Fault-Tolerant Streaming with FEC through Capillary Multi-Path Routing

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1 Fault-Tolerant Streaming with FEC through Caillary Multi-Path Routing Emin Gabrielyan Switzernet Sàrl and Swiss Federal Institute of Technology (EPFL) Lausanne, Switzerland Abstract Erasure resilient FEC codes in off-line acketized streaming rely on time diversity, which in its turn relies on unrestricted buffering time at the receiver. In real-time streaming the layback buffering time must be very short. Path diversity is an orthogonal strategy, but its drawback is that large number of long aths increases the number of underlying links and consecutively the overall link failure rate. It may result in increase of the overall requirement in redundant FEC ackets combating the link failures. We introduce Redundancy Overall Requirement (ROR), a routing coefficient of the total number of FEC ackets required for comensation of all underlying link failures. We resent caillary routing algorithm constructing layer by layer steadily diversifying multi-ath routing atterns. By measuring ROR coefficients of a dozen of routing layers on hundreds of network samles, we show that the number of required FEC ackets decreases substantially when the ath diversity is achieved by caillary routing algorithm. I. INTRODUCTION Erasure resilient FEC codes achieve high reliability in off-line streaming in most challenging network conditions [], [], [], [], []. Off-line streaming can significantly benefit from FEC due to the fact that in contrary to real-time streaming, the receiver is not obliged to deliver in time the fresh ackets to the user. Since long buffering is not a concern, ackets reresenting the same information can be received at different times. In real-time single-ath streaming, when buffering time is restricted, FEC can only mitigate short granular failures [], [7], [8] and [9]. Packets reresenting the same information cannot be collected at very remote eriods of time. Recent ublications show the alicability of FEC in real-time streaming with ath diversity. Author of [0] shows that strong FEC imroves video communication following two disjoint aths and that in two correlated aths weak FEC is still advantageous. [] rooses adative multi-ath routing for Mobile Ad-Hoc Networks (MANET) addressing the load balance and caacity issues, but mentioning also the ossible advantages for FEC. Authors of [] and [] suggests relacing in MANET the link level Automatic Reeat Query (ARQ) by a link level FEC assuming regenerating nodes. Authors of [] and [] studied video streaming from multile servers. The same author [] later studied real-time streaming over two aths using a static Reed-Solomon RS(0,) code (FEC blocks carrying source ackets and 7 redundant ackets). [], similarly to [0] comared two-ath scenarios with the single OSPF routing strategy and has shown clear advantages of the double ath routing. The ath diversity in all these studies is limited to either two (ossibly correlated) aths or in the most general case to a sequence of arallel and serial links. Various routing toologies, so far, were not regarded as a ground for searching a FEC efficient attern. In this aer we try to resent a comarative study for various multi-ath routing atterns. Single ath routing, being considered as too hostile, is excluded from our comarisons. Steadily diversifying routing atters are built layer by layer with caillary routing algorithm (sections II). In order to comare multi-ath routing atterns, we introduce Redundancy Overall Requirement (ROR), a routing coefficient relying on the sender s transmission rate increases in resonse to individual link failures. By default, the sender is streaming the media with a static amount of FEC codes in order to tolerate a certain weak acket loss rate. The acket loss rate is measured at the receiver and is constantly reorted back to the sender with the oosite flow. The sender increases the FEC overhead whenever the acket loss rate is about to exceed the tolerable limit. This end-to-end adative FEC mechanism is imlemented entirely on the end nodes, at the alication level, and is not aware of the underlying routing scheme [7], [8], [], [7] and [8]. The overall number of transmitted adative redundant ackets for rotecting the communication session against link failures is roortional () to the usual acket transmission rate of the sender, () to the duration of the communication, () to the single link failure rate, () to the single link failure duration and () to the ROR coefficient of the underlying routing attern followed by the communication flow. The novelty brought by ROR is that a routing toology of any comlexity can be rated by a single scalar value (section III). In section IV, we resent ROR coefficients of different routing layers built by caillary routing algorithm. Network 97

2 samles are obtained from a random walk MANET with several hundreds of nodes. We show that ath diversity achieved by caillary routing algorithm reduces substantially the amount of FEC codes required from the sender. II. CAPILLARY ROUTING Caillary routing may be imlemented by an iterative Linear Programming (LP) rocess transforming a singleath flow into a caillary route. First minimize the maximal value of the load of all links by minimizing an uer bound value alied to all links. The full mass of the flow will be slit equally across the ossible arallel routes. Find the bottleneck links of the first layer (see below) and fix their load at the found minimum. Minimize similarly the maximal load of all remaining links without the bottleneck links of the first layer. This second iteration further refines the ath diversity. Find the bottleneck links of the second layer. Minimize the maximal load of all remaining links, now without the bottlenecks of also the second layer. Reeat this iteration until the entire communication footrint is enclosed in the bottlenecks of the constructed layers. Fig., Fig. and Fig. show the first three layers of the caillary routing on a small network. The to node on the diagrams is the sender, the bottom node is the receiver and all links are oriented from to to bottom. Fig.. In the first layer the flow is equally slit across two aths, two links of which, marked by thick dashes, are the Fig.. The second layer minimizes to / the maximal load of the remaining seven links and identifies three Fig.. The third layer minimizes to / the maximal load of the remaining four links and identifies two Fig. shows the 0-th layer of caillary routing between a air of end nodes on a network with 0 nodes and links. Links not carrying traffic are not shown. The solid lines of the diagram reresent the bottleneck links belonging to one of the 0 layers. The dashed lines reresent a mincost solution of the remaining flow not enclosed in bottlenecks after the 0-th layer. There could be several tens of additional routing layers until comlete caillarization is achieved. links: nodes: 0 layers: 0 bottlenecks: 8 remaining: 97 : : : : : 0.7 : : : 0.7 9: 0.9 0: 0. Fig.. Routing attern of layer 0 built by caillary routing algorithm on a network samle with 0 nodes At each layer, after minimizing the maximal load of links, the bottlenecks of the layer are discovered in a bottleneck hunting loo. At each iteration of the hunting loo, we minimize the load of the traffic over all links having maximal load and being susected as Links not maintaining their load at the maximum are removed from the susect list. The bottleneck hunting loo stos if there are no more links to remove. For caillary routing layers, built simultaneously on 00 indeendent network samles each with 00 nodes (in average,.7 links er network), Fig. shows the decrease of the number of susected links during the bottleneck hunting loo of each caillary routing layer from to 0. average number of susected links layer layer layer layer layer layer layer7 layer8 layer9 layer0 Iterations of the hunting loo (from to ) for the layers of the caillary routing (from to 0) Fig.. Decrease of the number of susected links during the bottleneck hunting loo of each of 0 caillary routing layers At the end of each hunting loo (from to iterations) the susect list consists of only true bottleneck links, in average between.9 and 9.9 bottlenecks er network. 98

3 III. REDUNDANCY OVERALL REQUIREMENT (ROR) We assume a combination of the little static tolerance of the media stream, combating weak failures, with a dynamically added adative FEC combating the strong failures exceeding the tolerable acket loss rate. For a given routing attern, ROR is defined as the sum of all transmission rate overheads required from the sender for combating corresondingly all non-simultaneous link failures. For examle, if the communication footrint consists of five links, and in resonse to each individual link failure the sender increases the acket transmission rate by %, then ROR will be equal to the sum of these five FEC transmission rate increases, i.e. ROR = % =.. If P is the usual acket transmission rate and P l is the increased rate of the sender, resonding to the failure of a link l L, where L is the set of all links, then: Pl ROR = () P Let us consider a long communication, and let D be the total failure time of a single network link during the whole duration of the communication. D is the roduct of the average duration of a single link failure, the frequency of a single link failure and the total communication time. According to equation (): Pl D P ROR = D P () P = ( D Pl D P) () Assuming a single link failure at a time and a uniform robability and duration of link failures, according to equation (), D P ROR is the number of adative redundant ackets that the sender actually needs to transmit in order to comensate for all network failures occurring during the total communication time. Therefore ROR is a routing coefficient of the overall number of required redundant ackets. Redundant ackets are injected into the original media stream for every block of M source ackets. During streaming, M is suosed to stay constant. However, the number of redundant ackets for each block of M media ackets is variable, deending on the conditions of the erasure channel. The M source ackets with their related redundant ackets form a FEC block. By FEC we denote the FEC block size chosen by the sender in resonse to a acket loss rate. We assume that by default the media is streamed in FEC blocks of length of FEC such that the t flow has a static tolerance to weak losses 0 t <. When the loss rate measured at the receiver is about to exceed the tolerable limit t, the sender increases its transmission rate by injecting additional redundant ackets. The random acket loss rate, observed at the receiver during the failure time of a link in the communication ath, is the ortion of the traffic being still routed toward the faulty link. Thus a comlete failure of a link l carrying according to the routing attern a relative traffic load of 0 r ( roduces at the receiver a acket loss rate equal to the same relative traffic load r (. Equation () for ROR can thus be re-written as follows: FECr ( ROR = () t r( < FECt a sum over all links carrying a flow exceeding the tolerable loss limit The links carrying the entire traffic are skied in the sum index of equation (), since the FEC required for the comensation of failures of such links is infinite. By construction (sections II) none of the considered multi-ath routing schemes will ass its entire traffic through a noncritical single link. We comute the FEC function assuming a Maximum Distance Searable (MDS) code [9], [0]. With MDS code we can successfully decode the M source ackets if we receive any M ackets of the transmission FEC block. In order to collect a mean of M ackets at the receiver under random loss rate, M /( ) ackets must be transmitted at the sender. However the robability of receiving M ackets or M ackets (which makes the decoding imossible) remains high. In order to maintain a very low robability δ of receiving less than M ackets, we must send much more redundant ackets in the block than is necessary to receive an average of M ackets at the receiver side. We must fix the accetable Decoding Error Rate (DER), such that δ DER, in order to comute the FEC M function. The robability of having exactly n losses (erasures) in a block of N ackets with a random loss robability is comuted according to the binomial distribution: N n N n q, where N N! = and q = n n n! ( N n)! The robability of having N M + or more losses, i.e. the decoding failure robability, is comuted as follows: N N n N n δ = q () n= N M + n Therefore for comuting the carrier block s minimal length for a satisfactory communication (i.e. FEC function), it is sufficient to steadily increase the block length N until the desired decoding error rate (DER) is met. FEC functions divided by M (i.e. transmission rate increase factors FEC / M ) are bounded above by log ( DER) when M = and below by /( ) when 99

4 M (for acket loss rates much larger a very small DER). The larger the number of media ackets M in the FEC block, the smaller the cost of FEC overhead is, but the longer the buffering time at the receiver must be. For examle VOIP with 0 ms samling rate restricts the number of media ackets M in a single FEC block to 0 ackets. If the layback buffering time can be a coule of minutes long, with thousands of source ackets in a FEC block (for examle in acketized TV) we can assume that FEC = M /( ). Although for large numbers of source ackets MDS codes do not exist, other caacity aroaching LDPC [] or fountain codes [] can decode a large block of source ackets requiring only a very little excess of ackets (in this context this excess can be ignored). In such case the overall amount of FEC codes required from the sender as a function of the choice of the multi-ath routing attern, can be evaluated by an ROR coefficient according to the following equation, derived from equation () taking into account the above assumtions: t ROR = () t r( < r( Path diversity can be required in off-line large file downloads aiming at avoiding the idle times of the last kilometer bottleneck occurring due to arbitrary failures elsewhere, within the lossy Internet. Thanks to the sender s adative transmission rate and to multi-ath routing, one may feed the last kilometer bottleneck link constantly at its maximal bandwidth (see [] and [] for video streaming from multile servers). In this case also the choice of the multi-ath routing attern can be rated by equation (). Note that according to equations () and () the ROR coefficient of a routing attern deends also on the static tolerance t of the streaming media to weak failures. IV. FEC REQUIREMENT IN CAPILLARY ROUTING For caillary routing layers to 0, we comute the average ROR coefficients simultaneously over several networks. The network samles are drawn from timeframes of a random walk MANET. Initially the nodes are randomly distributed on a rectangular area, and then, at every timeframe, they move according to a random walk algorithm. If two nodes are close enough (and are within the coverage range) then there is a link between them. At the same time we consider also streaming media at different intensities of static FEC codes tolerating corresondingly weak acket loss rates from.% to (with an increment of 0.%). Fig., reresents a MANET with nodes and 00 timeframes divided into seven sets of network samles. For each set of samles and for each static FEC intensity we lot the average ROR coefficient (over all considered network samles) as the routing layer increases. Fig.. shows that the overall requirement in FEC codes decreases with caillarization. The ROR coefficients of the routing samles are comuted assuming a short layback buffering time according to equation (), where the FEC block size (as function of the acket loss rate ) is comuted according to equation (), the number of media ackets (M) er transmission block is 0 and the desired decoding failure rate (DER) is 0. Average ROR layers: Caillary routing layers from to 0 for each set of samles weak static tolerance:.%.9%.%.8%.0%.% 7.% Fig.. Average ROR as a function from the caillary routing layer Fig. 7 reresents a MANET with 0 nodes and 0 timeframes divided into four sets of network samles. The uer curves similarly to the curves of Fig. are comuted according to equations () and (), where M = 0 and DER = 0. However, the lower curves of Fig. 7 are comuted according to equation () for streaming with large FEC blocks. Average ROR %.9%.%.%.8%.%.0%.% 7.% %.%.% %.9%.%.%.8%.%.0%.% 7.% Caillary routing layers from to 0 for each set of samles Fig. 7. Average ROR comuted assuming real-time streaming (the grou of curves above) and off-line streaming (the grou below) When streaming with large blocks the Redundancy Overall Requirement is twice as low as in streaming with restricted layback buffering time, but the caillarization of routing is beneficiary in both cases. 00

5 Logically, the ROR curve of the media stream is shifted down as the statically added tolerance increases, but the increase of the weak static tolerance yields also a stronger efficiency gain achieved by caillarization. The drawback of ath diversity in general is that by forming long aths we may unjustifiably increase the number of links in the communication footrint raising the overall failure rate and thus ossibly increasing the overall requirement in FEC codes. Fig. and Fig. 7 however show that desite the communication footrint becomes larger; with the routing atters built by caillary routing algorithm the requirement in redundant ackets decreases noticeably most of the time. V. CONCLUSION The resiliency and reliability issues of acketized realtime streaming are of growing imortance. Commercial real-time streaming alications however do not consider channel coding as a serious solution for imroving the reliability of communication. That is because in single ath communications, even heavy FEC overheads cannot rotect against failures lasting more than the short duration of the layback buffer. Recent studies demonstrated that ath diversity makes FEC alicable for real-time streaming. By studying a wide range of routing toologies, we show that combination of channel coding with aroriate multi-ath routing allows reliable real-time streaming with a low overall requirement in FEC codes. For this urose we introduce a layer by layer strategy for building multi-ath caillary routing atterns. The first layer rovides a simle multi-ath solution. As the layer number increases, the underlying routing attern relies on the network more securely. Unlike max-flow or shortest ath solutions, for a given source and destination, by construction (section II) there exists only one solution of caillary routing. We introduce ROR, a method for rating multi-ath routing atterns by a single scalar value. The ROR rating corresonds to the total redundancy overhead that the sending node must rovide in order to combat the losses occurring from non-simultaneous failures of links in the communication ath. Desite the fact that sreading out of the routing results in the increase of the overall failure rate of underlying links and consecutively maybe also of the need in adative FEC codes; with caillarization the overall requirement in FEC codes in fact decreases substantially. Caillary routing can be alicable to multi-ho mobile wireless networks, where wireless content can be streamed to and from the user via multile base stations; or to the ublic internet, where, if the hysical routing cannot be accessed, an overlay network can be used []. We hoe that our investigation will rovide some guidelines for future design of ath diversity-based real-time streaming systems. REFERENCES [] David J. C. 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