling for MANETs under a general limited buffer constraint, where each network node maintains a limited source buffer of size $B_s$ to store its locally generated packets and also a limited shared relay buffer of size $B_r$ to store relay packets for other nodes. Based on the Queuing theory and birth-death chain t…
We consider distributed Luby transform (DLT) codes for efficient packet transmission in a multi-way relay network, where the links are modeled as erasure channels. Density evolution is applied for asymptotic performance analysis, and subsequently used in a linear-programming design framework for optimizing the degree distribution at the relay in terms of overhead. Moreover a buffer is introduced at the relay to enable efficient downlink transmission even if packets are lost during uplink transmission. Performance losses in terms of delay and/or erasure rates caused by link erasures during upli…
Fast-decodable distributed space-time codes are constructed by adapting the iterative code construction introduced in [1] to the N -relay multiple-input multiple-output channel, leading to the first fast-decodable distributed space-time codes for more than one antenna per user. Explicit constructions are provided alongside with a performance comparison to non-iterated (non-) fast-decodable codes.
This paper presents a new erasure code called Treeplication designed for distributed recovery of the full information word, while most prior work in coding for distributed storage only supports distributed repair of individual symbols. A Treeplication code for $k$ information symbols is defined on a binary tree with $2k-1$ vertices, along with a distribution for selecting code symbols from the tree layers. We analyze and optimize the code under a random-multiset model, which captures the system property that the nodes available for recovery are drawn randomly from the nodes storing the code sy…
When multiple sources of data need to transmit their rateless coded symbols through a single relay to a common destination, a distributed rateless code instead of several separate conventional rateless codes can be employed to encode the input symbols to increase the transmission efficiency and flexibility. In this paper, we propose distributed rateless codes DU-rateless that can provide unequal error protection (UEP) for distributed sources with different data block lengths and different importance levels. We analyze our proposed DU-rateless code employing And-Or tree analysis technique. Next…
We consider the problem of secure distributed matrix multiplication (SDMM) in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We construct polynomial codes for SDMM by studying a combinatorial problem on a special type of addition table, which we call the degree table. The codes are based on arithmetic progressions, and are thus named GASP (Gap Additive Secure Polynomial) Codes. GASP Codes are shown to outperform all previously known polynomial codes for secure distributed matrix multiplication in terms of download rate.
Distributed storage systems based on equidistant constant dimension codes are presented. These equidistant codes are based on the Plücker embedding, which is essential in the repair and the reconstruction algorithms. These systems posses several useful properties such as high failure resilience, minimum bandwidth, low storage, simple algebraic repair and reconstruction algorithms, good locality, and compatibility with small fields.
We propose two coding schemes for distributed matrix multiplication in the presence of stragglers. These coding schemes are adaptations of LT codes and Raptor codes to distributed matrix multiplication and are termed \emph{factored LT (FLT) codes} and \emph{factored Raptor (FR) codes}. Empirically, we show that FLT codes have near-optimal recovery thresholds when the number of worker nodes is very large, and that FR codes have excellent recovery thresholds while the number of worker nodes is moderately large. FLT and FR codes have better recovery thresholds when compared to Product codes and t…
In this paper, we study the throughput utility functions in buffer-equipped monostatic backscatter communication networks with multi-antenna Readers. In the considered model, the backscatter nodes (BNs) store the data in their buffers before transmission to the Reader. We investigate three utility functions, namely, the sum, the proportional and the common throughput. We design online admission policies, corresponding to each utility function, to determine how much data can be admitted in the buffers. Moreover, we propose an online data link control policy for jointly controlling the transmit …
We study the exact-repair tradeoff between storage and repair bandwidth in distributed storage systems (DSS). We give new inner bounds for the tradeoff region and provide code constructions that achieve these bounds.
Distributed source coding schemes are typically based on the use of channels codes as source codes. In this paper we propose a new paradigm, termed "distributed arithmetic coding", which exploits the fact that arithmetic codes are good source as well as channel codes. In particular, we propose a distributed binary arithmetic coder for Slepian-Wolf coding with decoder side information, along with a soft joint decoder. The proposed scheme provides several advantages over existing Slepian-Wolf coders, especially its good performance at small block lengths, and the ability to incorporate arbitrary…
We propose an information-theoretic private information retrieval (PIR) scheme for distributed storage systems where data is stored using a linear systematic code of rate $R > 1/2$. The proposed scheme generalizes the PIR scheme for data stored using maximum distance separable codes recently proposed by Tajeddine and El Rouayheb for the scenario of a single spy node. We further propose an algorithm to optimize the communication price of privacy (cPoP) using the structure of the underlying linear code. As an example, we apply the proposed algorithm to several distributed storage codes, showing …
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a source code that is optimal in the sense of minimizing expected codeword length. For some applications, however, a source code should instead minimize one of a family of nonlinear objective functions, $β$-exponential means, those of the form $\log_a \sum_i p(i) a^{n(i)}$, where $n(i)$ is the length of the $i$th codeword and $a$ is a positive constant. Applic…
In this paper, we investigate network nest coded modulation schemes for multiple access relay channels. The performance of the distributed systems which are based on distributed convolutional codes with network coded modulation is presented. An analytical upper bound on bit error probability performance for the studied distributed systems with Maximum Likelihood Sequence Detection (MLSD) is derived. The constructured bounds for the investigated systems are shown to be asymptotically tight for increasing channel Signal-to-Noise Ratio (SNR) values
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed nodes. The goal is to reduce the average execution time of the computational job. We provide a connection between the problem of characterizing the average execution time of a coded distributed computing system and the problem of analyzing the error probability of codes of length $n$ used over erasure channels. Accordingly, we present closed-form expressions for…
Self-Repairing Codes (SRC) are codes designed to suit the need of coding for distributed networked storage: they not only allow stored data to be recovered even in the presence of node failures, they also provide a repair mechanism where as little as two live nodes can be contacted to regenerate the data of a failed node. In this paper, we propose a new instance of self-repairing codes, based on constructions of spreads coming from projective geometry. We study some of their properties to demonstrate the suitability of these codes for distributed networked storage.
Regenerating codes are a class of codes for distributed storage networks that provide reliability and availability of data, and also perform efficient node repair. Another important aspect of a distributed storage network is its security. In this paper, we consider a threat model where an eavesdropper may gain access to the data stored in a subset of the storage nodes, and possibly also, to the data downloaded during repair of some nodes. We provide explicit constructions of regenerating codes that achieve information-theoretic secrecy capacity in this setting.
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during the data-reconstruction and node-repair operations. We provide explicit regenerating codes that are resilient to errors and erasures, and show that these codes are optimal with respect to storage and bandwidth requirements. As a special case, we also establish the capacity of a class of distributed storage systems in the presence of malicious adversaries. W…
