Batched Sparse Codes

Network coding can significantly improve the transmission rate of communication networks with packet loss compared with routing. However, using network coding usually incurs high computational and storage costs in the network devices and terminals. For example, some network coding schemes require the computational and/or storage capacities of an intermediate network node to increase linearly with the number of packets for transmission, making such schemes difficult to be implemented in a router-like device that has only constant computational and storage capacities. In this paper, we introduce BATched Sparse code (BATS code), which enables a digital fountain approach to resolve the above issue. BATS code is a coding scheme that consists of an outer code and an inner code. The outer code is a matrix generation of a fountain code. It works with the inner code that comprises random linear coding at the intermediate network nodes. BATS codes preserve such desirable properties of fountain codes as ratelessness and low encoding/decoding complexity. The computational and storage capacities of the intermediate network nodes required for applying BATS codes are independent of the number of packets for transmission. Almost capacity-achieving BATS code schemes are devised for unicast networks, two-way relay networks, tree networks, a class of three-layer networks, and the butterfly network. For general networks, under different optimization criteria, guaranteed decoding rates for the receiving nodes can be obtained.Comment: 51 pages, 12 figures, submitted to IEEE Transactions on Information Theor

Expander Chunked Codes

Chunked codes are efficient random linear network coding (RLNC) schemes with low computational cost, where the input packets are encoded into small chunks (i.e., subsets of the coded packets). During the network transmission, RLNC is performed within each chunk. In this paper, we first introduce a simple transfer matrix model to characterize the transmission of chunks, and derive some basic properties of the model to facilitate the performance analysis. We then focus on the design of overlapped chunked codes, a class of chunked codes whose chunks are non-disjoint subsets of input packets, which are of special interest since they can be encoded with negligible computational cost and in a causal fashion. We propose expander chunked (EC) codes, the first class of overlapped chunked codes that have an analyzable performance,where the construction of the chunks makes use of regular graphs. Numerical and simulation results show that in some practical settings, EC codes can achieve rates within 91 to 97 percent of the optimum and outperform the state-of-the-art overlapped chunked codes significantly.Comment: 26 pages, 3 figures, submitted for journal publicatio

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.Comment: 12 pages and 9 figure

Upper Bound Scalability on Achievable Rates of Batched Codes for Line Networks

The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched codes enable a range of buffer size constraints, and are general enough to include special coding schemes studied in the literature for line networks. Existing works have characterized the achievable rates of batched codes for several classes of parameter sets, but leave the cut-set bound as the best existing general upper bound. In this paper, we provide upper bounds on the achievable rates of batched codes as functions of line network length for these parameter sets. Our upper bounds are tight in order of the network length compared with the existing achievability results.Comment: 6 pages, 1 tabl

Inactivation Decoding of LT and Raptor Codes: Analysis and Code Design

In this paper we analyze LT and Raptor codes under inactivation decoding. A first order analysis is introduced, which provides the expected number of inactivations for an LT code, as a function of the output distribution, the number of input symbols and the decoding overhead. The analysis is then extended to the calculation of the distribution of the number of inactivations. In both cases, random inactivation is assumed. The developed analytical tools are then exploited to design LT and Raptor codes, enabling a tight control on the decoding complexity vs. failure probability trade-off. The accuracy of the approach is confirmed by numerical simulations.Comment: Accepted for publication in IEEE Transactions on Communication