Batched Sparse Codes Research Articles

Weighted BATS Codes with LDPC Precoding

Batched Sparse (BATS) codes are a type of network coding scheme that use a combination of random linear network coding (RLNC) and fountain coding to enhance the reliability and efficiency of data transmission. In order to achieve unequal error protection for different data, researchers have proposed unequal error protection BATS (UEP-BATS) codes. However, current UEP-BATS codes suffer from high error floors in their decoding performance, which restricts their practical applications. To address this issue, we propose a novel UEP-BATS code scheme that employs a precoding stage prior to the weighted BATS code. The proposed precoding stage utilizes a partially regular low-density parity-check (PR-LDPC) code, which helps to mitigate the high error floors in the weighted BATS code We derive the asymptotic performance of the proposed scheme based on density evolution (DE). Additionally, we propose a searching algorithm to optimize precoding degree distribution within the complexity range of the precoding stage. Simulation results show that compared to the conventional weighted BATS codes, our proposed scheme offers superior UEP performance and lower error floor, which verifies the effectiveness of our scheme.

Design of Improved Expanding-Window BATS Codes

Batched sparse (BATS) coding is a promising new technique designed for reliable transmissions over erasure networks, which can achieve asymptotic bandwidth optimality. However, the decoder of the conventional BATS codes begins to recover the source packets only after receiving a sufficient number of encoded packets which induces delay. Moreover, the larger the source block size is, the longer the time delay will be. In this paper, we propose a scheme by using expanding window applied over BATS codes, termed the expanding-window BATS codes, which divide the source data into smaller blocks for reducing delay. Furthermore, for improving the decoding performance we design an adaptive encoder which encodes the source packets with dynamic encoding probabilities. Because the performance of BATS codes highly depends on the degree distribution, we further optimize the degree distributions for the proposed expanding-window BATS codes with linear programming and the performances have been verified by the simulation results.

Wireless Communication Strategy with BATS Codes for Butterfly Network

In this paper, two transmission schemes for batched sparse(BATS) codes based on a multicast protocol in a butterfly network are studied. For both of the schemes, a source file is first segmented into several packets at the source node, which are then coded with outer coder of the BATS codes to generate potentially unlimited batches. Rather than the linear network, in which the packets are directly transmitted to the next node, the packets will be forwarded to multiple nodes in the butterfly network. All the intermediate nodes which receive the packets recode them with random linear network coding (RLNC). At the destination node receivers, the sink node decodes the packets transmitted from different links. The Scheme I requires the intermediate nodes to recode the packets until all of them are received. On the contrary, the intermidate nodes of Scheme II just recode the packets as soon as receiving them and forward the recoded packets to the next node immediately. The Belief Propagation(BP) decoders of these two schemes are studied and applied to Scheme I and Scheme II respectively. The simulation results show that Scheme I consumed fewer batches than Scheme II, which indicates Scheme I outperforms Scheme II.

Utility Maximization for Multihop Wireless Networks Employing BATS Codes

BATS (BATched Sparse) codes are a class of efficient random linear network coding variation that has been studied for multihop wireless networks mostly in scenarios of a single communication flow. Towards sophisticated multi-flow network communications, we formulate a network utility maximization (NUM) problem that jointly optimizes the BATS code parameters of all the flows and network scheduling. The NUM problem adopts a batch-wise packet loss model that can be obtained from the network local statistics without any constraints on packet loss patterns. Moreover, the NUM problem allows a different number of recoded packets to be transmitted for different batches in a flow, which is called adaptive recoding. Due to both the probably nonconcave objective and the BATS code-related variables, the algorithms developed for the existing flow optimization problems cannot be applied directly to solve our NUM problem. We introduce a two-step algorithm to solve our NUM problem, where the first step solves the problem with nonadaptive recoding schemes, and the second step optimizes adaptive recoding hop-by-hop from upstream to downstream in each flow. We perform various numerical evaluations and simulations to verify the effectiveness and efficiency of the algorithm.

A Protocol Design Paradigm for Batched Sparse Codes.

Internet of Things (IoT) connects billions of everyday objects to the Internet. The mobility of devices can be facilitated by means of employing multiple wireless links. However, packet loss is a common phenomenon in wireless communications, where the traditional forwarding strategy undergoes severe performance issues in a multi-hop wireless network. One solution is to apply batched sparse (BATS) codes. A fundamental difference from the traditional strategy is that BATS codes require the intermediate network nodes to perform recoding, which generates recoded packets by network coding operations. Literature showed that advanced recoding schemes and burst packet loss can enhance and diminish the performance of BATS codes respectively. However, the existing protocols for BATS codes cannot handle both of them at the same time. In this paper, we propose a paradigm of protocol design for BATS codes. Our design can be applied in different layers of the network stack and it is compatible to the existing network infrastructures. The modular nature of the protocol can support different recoding techniques and different ways to handle burst packet loss. We also give some examples to demonstrate how to use the protocol.

Optimised design and tree analysis of regularised variable‐node BATS codes

In this Letter, the authors investigate a modified encoding scheme of batched sparse (BATS) codes to improve the erasure floor performance. In the proposed regularised variable-node (RBATS) codes, variable-node degrees are regularised to maximise the minimum degree for transmission. The asymptotical decoding performance of RBATS codes is analysed by a tree-based analysis. Furthermore, they optimise check-node degree distribution of RBATS codes to decrease decoding overhead according to the decoding condition. It is demonstrated through simulation results that the optimised RBATS codes can not only lower the transmission overhead but also improve erasure floor performance compared with traditional BATS codes.

Joint BATS Code and Periodic Scheduling in Multihop Wireless Networks

Batched sparse (BATS) code is a promising technology for reliable data transmission in error-prone environments. A BATS code consists of an outer code and an inner code. It has been shown that a well-designed inner code is critical to the performance of BATS. Though great efforts have been made in the design of inner codes, the impact of scheduling (that determines when inner codes take place at nodes in the path) on inner codes is still unclear. In this paper, we study the joint design of inner code and scheduling in multihop wireless networks. We first introduce a new network utility from which to associate inner codes with scheduling, and formulate the coding constraint and the scheduling constraint using independent sets of a graph. With the utility, the joint design problem is then transformed to a network utility maximization problem under the constraints. We next exploit the property of the proposed optimization problem and reveal the relation between the expected batch transfer matrix rank and maximal independent sets. In the light of their relationship, we propose joint coding and scheduling rules and show that a periodic scheduling can be used to achieve provable performance guarantees. However, under most realistic coding settings, the proposed coding and scheduling problem is NP-hard. In order to meet the practical needs of the implementation, we develop greedy algorithms that attempt to iteratively improve the current best solution. Numerical results show that our algorithms enables us to approach the utilization of multi-hop wireless networks with a relatively low end-to-end delay.

Design of Optimized Sliding-Window BATS Codes

Batched sparse (BATS) codes are a low-complexity random linear network coding scheme that can achieve asymptotic bandwidth optimality. The destination node of BATS codes starts to decode the information packets only after receiving a sufficient number of coded packets which induces delay. Furthermore, the larger the size of source block is, the longer the delay is. In this letter, we propose a scheme by using sliding windows applied over BATS codes, named sliding-window BATS codes, which divides the information data into smaller blocks so as to reduce delay. Moreover, for improving the performance, we optimize the degree distributions with linear programming, and its performance is verified by computer simulations.

Practical Inner Codes for BATS Codes in Multi-Hop Wireless Networks

Batched sparse (BATS) codes are a promising technique for reliable data transmission in multihop wireless networks. A BATS code consists of an outer code and an inner code, the design of which can be separated. In this paper, we investigate the design of the inner code and focus on maximizing the expected batch transfer matrix rank normalized by the total number of packets transmitted by both the source and intermediate nodes. By allowing different recoding decisions at different nodes, the problem is formulated as a nonlinear integer programming (NLIP) problem, which is non-deterministic polynomial (NP)-hard in general. We derive a noniterative formula to simplify the evaluation of the expected batch transfer matrix rank. By considering large finite fields and relaxing the integer constraints, we obtain an upper bound on the optimal value of the original maximization NLIP problem. We also derive a centralized and a decentralized algorithm to find suboptimal solutions of the NLIP problem, with different tradeoffs between complexity and performance. Numerical results show that our proposed inner codes outperform the standard BATS, and achieve very close to the upper bound, which verifies the near optimality of our algorithms.

Efficient Coastal Communications with Sparse Network Coding

The demand for wideband communication in the coastal area (i.e., ≤ 100 km from the coastline) has been rapidly increasing in recent years. Compared to the terrestrial scenario, the coastal environment has long-distance and highly dynamic channels, and the communication devices are more strictly constrained by energy supplies. While the RLNC has the fountain erasure-correction property and is suitable for transmissions over the long-distance dynamic channels, it suffers from high coding coefficient delivery cost and decoding complexity. In this article, we look into the application of sparse network coding in coastal communication systems. We identify two typical multicast scenarios that may appear in coastal communications, namely the relay-aided multicast and multicast from a shore-based base station with D2D communication enabled among the subscribers. We provide a detailed comparison of existing sparse network coding schemes. Based on that, we demonstrate through simulations that an appropriate choice of sparse codes is critical to meet the unique requirements in coastal communication systems. We show that batched sparse code is suitable for relay-aided multicast, and subset-based sparse codes are preferable for D2D-enabled multicast.

Expanding-Window BATS Code for Scalable Video Multicasting Over Erasure Networks

In this paper we consider scalable video multicasting over erasure networks with heterogeneous video quality requirements. With random linear network coding (RLNC) applied at the intermediate nodes the information received by the destinations is determined by the associated channel rank distributions based on which we obtain the optimal achievable code rate at the source node. We show that although a concatenation of priority encoded transmission (PET) with RLNC achieves the optimal code rate it incurs prohibitive high coding complexity. On the other hand batched sparse (BATS) code has been recently proposed for unicast networks which has low coding complexity with near-optimal overhead. However the existing BATS code design cannot be applied for multicast networks with heterogeneous channel rank distributions at different destinations. To this end we propose a novel expanding window BATS (EW-BATS) code where the input symbols are grouped into overlapped windows according to their importance levels. The more important symbols are encoded with lower rate and hence they can be decoded by more destinations while the less important symbols are encoded with higher rate and are only decoded by the destinations with high throughput for video quality enhancement. Based on asymptotical performance analysis we formulate the linear optimization problems to jointly optimize the degree distributions for each window and the window selection probabilities. Simulation results show that the proposed EW-BATS code satisfies the decoding requirements with much lower transmission overhead compared with separate BATS code where the degree distributions are separately optimized for each destination.

V2X Content Distribution Based on Batched Network Coding With Distributed Scheduling

Content distribution is an application in intelligent transportation system to assist vehicles in acquiring information such as digital maps and entertainment materials. In this paper, we consider content distribution from a single roadside infrastructure unit to a group of vehicles passing by it. To combat the short connection time and the lossy channel quality, the downloaded contents need to be further shared among vehicles after the initial broadcasting phase. To this end, we propose a joint infrastructure-to-vehicle (I2V) and vehicle-to-vehicle (V2V) communication scheme based on batched sparse (BATS) coding to minimize the traffic overhead and reduce the total transmission delay. In the I2V phase, the roadside unit (RSU) encodes the original large-size file into a number of batches in a rateless manner, each containing a fixed number of coded packets, and sequentially broadcasts them during the I2V connection time. In the V2V phase, vehicles perform the network coded cooperative sharing by re-encoding the received packets. We propose a utility-based distributed algorithm to efficiently schedule the V2V cooperative transmissions, hence reducing the transmission delay. A closed-form expression for the expected rank distribution of the proposed content distribution scheme is derived, which is used to design the optimal BATS code. The performance of the proposed content distribution scheme is evaluated by extensive simulations that consider multi-lane road and realistic vehicular traffic settings, and shown to significantly outperform the existing content distribution protocols.

Fast degree-distribution optimization for BATS codes

Batched sparse (BATS) codes have been proposed for communication through networks with packet loss. BATS codes include a matrix generalization of fountain codes as the outer code and random linear network coding at the intermediate network nodes as the inner code. BATS codes, however, do not possess a universal degree distribution that achieves an optimal rate for any distribution of the transfer matrix ranks. Therefore, it is important to have a fast degree-distribution optimization approach for finite-length BATS codes. In this paper, we propose the concept of batch release probability (BRP), and demonstrate some characteristics of BRPs from the degree distributions achieving nearly optimal performance. Based on these BRP characteristics, we propose a novel degree-distribution optimization approach that achieves the similar decoding performance with a much shorter optimization time, compared with the previous approach. Moreover, the universality of BRPs observed in this paper can further simplify the degree-distribution optimization of BATS codes.

Quasi-Universal BATS Code

Batched sparse (BATS) code is a class of temporal network code that achieves near-optimal tradeoff between network throughput and coding length for multi-hop erasure networks. However, the performance of the traditional BATS code degrades dramatically when the designed degree distribution does not match the actual channel condition. In this paper, we first prove that a universal degree distribution that asymptotically achieves the optimal rate for all channel rank distributions does not exist for BATS code with batch size greater than one. We then propose a quasi-universal BATS (QU-BATS) code that achieves near-optimalperformance for a range of channel conditions. This makes it suitable for use in scenarios where the end-to-end channel rank distribution is not fixed or not exactly known, e.g., in multicast or wireless transmission. In the proposed QU-BATS coding scheme, multiple degree distributions are designed, and the coded packets are generated according to different degree distributions at different transmission stages. Simulation results show that the proposed QU-BATS code strictly outperforms the fountain code and the traditional BATS codes for multihop data streaming over uncertain or time-varying network links, with lower decoding complexity.

A Polynomial Formula for Finite-Length BATS Code Performance

Batched sparse (BATS) codes have been proposed for communication through networks with packet loss. BATS codes include a matrix generalization of fountain codes as the outer code and random linear network coding at the intermediate network nodes as the inner code. BATS codes, however, do not possess a universal degree distribution that achieves the optimal rate for any distribution of the transfer matrix ranks, so that fast performance evaluation of finite-length BATS codes is important for optimizing the degree distribution. The state-of-the-art finite-length performance evaluation method has a computational complexity of $\mathcal {O}(K^{2}n^{2}M)$ , where $K$ , $n$ , and $M$ are the number of input symbols, the number of batches, and the batch size, respectively. We propose a polynomial-form formula for finite-length BATS codes performance evaluation with the computational complexity of $\mathcal {O}(K^{2}n\ln n)$ . Numerical results demonstrate that the polynomial-form formula can be significantly faster than the previous methods.

Two-Phase Cooperative Broadcasting Based on Batched Network Code

In this paper, we consider the wireless broadcasting scenario with a source node sending some common information to a group of closely located users, where each link is subject to certain packet erasures. To ensure reliable information reception by all users, the conventional approach generally requires repeated transmission by the source until all the users are able to decode the information, which is inefficient in many practical scenarios. In this paper, by exploiting the close proximity among the users, we propose a novel two-phase wireless broadcasting protocol with user cooperations based on an efficient batched network code, known as batched sparse (BATS) code. In the first phase, the information packets are encoded into batches with BATS encoder and sequentially broadcasted by the source node until certain terminating criterion is met. In the second phase, the users cooperate with each other by exchanging the network-coded information via peer-to-peer (P2P) communications based on their respective received packets. A fully distributed and light-weight scheduling algorithm is proposed to improve the efficiency of the P2P communication in the second phase. The performance of the proposed two-phase protocol is analyzed and the channel rank distribution at the instance of decoding is derived, based on which the optimal BATS code is designed. Simulation results show that the proposed protocol outperforms most existing cooperative packet exchange schemes, especially when the inter-user links are not reliable. Lastly, the performance of the proposed scheme is further verified via testbed experiments.