arXiv subjects

Ka Hei Ng

Publications and source records attributed to Ka Hei Ng.

5 recordsLinked to original sources

arXiv2021

Intrablock Interleaving for Batched Network Coding with Blockwise Adaptive Recoding

Batched network coding (BNC) is a low-complexity solution to network transmission in multi-hop packet networks with packet loss. BNC encodes the source data into batches of packets. As a network coding scheme, the intermediate nodes perform recoding on the received packets belonging to the same batch instead of just forwarding them. A recoding scheme that may generate more recoded packets for batches of a higher rank is also called adaptive recoding. Meanwhile, in order to combat burst packet loss, the transmission of a block of batches can be interleaved. Stream interleaving studied in literature achieves the maximum separation among any two consecutive packets of a batch, but permutes packets across blocks and hence cannot bound the buffer size and the latency. To resolve the issue of stream interleaver, we design an intrablock interleaver for adaptive recoding that can preserve the advantages of using a block interleaver when the number of recoded packets is the same for all batches. We use potential energy in classical mechanics to measure the performance of an interleaver, and propose an algorithm to optimize the interleaver with this performance measure. Our problem formulation and algorithm for intrablock interleaving are also of independent interest.

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arXiv2021

A Unified Adaptive Recoding Framework for Batched Network Coding

Batched network coding is a variation of random linear network coding which has low computational and storage costs. In order to adapt to random fluctuations in the number of erasures in individual batches, it is not optimal to recode and transmit the same number of packets for all batches. Different distributed optimization models, which are called adaptive recoding schemes, were formulated for this purpose. The key component of these optimization problems is the expected value of the rank distribution of a batch at the next network node, which is also known as the expected rank. In this paper, we put forth a unified adaptive recoding framework with an arbitrary recoding field size. We show that the expected rank functions are concave when the packet loss pattern is a stationary stochastic process, which covers but not limited to independent packet loss and Gilbert-Elliott packet loss model. Under this concavity assumption, we show that there always exists a solution which not only can minimize the randomness on the number of recoded packets but also can tolerate rank distribution errors due to inaccurate measurements or limited precision of the machine. We provide an algorithm to obtain such an optimal optimal solution, and propose tuning schemes that can turn any feasible solution into a desired optimal solution.

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arXiv2021

BAR: Blockwise Adaptive Recoding for Batched Network Coding

Multi-hop networks become popular network topologies in various emerging Internet of things applications. Batched network coding (BNC) is a solution to reliable communications in such networks with packet loss. By grouping packets into small batches and restricting recoding to the packets belonging to the same batch, BNC has a much smaller computational and storage requirements at the intermediate nodes compared with a direct application of random linear network coding. In this paper, we propose a practical recoding scheme called blockwise adaptive recoding (BAR) which learns the latest channel knowledge from short observations so that BAR can adapt to the fluctuation of channel conditions. We focus on investigating practical concerns such as the design of efficient BAR algorithms. We also design and investigate feedback schemes for BAR under imperfect feedback systems. Our numerical evaluations show that BAR has significant throughput gain for small batch size compared with the existing baseline recoding scheme. More importantly, this gain is insensitive to inaccurate channel knowledge. This encouraging result suggests that BAR is suitable to be realized in practice as the exact channel model and its parameters could be unknown and subject to change from time to time.

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arXiv2021

On Multi-Channel Huffman Codes for Asymmetric-Alphabet Channels

Zero-error single-channel source coding has been studied extensively over the past decades. Its natural multi-channel generalization is however not well investigated. While the special case with multiple symmetric-alphabet channels was studied a decade ago, codes in such setting have no advantage over single-channel codes in data compression, making them worthless in most applications. With essentially no development since the last decade, in this paper, we break the stalemate by showing that it is possible to beat single-channel source codes in terms of compression assuming asymmetric-alphabet channels. We present the multi-channel analog of several classical results in single-channel source coding, such as that a multi-channel Huffman code is an optimal tree-decodable code. We also show some evidences that finding an efficient construction of multi-channel Huffman codes may be hard. Nevertheless, we propose a suboptimal code construction whose redundancy is guaranteed to be no larger than that of an optimal single-channel source code.

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arXiv2019

Decision Procedure for the Existence of Two-Channel Prefix-Free Codes

The Kraft inequality gives a necessary and sufficient condition for the existence of a single channel prefix-free code. However, the multichannel Kraft inequality does not imply the existence of a multichannel prefix-free code in general. It is natural to ask whatever there exists an efficient decision procedure for the existence of multichannel prefix-free codes. In this paper, we tackle the two-channel case of the above problem by relating it to a constrained rectangle packing problem. Although a general rectangle packing problem is NP-complete, the extra imposed constraints allow us to propose an algorithm which can solve the problem efficiently.

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