5 research outputs found
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
A Markov chain model for the decoding probability of sparse network coding
Random linear network coding has been shown to offer an efficient communication scheme, leveraging a remarkable robustness against packet losses. However, it suffers from a high-computational complexity, and some novel approaches, which follow the same idea, have been recently proposed. One of such solutions is sparse network coding (SNC), where only few packets are combined with each transmission. The amount of data packets to be combined can be set from a density parameter/distribution, which could be eventually adapted. In this paper, we present a semi-analytical model that captures the performance of SNC on an accurate way. We exploit an absorbing Markov process, where the states are defined by the number of useful packets received by the decoder, i.e., the decoding matrix rank, and the number of non-zero columns at such matrix. The model is validated by the means of a thorough simulation campaign, and the difference between model and simulation is negligible. We also include in the comparison of some more general bounds that have been recently used, showing that their accuracy is rather poor. The proposed model would enable a more precise assessment of the behavior of SNC techniques.This work has been supported by the Spanish Government (Ministerio de Economía y Competitividad, Fondo Europeo de Desarrollo Regional, FEDER) by means of the projects COSAIF, “Connectivity as a Service: Access for the Internet of the Future” (TEC2012-38754-C02-01), and ADVICE (TEC2015-71329-C2-1-R). This work was also financed in part by the TuneSCode project (No. DFF 1335-00125) granted by the Danish Council for Independent Research
On Achievable Rates of Line Networks with Generalized Batched Network Coding
To better understand the wireless network design with a large number of hops,
we investigate a line network formed by general discrete memoryless channels
(DMCs), which may not be identical. Our focus lies on Generalized Batched
Network Coding (GBNC) that encompasses most existing schemes as special cases
and achieves the min-cut upper bounds as the parameters batch size and inner
block length tend to infinity. The inner blocklength of GBNC provides upper
bounds on the required latency and buffer size at intermediate network nodes.
By employing a bottleneck status technique, we derive new upper bounds on the
achievable rates of GBNCs These bounds surpass the min-cut bound for large
network lengths when the inner blocklength and batch size are small. For line
networks of canonical channels, certain upper bounds hold even with relaxed
inner blocklength constraints. Additionally, we employ a channel reduction
technique to generalize the existing achievability results for line networks
with identical DMCs to networks with non-identical DMCs. For line networks with
packet erasure channels, we make refinement in both the upper bound and the
coding scheme, and showcase their proximity through numerical evaluations.Comment: This paper was presented in part at ISIT 2019 and 2020, and is
accepted by a JSAC special issu