链路丢包模型与多径fec

 [1]针对fec数据包,通过在多路径下的调度,使其最终的丢包率最小,并满足数据到达接收端的时延约束。因为多径传输,路径时延具有差异性,因为数据包丢包的突发性,这个特性可以用来降低丢包率。
 Several has shown the internet packet loss often exhibit burstiness due to internet temporal dependency. This packet loss behavior make it suitable to be modeled by two state Gilbert model.which is a two state stationary continuous time markovian chain X ( t ) X(t) X(t).在 X ( t ) = G X(t)=G X(t)=G状态数据包可以成功发送,但是在 X ( t ) = B X(t)=B X(t)=B状态,则发送失败。

symbol meaning
μ G r \mu_{G}^{r} μGr transition rates from G to B
μ B r \mu_{B}^{r} μBr transition rates from B to G
π G r \pi_{G}^{r} πGr 路径r处于“G”状态
π B r \pi_{B}^{r} πBr 路径r处于“B”状态
FEC(n,k) n,冗余后总的数据包;k,原有数据包,(n-k),冗余包个数

 其中,(i) π B r \pi_{B}^{r} πBr是平均丢包率,(ii) 1 μ B r \frac{1}{\mu_{B}^{r}} μBr1为突发丢包长度。 π G r = μ G r μ G r + μ B r \pi_{G}^{r}=\frac{\mu_{G}^{r}}{\mu_{G}^{r}+\mu_{B}^{r}} πGr=μGr+μBrμGr, π B r = μ B r μ G r + μ B r \pi_{B}^{r}=\frac{\mu_{B}^{r}}{\mu_{G}^{r}+\mu_{B}^{r}} πBr=μGr+μBrμBr
 在采用冗余发送数据包,FEC(n,k),冗余度为n-k。在链路丢失数据包小于冗余度,接收端可以恢复出原有的数据包。在丢失的数据包大于冗余度,接收端的丢包率可以用下式计算。
(2) π B ∗ = 1 k ∑ D ( c ) P ( c ) \pi_{B}^{*}=\frac{1}{k}\sum{D(c)}\mathbb P(c)\tag{2} πB=k1D(c)P(c)(2)
 c为一个序列,表示相应的数据包在发送时刻,路径处于的状态,例如GGGGBBGGG。D©表示fec解码后可恢复的数据包个数。
f ( x ) = { 0   if ∑ i = 1 n 1 c i = B ≤ n − k ∑ i = 1 k 1 c i = B   otherwise f(x)=\left\{ \begin{aligned} & 0 \ \ \text{if} \sum_{i=1}^{n}1_{c_i=B}\leq n-k\\ & \sum_{i=1}^{k}1_{c_i=B} \ \ \text{otherwise}\\ \end{aligned} \right. f(x)=0  ifi=1n1ci=Bnki=1k1ci=B  otherwise
 状态i转移到状态j的概率,可以表示为 p ( i , j ) r ( τ ) = P [ X r ( τ ) = j ∣ X r ( 0 ) = i ] p_{(i,j)}^r(\tau)=\mathbb P[X_{r}(\tau)=j|X_{r}(0)=i] p(i,j)r(τ)=P[Xr(τ)=jXr(0)=i].
 根据markov chain analysis,可得:
KaTeX parse error: No such environment: split at position 7: \begin{̲s̲p̲l̲i̲t̲}̲ p_{G,G}^r(\tau…
 其中: α = e x p ( − ( μ G r + μ B r ) τ ) \alpha=exp(-(\mu_{G}^{r}+\mu_{B}^{r})\tau) α=exp((μGr+μBr)τ)
 本篇文章,就是通过控制发送间隔,使得fec的数据包丢包概率最小。
 理论很好,但是感觉同实际结合不是十分紧密。相似文献[4]。

[1]Exploiting the Path Propagation Time Differences in Multipath Transmission with FEC
[2]SmartTunnel: Achieving Reliability in the Internet
[3]Forward Error Correction for Multipath Media Streaming
[4]Leveraging the Delay-Friendliness of TCP With FEC Coding in Real-Time Video Communication
[5] Adaptive FEC-Based Error Control for Internet Telephony

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