email: {rasorey,javier}@det.uvigo.es ... In recent years, multimedia delivery services have evolved ... Periodic broadcast protocols split files into n segments.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
A Multicast nVoD Schema with Zero-Overhead Implicit Error Correction R. Asorey-Cacheda and F.J. Gonz´alez-Casta˜no Departamento de Enxe˜ner´ıa Telem´atica, Universidade de Vigo, Spain ETSE Telecomunicaci´on, Campus, 36310 Vigo, Spain, phone: (+34) 986 814 081, fax: (+34) 986 812 116, email: {rasorey,javier}@det.uvigo.es Abstract—In this paper we present a novel multicast nearVideo on Demand (nVoD) schema which relies on the intrinsic redundancy of nVoD protocols to provide implicit error correction, by employing content segments as blocks for coding operations. The results in this paper show that our proposal outperforms previous approaches involving explicit error correction (error protection within content segments) in terms of transmission bandwidth for the same packet loss probability. Index Terms—nVoD, Digital Fountains, Erasure Codes
I. I NTRODUCTION In recent years, multimedia delivery services have evolved thanks to a range of factors including the emergence of broadband networks and enhanced user terminal capabilities. Many unresolved problems still exist, however. This paper addresses the problem of on-demand media delivery to large user communities across lossy networks, such as heterogeneous networks that do not offer quality of service guarantees. Ideally, digital fountain coding [1] allows data delivery across lossy networks such as satellite, terrestrial wireless networks and the Internet. Digital fountains are an ideal paradigm, however, which is why erasure codes [2] are used instead. Erasure codes generate packet streams that allow a original content to be reconstructed from any coded sequence with as many packets as the original content plus a reasonable overhead. This means that clients can access the multicast stream at any time, and keep listening until enough information is received to reconstruct the content. This method is scalable because bandwidth is independent of the number of clients and coding overhead is low. Also, there is no need for return channels. Reproduction delay (the time-to-availability of the first segments), however, may be excessively long. (User devices also require large memories to store unplayed content segments, but this issue is becoming irrelevant with current hardware costs). Protocols also exist for scalable on-demand media streaming. Examples include periodic broadcast protocols [3], patching protocols [4], and bandwidth skimming protocols [5], [6]. Initially, these protocols, which multicast different content segments simultaneously, did not address the issue of packet error recovery. Clients had to receive multiple streams at a time, although aggregate transmission rates were proportional to real-time content playing rate. Even when high bandwidths are available, network congestion could cause packet errors.
For this reason, protocols may, in certain cases, be valid in terms of multicast bandwidth availability, yet unfeasible if they do not admit a non-zero loss probability. The authors are only aware of one nVoD study [7] dealing with the problem of error protection: specifically it proposed encoding content segments independently for error recovery. In this scenario, given a block loss probability, it would be possible to estimate the transmission overheads and therefore ensure that the client would reconstruct the content. The approach, therefore, requires more bandwidth than uncoded schemas, and it may be unfeasible for high error probabilities. We have called this approach explicit error correction. In this paper, we propose a novel multicast nVoD schema that combines segments of the original content without any overhead by taking advantage of the intrinsic redundancy of nVoD protocols. Basically, previously downloaded segments allow recovering from future errors. We have called our approach implicit error correction. The paper is organized as follows: the rest of this section discusses the background of our research. Section II describes the concept of implicit error correction. Section III presents some preliminary analytical results, and Section IV concludes the paper. We will now describe the background of our research in greater detail. We will look at periodic broadcast and bandwidth skimming protocols, as well as explicit error correction (we have chosen to ignore patching protocols due to their poorer performance). Periodic broadcast protocols split files into n segments (s1 , s2 , . . . , sn ) to be multicast through independent channels (c1 , c2 , . . . , cL ) at fixed rates (r1 , r2 , . . . , rL ). The variants differ in terms of segment size, order and transmission rates and the schemas ignore the distribution of request arrivals. Uplink channels are unnecessary. A representative example is the skyscraper protocol [8], in which clients listen to a maximum of two channels at a time. Each channel carries a different segment, and segment lengths follow a known progression (1, 2, 2, 5, 5, 12, 12, 25, 25,...). Assuming that two channels are received simultaneously, the content can be played without interruption. Harmonic broadcasting algorithms [9] also belong to this class of protocols. They assign different retransmission fre-
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
quencies to segments of a fixed length in different channels1 . In order to minimize bandwidth usage, the frequencies must be as low as possible. Figure 1 shows a suboptimal harmonic broadcasting schema (periodic broadcasting schema with a fixed number of channels per time slot and a single segment size). The rows and columns represent multicast channels and time slots, respectively. Segment s1 has frequency 1, segment s3 has frequency 1/2, and segment s6 has frequency 1/4. This schema requires a suboptimal, albeit constant, bandwidth (this obviously may be advantageous in terms of teletraffic management). We can generalize it to L channels as follows: • A segment si is transmitted through a channel m (m ∈ {1, . . . , L}) such that 2m−1 ≤ i < 2m . This implies that 1 + log2 n ≥ L > log2 n. • Given the first condition, the maximum number of segments in channel m is 2m − 2m−1 = 2m−1 . The retransmission of a segment in channel m has a period of 2m−1 slots. A regular schema satisfies T (si ) ≤ i (T (): period). This holds in our case, since T (si ) = 2m−1 ≤ i. Bandwidth skimming protocols minimize bandwidth based on request arrivals. Each time a new demand arrives, these protocols initiate a multicast transmission in a new channel to deliver the information that the user has not yet received. To determine the missing information, the clients listen to a subset of previous channels (in the simplest case they listen to just one channel). Bandwidth demand increases logarithmically with the rate of client requests. Although these protocols perform better than patching protocols, they only outperform periodic broadcast at low client request rates. Obviously, they require a return channel, which is unavailable in certain scenarios (e.g. satellite networks). nVoD with erasure codes: The nVoD protocol in [7] employs erasure coding within each content segment to improve robustness. Given a packet loss probability p, and a source division of every segment into k blocks, it is necessary to transmit α = k/(1 − p) blocks per original segment to recover it (i.e. bandwidth increases by 1/(1 − p)). We refer to this model as explicit error correction. Encoded segments may grow considerably for high admissible packet loss probabilities. II. IMPLICIT ERROR CORRECTION Let us introduce a basic notation. Content S is composed by segments, S = {s1 , s2 , . . . , sn }, si ∩sj = ∅, {i, j} = 1, . . . , n. The encoded segment si , . . . sj m,t for channel m and time slot t (card({si , . . . , sj }) = l(t) ≤ L ≤ n) results from the following operation on the original segments {si , . . . , sj } ∈ S: m,t si . . . sj m,t = cm,t si · si ⊕ . . . ⊕ csj · sj ,
(1)
m,t {cm,t si . . . csj } ∈ {0, 1}
Channel 1 Channel 2 Channel 3
t s1 s2 s4
t+1 t+2 t+3 t+4 t+5 t+6 t+7 s1 s1 s1 s1 s1 s1 s1 . . . s3 s2 s3 s2 s3 s2 s3 . . . s5 s6 s7 s4 s5 s6 s7 . . .
Fig. 1. Example of a suboptimal harmonic broadcasting schema (constant number of channels per time slot and a single segment size).
t+2 t+3 t+1 t Channel 1 s1 , s2 , s4 1,t s1 , s3 , s5 1,t+1 s1 , s2 , s6 1,t+2 s1 , s3 , s7 1,t+3 . . . Channel 2 s1 , s2 , s4 2,t s1 , s3 , s5 2,t+1 s1 , s2 , s6 2,t+2 s1 , s3 , s7 2,t+3 . . . Channel 3 s1 , s2 , s4 3,t s1 , s3 , s5 3,t+1 s1 , s2 , s6 3,t+2 s1 , s3 , s7 3,t+3 . . . Fig. 2.
The same schema in figure 1 with implicit error correction.
segment size), we chose harmonic broadcasting as the base schema to optimize latency and bandwidth [9]. Basic schema (harmonic broadcasting): In principle, there is no loss recovery. If a segment si is lost, users must wait for it for up to i time slots (an average of (i + 1)/2 time slots). The minimum bandwidth Bn to transmit a content S with n segments is: n
Bn = r · (1 +
r 1 1 + ... + ) = , 2 n k
(2)
k=1
where r is the rate of the content. For the suboptimal schemas in Figures 1 and 2, the required bandwidth Bn to transmit a video file is: Bn = r · log2 (n + 1), Bn ≥ Bn
(3)
Encoded harmonic broadcasting schema: This is a trivial evolution of the previous schema to provide error protection. The original segments are replaced by independently encoded ones. Assuming ideal decoding efficiency2 , this solution splits each original segment into k blocks and sends k/(1−p) blocks per segment every time slot, where p is the cumulative packet loss probability. Thus, a loss probability p is admissible, but the bandwidth must grow by a factor 1/(1 − p). Expression (2) becomes Bn =
n k=1
r . (1 − p) · k
(4)
If p is too high, the extra bandwidth may be unaffordable. Again, for the examples of Figures 1 and 2, expression (3) becomes Bn =
r · log2 (n + 1), Bn ≥ Bn 1−p
(5)
Although our proposal is independent of the underlying periodic broadcasting schema (insofar as it employs a single
Harmonic broadcasting with implicit error correction: Once the client obtains an original segment, it may correct errors in other slots. Multicast channels do not transmit
1 Segment frequency sets a deadline for segment retransmission. For example, a segment with a frequency of 1/2 at a given slot must be retransmitted within the next two slots.
2 Decoding efficiency is the ratio of the number of packets that must be received to reconstruct a segment to the number of packets in the segment. Ideal decoding efficiency is 1.0.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
c1,t si c2,t si Ct = . .. l(t),t csi
··· ··· .. . ···
··· ··· .. . ···
c1,t sj 2,t csj .. , l(t) ≤ L . l(t),t csj
Estimation of maximum admissible loss probability when s1 has been downloaded 1 0.9 0.8 0.7 0.6 pn,1
either original or independently encoded segments. Instead, the schema combines original segments as macro-blocks to produce encoded segments si . . . sj m,t with zero overhead3 . This solution requires extra memory at the client side, but this is an inexpensive resource nowadays and, depending on the target p, it is possible to limit the number of downloaded segments to be temporally stored. This solution cannot recover packets beyond a certain packet loss probability p, but that probability increases whenever the client obtains a new segment. Let C t be a binary matrix whose components are:
0.5 0.4 0.3 0.2 0.1 0
(6)
In order to recover all the segments in time slot t, the rank of C t must equal the number of original segments that are transmitted in the slot. This paper does not address the generation of sequence C t , although in section III we will suppose that it provides maximum decoding efficiency. Figure 2 shows the implicit error correction schema that corresponds to the structure in figure 1.
20
40
60 Number of segments (n)
80
100
120
Fig. 3. Maximum admissible pn,1 as a function of the number of original segments. Estimation of maximum admissible loss probability, n=120 1 0.9 0.8 0.7 0.6 pn,b
III. A NALYTICAL E VALUATION A. Implicit error correction
0.5 0.4
Let us assume an optimum schema. From (2), at every time ¯ n original segments: slot the system transmits an average of L ¯ n = 1 · Bn = 1 + 1 + · · · + 1 = L r 2 n
n k=1
1 k
(7)
0.2 0.1 0 0
¯ n original segments to Therefore, we need at least n · L completely reconstruct the original content. We shall now consider packet loss recovery. Let us assume that cumulative packet loss probability upon reception of an original segment never exceeds p. Consider the schema in figure 2. In general, if we assume that the first segment s1 is available, the packet loss probability pn,1 for full correction must satisfy ¯ n ≤ 1 ⇒ pn,1 ≤ 1 = 1 pn,1 · L n ¯n L 1 k
0.3
(8)
k=1
(a single segment is available so far). Figure 3 shows how the maximum admissible pn,1 (bound given by 8) decreases with the number of original segments. Note that, if a single original segment is available, it is possible to recover up to 18.62% packet losses for n = 120. It is also possible to obtain maximum admissible error rates as downloading progresses. Expression (8) can be extended for the case when b − 1 original segments are available: 3 Hereafter, we will talk about original segments, encoded segments or simply segments depending on the context.
20
40
60
80
100
120
Downloaded segments (b)
Fig. 4. Maximum admissible pn,b as new original segments become available, for n = 120.
¯n ≤ pn,b · L
b−1 1 k
b−1 ¯ b−1 L 1 ⇒ pn,b ≤ k=1 = ¯ . n 1 k Ln k=1 k
(9)
k=1
Figure 4 shows that the maximum admissible pn,b (bound given by 9) increases as new original segments become available. With 1/6 of the original segments, the client may recover from packet losses up to 66%. By the end of the download the curve converges to 1 as expected. B. Implicit vs. explicit error correction In contrast to our approach, explicit error correction, adds overhead to each segment si . It is important to stress that, compared to non-error correction approaches, both implicit and explicit error correction perform similarly in terms of
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
Estimation of maximum average admissible loss probability
Bandwidth increase factor of explicit error correction compared with implicit error correction 5.5
0.8
5
0.7
4.5 Bandwidth increase factor
0.9
0.6
¯
pn
0.5 0.4 0.3
4 3.5 3 2.5 2
0.2
1.5
0.1
1 0
0 0
20
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60 Number of segments (n)
80
100
120
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
¯
pn
Fig. 5. Maximum average admissible packet loss probability p¯n as a function of the number of original segments.
Fig. 6. Bandwidth increase required for explicit error correction to achieve the same performance as implicit error correction.
average waiting times. For full recovery in explicit error correction, at least 1/(1 − p) times the information in the original segments must be transmitted. When the content starts playing (i.e. when the first segment becomes available), to correct the same proportion of errors as with implicit error ¯ n · (1/1 − pn,1 ) original segments per slot need correction, L ¯ n − 1) (pn,1 given by 8). ¯ 2n /(L to be transmitted, i.e. up to L Next we shall consider expression (9). By averaging it, we obtain:
R EFERENCES
p¯n ≤
n ¯ 1 L 1 b−1 · lim p¯n = 1 ¯n = 1 − L ¯ n , n→∞ n L b=1
(10)
Figure 5 shows the maximum average admissible packet loss probability for full correction as a function of the number of content segments. It converges asymptotically to 1 as the number of original segments increases. To recover from the same packet losses with explicit error correction, the number ¯n · 1 , of original segments per time slot would have to be L 1−p¯n ¯ 2n . i.e. up to L Figure 6 shows the relative increase in bandwidth required for explicit error correction to achieve the same performance as with implicit error correction. As the number of segments increases, the burden of explicit error correction is considerable. IV. C ONCLUSIONS We have presented a new approach to multicast nVoD. Our main contribution is the concept of implicit error correction, whereby previously downloaded content segments prevent the loss of future packets. Our approach outperforms explicit error correction as our schema has zero bandwidth overhead, for the same waiting times as for explicit error correction. ACKNOWLEDGMENTS This work has been supported by grant TEC2007-67966C03-02 (Spanish Ministry of Education and Science).
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