Localized Dimension Growth: A Convolutional Random Network Coding Approach to Managing Memory and Decoding Delay

Abstract

We consider an Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and numerical simulations. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The cardinality of local encoding kernels increases with time until the global encoding kernel matrices at the related sink nodes have full rank. ARCNC adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved. We show that this method performs no worse than block linear network codes in terms of decodability, and can provide significant gains in terms of average decoding delay or memory in combination, shuttle and random geometric networks.

Adaptive Causal Network Coding With Feedback

“…Using FEC, in order delivery delay over packet erasure channels can be reduced [13], and the performance of SR-ARQ protocols can be boosted [3]. Delay bounds for convolutional codes have been provided in [4], [17]. Packet dropping to reduce the playback delay of streaming over an erasure channel has been investigated in [5], [6], [18].…”

“…Such low delays cannot be achieved using very large blocklengths; therefore the classical approaches do not provide the desired throughput-delay tradeoffs. To alleviate the problem of large in order delivery delays, different forward error correction (FEC) techniques for packet-level coding have been contemplated [1]- [4]. We discuss their benefits and shortcomings in this section.…”

Network-Coding Solutions for Minimal Combination Networks and Their Sub-Networks

“…One of the most celebrated families of networks is the family of combination networks [24], which has been used for various topics in network coding, e.g., [13], [14], [20], [22], [27]. The N h,r,s combination network, where s h, is shown in Fig.…”

Concatenation of convolutional codes and rank metric codes for multi-shot network coding

“…For a more general theoretical approach to rank metric convolutional codes see [19]. Finally we note that in the last years others papers have also appeared dealing with convolutional network coding using very different approaches [9,24]. These codes do not transmit over the operator channel and therefore are not equipped with the rank metric.…”