网络编码基础与无线网络应用

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“网络编码应用（英文版）——基础与趋势” 这篇资源是关于网络编码技术的应用介绍，主要面向初学者，由Christina Fragouli和Emina Soljanin撰写，发表在2007年的"Foundations and Trends in Networking"期刊上。文章深入浅出地探讨了网络编码在无线网络和内容分发网络中的应用，并展望了这一技术在新兴领域如网络监控和管理中的潜力。同时，它也涵盖了多播、安全性、不可靠链路网络以及量子网络等方面。网络编码是一种21世纪初提出的创新技术，旨在提升网络的吞吐量和性能，被认为是未来网络的关键技术之一。在无线网络中，网络编码能够优化数据传输效率，尤其是在多跳网络中，通过在中间节点进行编码操作，可以减少重复数据传输，提高网络资源利用率。在内容分发网络中，网络编码可以加速内容的传播，减少延迟，同时增强系统的容错能力。此外，文中还讨论了网络编码在新兴应用中的角色，比如网络监控和管理。通过网络编码，可以更有效地跟踪网络状态，及时发现并解决问题，提高网络的稳定性和可靠性。在多播场景下，网络编码可以解决传统广播中可能出现的包丢失或冲突问题，确保所有接收者都能接收到完整的信息。对于网络安全，网络编码提供了新的思路。它可以用于构建抗干扰和抗攻击的通信系统，因为编码过程可以增加信息的复杂性，使得破解变得更加困难。在网络中存在不可靠链路的情况下，网络编码能够通过错误纠正码来提高数据传输的鲁棒性。最后，作者还触及了量子网络这一前沿领域。在量子通信中，网络编码可能有助于提高量子信息的传输效率，增强量子保密通信的安全性，这在量子计算和量子互联网的发展中具有重要意义。这篇文章是理解网络编码如何在不同网络环境中发挥作用的宝贵资源，不仅涵盖了基础应用，还展望了未来可能的技术发展趋势。对于想要进入这个领域的初学者，它提供了一个全面且易懂的入门指南。

150 Decentralized Network Operation

Notes

The coupon collectors problem is one of the most popular topics in

discrete probability, and its description can be found in many stan-

dard textbooks on probability (e.g., [21, Ch. 9]) or algorithms (e.g.,

[61, Ch. 3]). The observation that network coding oﬀers beneﬁts for

this problem was originally made by Deb et al. [12]. Information dis-

semination using network coding was studied by Mosk-Aoyamam and

Shah [60]. Results for network coding performance over random graphs

were investigated for example by Ramamoorthy et al. [66].

152 Content Distribution

of the content to other nodes by acting themselves as servers. Thus the

network is inherently scalable: the nodes that join the network bring in

not only new demands but also additional computing power and band-

width. Moreover, there no longer exists a single point of failure (server

crashing) in the system, as the information is distributed among mul-

tiple nodes throughout the network.

Having thus addressed the problem of ensuring suﬃcient network

resources, P2P networks still face the challenge of how to optimally

use these resources in a decentralized and low complexity manner. For

example, optimal information routing is a diﬃcult problem in such

large scale networks that change very fast over time (with thousands

of nodes joining and leaving within a short span of time) and where,

moreover, nodes only have local information about the network.

BitTorrent is an example of a P2P system that uses swarming tech-

niques to simultaneously disseminate diﬀerent fragments of a ﬁle among

peers. Acquiring a ﬁle by collecting its fragments can be to a certain

extent modeled by the classic coupon collector problem, which indi-

cates some problems such systems may have. For example, probabil-

ity of acquiring a novel fragment drops rapidly with the number of

those already collected. In addition, as the number of peers increases,

it becomes harder to do optimal scheduling of distributing fragments

to receivers. One possible solution is to use a heuristic that prioritizes

exchanges of locally rarest fragments. But, such fragments often fail to

match those that are globally rarest. The consequences include, among

others, slower downloads and stalled transfers.

The Microsoft Secure Content Distribution (MSCD), also known

as Avalanche, is an example of a P2P system attempting to alleviate

such problems using network coding. Instead of distributing the origi-

nal ﬁle fragments, peers produce linear combinations of the fragments

they already hold. Such combinations are distributed together with a

tag that describes the coeﬃcients in the combination. When a peer has

enough linearly independent combinations of the original fragments,

it can decode and build the original ﬁle. Many of the advantages of

Avalanche over BitTorrent can be understood from our previous discus-

sion on collecting numbers as coupons vs. collecting numbers through

their linear combinations.

154 Content Distribution

Which of its blocks a peer transfers is decided based for example on

one of the following common content propagation strategies:

•

a random block in the beginning of the distribution, and

•

a local rarest after a few blocks have been downloaded, or

•

a global rarest in small P2P networks.

3.2 Microsoft Secure Content Distribution

Microsoft Secure Content Distribution (MSCD), that used to be called

Avalanche, follows BitTorrent to a large extent. It follows, for example,

the same basic principles for topology management. Here, however,

randomized network coding is employed for content distribution, as is

described in the following.

3.2.1 Content Propagation

The source splits the ﬁle to be distributed into N blocks (1000–2000 in

experiments). These blocks are grouped into generations (segments),

where each generation contains h blocks. Only packets in the same

generation are allowed to be linearly combined. Each packet is assumed

to consist of symbols over a ﬁnite ﬁeld F

. This simply means that,

for q =2

, a packet of length L bits is considered to contain L/m

symbols over F

, where sets of m bits are treated as one symbol over

. Typically, L is 1400 × 8 bits, and m is 8 or 16. Note that linear

combining occurs symbol wise: each symbol in a packet is multiplied by

the same number in F

prior to adding to other (multiplied) packets.

The source transmits linear combinations of the original h ﬁle pack-

ets in a generation, while peers recursively and uniformly at random

combine their collected packets and create new coded packets that they

propagate through the network. Thus each coded packet carries a lin-

ear combination of the original ﬁle packets. This linear combination is

described by the (global) coding vector of size h symbols over F

, that

speciﬁes which linear combination each coded packet carries. The gen-

eration tag and the coding vector are appended in the packet header.

For generation size h, the overhead caused by coding is h/L. For a

generation of size 50, the typical overhead is 50/1400 ≈ 3%.

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