WO2010085212A1

WO2010085212A1 - Method and system for linear network coding in broadcast systems

Info

Publication number: WO2010085212A1
Application number: PCT/SG2010/000015
Authority: WO
Inventors: Wai-Leong Yeow; Anh Tuan Hoang; Chen-Khong Tham
Original assignee: Agency For Science, Technology And Research
Priority date: 2009-01-21
Filing date: 2010-01-21
Publication date: 2010-07-29

Abstract

A method and system for linear network coding in a lossy network with link-by-link feedback. The method comprises the steps of buffering incoming packets in a first buffer; moving a batch of packets from the first buffer into a second buffer having a maximum operating size, K?max#191; applying linear coding on the batch of packets in the second buffer; transmitting the coded packets to receivers of the network; flushing the second buffer once all receivers have decoded the batch of packets; and refilling the second buffer with a new batch of packets from the first buffer.

Description

Method and System for Linear Network Coding in Broadcast

Systems

FIELD OF INVENTION

The present invention relates broadly to a method and system for linear network coding in broadcast systems.

BACKGROUND

In a broadcast system based on a lossy network with link-by-link feedback, when one node is required to transmit the same data to multiple other nodes, it has been shown that the use of network coding can increase system capacity [1 ,2]. In network coding, or simply coding hereinafter, the transmitting (broadcasting) node forms linear combinations of one or more packets and broadcast the combinations to the receiving nodes. This is to differentiate from the conventional scheduling operation, when each individual data packet is broadcasted until being successfully received by all the receivers.

While the throughput/capacity gain of network coding in broadcast scenarios is well agreed upon, its effect in terms of queueing and transmission delay varies greatly depending on specific scenarios. For example, in [3], it has been shown that network coding reduces packet transmission delay when the system is symmetric, i.e., all receiving users see the same statistical erasure channel. However, in asymmetric systems, where some users experience a much worse erasure channel than others, it can be shown that network coding can seriously increase delay experienced by users with worse channels.

Existing approaches in employing network coding for broadcast transmission can be classified into two categories, i.e. those assuming that data packets arrive in batches of fixed size, and those assuming that data packets arrive in a stochastic manner.

For the first category, as packets arrive in batches of fixed sizes, it is natural to carry out network coding on all arriving packets. As an example, in [3], it is assumed that each time, a file consisting of K packets arrive to the transmitter buffer. The transmitter then carries out network coding over the K packets.

For the second category, as packets arrive in a stochastic manner, the number of packets available for transmission (and coding) varies over time. The control decisions then are how many packet should be coded and in what manner. In [4], a scheme is proposed to ensure that, in each successful reception, every receiving node gets some new information. This guarantees that the capacity of broadcast communication with network coding is achieved.

There are two shortcomings of the approach in [3]. First, it cannot be efficiently applied to scenarios in which individual packets arrive in stochastic manner. This is because in that case, the transmitter may not have enough packets to code at a fixed size. Second, for asymmetric systems in which some users have much worse channels than the rest, the delay of these users will be large.

The shortcoming of the approach in [4] is that, for asymmetric systems in which some receiving users have much worse channels than the rest, the delay of these users can grow unbounded. This is because, when receiving users with good channel conditions finish their reception, new packets will be added to the coding process and this increases the decoding time of the worse-off users.

A need therefore exists to provide a method and system for linear network coding that seeks to address at least one of the above problems.

SUMMARY

In accordance with a first aspect of the present invention there is provided a method of linear network coding in a lossy network with link-by-link feedback, the method comprising the steps of buffering incoming packets in a first buffer; moving a batch of packets from the first buffer into a second buffer having a maximum operating size, K_max; applying linear coding on the batch of packets in the second buffer; transmitting the coded packets to receivers of the network; flushing the second buffer once all receivers have decoded the batch of packets; and refilling the second buffer with a new batch of packets from the first buffer.

The method may further comprise dynamically adjusting K_max based on respective occupancies of the first and second buffers.

K_max may be adjusted based on respective averages of the occupancies of the first and second buffer.

The respective averages may comprise one of a group consisting of a mean over a period of time, a running average, a moving average over a sliding time window; and a weighted moving average.

Applying the linear coding may comprise applying a selection algorithm based on combinations of the packets in the second buffer.

The selection algorithm may comprise sorting the combinations according to priority.

The priority may be based on a current delay of the packets in each combination and a number of packets that can be decoded if each combination is received.

The method may further comprise, when all but one of the receivers have decoded all packets in the batch, transmitting remaining packets without coding in a highest priority first order to said one of the receivers.

The method may further comprise controlling in which time slots feedback from the receivers is to be provided to the.transmitter.

Said controlling may comprise determining, after feedback from the receivers has been received in one time slot, the number of packets, K_u, that have not been decoded by all receivers, and instructing the receivers to only sent feedback after the next K_u time slots.

In accordance with a second aspect of the present invention there is provided a system for linear network coding in a lossy network with link-by-link feedback, the system comprising a first buffer for buffering incoming packets; means for moving a batch of packets from the first buffer into a second buffer having a maximum operating size, K_max; means for applying linear coding on the batch of packets in the second buffer; means for transmitting the coded packets to receivers of the network; means for flushing the second buffer once all receivers have decoded the batch of packets; and means for refilling the second buffer with a new batch of packets from the first buffer.

The system may further comprise means for dynamically adjusting K_max based on respective occupancies of the first and second buffers.

The means for applying the linear coding may apply a selection algorithm based on combinations of the packets in the second buffer.

When all but one of the receivers have decoded all packets in the batch, the means for transmitting may transmit remaining packets without coding in a highest priority first order to said one of the receivers. The system may further comprise means for controlling in which time slots feedback from the receivers is to be provided to the transmitter.

Said means for controlling may determine, after feedback from the receivers has been received in one time slot, the number of packets, K_u, that have not been decoded by all receivers, may instruct the receivers to only sent feedback after the next K₀ time slots.

In accordance with a third aspect of the present invention there is provided a data storage medium having computer code means for instructing a computing device to execute a method of linear network coding in a lossy network with link-by-link feedback, the method comprising the steps of buffering incoming packets in a first buffer; moving a batch of packets from the first buffer into a second buffer having a maximum operating size, K_max\ applying linear coding on the batch of packets in the second buffer; transmitting the coded packets to receivers of the network; flushing the second buffer once all receivers have decoded the batch of packets; and refilling the second buffer with a new batch of packets from the first buffer.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will be better understood and readily apparent to one of ordinary skill in the art from the following written description, by way of example only, and in conjunction with the drawings, in which:

Figure 1 shows a schematic drawing illustrating a buffering architecture at a broadcast station/transmitter of a broadcast network according to an example embodiment. Figure 2 shows a flowchart illustrating the buffering operation of the transmitter according to an example embodiment.

Figure 3 shows a flowchart illustrating updating the size of the coding buffer by the transmitter, according to an example embodiment. Figure 4 shows a flowchart illustrating calculating the feedback interval by the transmitter or a receiver, according to an example embodiment.

Figure 5 shows a flowchart illustrating the decoding operation by the receiver according to an example embodiment. Figure 6 shows a graph of comparative data for delay performance against network load.

Figure 7 shows another graph of comparative data for delay performance against arrival rate.

Figure 8 shows another graph of comparative data for delay performance against network load.

Figure 9 shows a graph of percentage gain in average delay per packet for 2 nodes, with a channel 1 node fixed at 0.2 and the other varied.

Figure 10 shows a graph of percentage gain in average delay per packet for 2 nodes, with the channel of one node fixed at 0.4 and the other varied. Figure 11 shows a graph illustrating a comparison between a static maximum number of packets in the coding buffer and a dynamic maximum number of packets in the coding buffer.

Figure 12 shows another graph illustrating a comparison between a static maximum number of packets in the coding buffer and an optimal number of packets in the coding buffer.

Figure 13 shows a flow chart illustrating a method of linear network coding according to an example embodiment.

Figure 14 shows a schematic diagram illustrating a computer system fir implementing a method and system according to an example embodiment.

DETAILED DESCRIPTION

Embodiments of the present invention introduce a queueing mechanism that helps reduce delay when network coding is used in broadcast scenarios. In one embodiment the mechanism includes of: i) a method of organizing packets at the transmitter into queueing and coding buffers in tandem to restrict the number of packets being processed each time ii) an efficient algorithm that determines which packets should be coded/scheduled for each transmission/broadcast and iii) an iterative procedure to determine the optimal parameter for (i). The mechanisms in example embodiments are generally referred to as Dynamic Queueing Dynamic Coding (DQDC) in this description.

Dynamic Queueing Dynamic Coding (DQDC), can achieve the inherent throughput gain of network coding while ensuring the delay performance of all users is also improved. The description focuses on broadcast scenarios, i.e., when one transmitter is required to transmit the same data to one or more receivers.

Some portions of the description which follows are explicitly or implicitly presented in terms of algorithms and functional or symbolic representations of operations on data within a computer memory. These algorithmic descriptions and functional or symbolic representations are the means used by those skilled in the data processing arts to convey most effectively the substance of their work to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of steps leading to a desired result. The steps are those requiring physical manipulations of physical quantities, such as electrical, magnetic or optical signals capable of being stored, transferred, combined, compared, and otherwise manipulated.

Unless specifically stated otherwise, and as apparent from the following, it will be appreciated that throughout the present specification, discussions utilizing terms such as "queueing", "buffering", "calculating", "determining", "replacing", "generating", "initializing", "outputting", or the like, refer to the action and processes of a computer system, or similar electronic device, that manipulates and transforms data represented as physical quantities within the computer system into other data similarly represented as physical quantities within the computer system or other information storage, transmission or display devices.

The present specification also discloses apparatus for performing the operations of the methods. Such apparatus may be specially constructed for the required purposes, or may comprise a general purpose computer or other device selectively activated or reconfigured by a computer program stored in the computer. The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Various general purpose machines may be used with programs in accordance with the teachings herein. Alternatively, the construction of more specialized apparatus to perform the required method steps may be appropriate. The structure of a conventional general purpose computer will appear from the description below.

In addition, the present specification also implicitly discloses a computer program, in that it would be apparent to the person skilled in the art that the individual steps of the method described herein may be put into effect by computer code. The computer program is not intended to be limited to any particular programming language and implementation thereof. It will be appreciated that a variety of programming languages and coding thereof may be used to implement the teachings of the disclosure contained herein. Moreover, the computer program is not intended to be limited to any particular control flow. There are many other variants of the computer program, which can use different control flows without departing from the spirit or scope of the invention.

Furthermore, one or more of the steps of the computer program may be performed in parallel rather than sequentially. Such a computer program may be stored on any computer readable medium. The computer readable medium may include storage devices such as magnetic or optical disks, memory chips, or other storage devices suitable for interfacing with a general purpose computer. The computer readable medium may also include a hard-wired medium such as exemplified in the Internet system, or wireless medium such as exemplified in the GSM mobile telephone system. The computer program when loaded and executed on such a general-purpose computer effectively results in an apparatus that implements the steps of the preferred method.

The invention may also be implemented as hardware modules. More particular, in the hardware sense, a module is a functional hardware unit designed for use with other components or modules. For example, a module may be implemented using discrete electronic components, or it can form a portion of an^' entire electronic circuit such as an Application Specific Integrated Circuit (ASIC). Numerous other possibilities exist. Those skilled in the art will appreciate that the system can also be implemented as a combination of hardware and software modules.

Fig. 1 shows a schematic diagram illustrating a lossy network 100 with link-by- link feedback, such as a network with packet erasure broadcast channel, embodying a system for linear network coding according to an example embodiment. At the broadcast station 102 (transmitter), two buffers are implemented, namely a queueing buffer 104, and a coding buffer 106. Transmission from the broadcast station 102 occurs simultaneously to a plurality of receivers e.g. 108, 110, 112, experiencing respective packet erasure channel conditions. Incoming packets 114 are buffered in the queueing buffer 104, from which packets are moved to the coding buffer 106, the coding buffer 106 having a maximum operating size K_max. The broadcast station 102 applies linear coding on the packets in the coding buffer only. Once the batch of packets has been decoded by all receivers 108, 110, 112, the coding buffer is flushed, and refilled from the queueing buffer.

The operation of the example embodiment will now be described in more detail with reference to Fig. 2 to Fig. 5.

Fig. 2 shows the operation of the transmitter 102 (Fig. 1) in the example embodiment. The functions carried out by the transmitter are the process include to optimize the coding buffer size (step 200), the ranking of different coding combinations (step 206), and determination of feedback intervals (step 210). Note that the ranking operation (step 206) may also be skipped if there is no feedback information from the receivers. In that case, old ranking of combinations can be reused.

In more detail, the transmitter, after optimizing the coding buffer size at step 200, fills the coding buffer with packets from the queueing buffer to the determined coding buffer size, at step 202. Subsequently, at step 204 the new batch of packets in the coding buffer is processed for coding at step 204, including generating all possible combinations. Next, the ranking of the different coding combinations is performed at step 206, followed by transmission of a linear coding of the highest-ranked combination at step 208. In this example embodiment, the linear coded combination is formed by multiplying random non-zero coefficients to packets of that combination and adding them under Galois Field operations. A header indicating what coefficients are used for each packet is sent along with that transmission. Next, the feedback interval is determined at step 210. At step 212, a determination is made whether feedback is needed / expected to be received for this particular timeslot. If not, the transmitter estimates the system state at step 214. There are a different ways to estimate the system state, including, but not limited to:

(i) PESSIMISTIC - assume none of the receivers has received the last transmission;

(ii) OPTIMISTIC - assume every receiver has received the last transmission; and

(iii) PROBABILISTIC - assume a receiver has received the last transmission if the history of reception is more than 50%.

Ranking at step 206 is then based on this estimated state.

If feedback is being received in this timeslot, the feedback is obtained and the system state updated accordingly in step 216.

In step 218, it is determined whether all receivers have correctly decoded all packets. If not, the process returns to step 206. On the other hand, if yes, the coding buffer is flushed at step 220, and the process reverts to step 200.

Fig. 3 illustrates the algorithms involved in the transmitter updating the optimized size of the coding buffer, in the example embodiment. More particular, at step 300, the maximum coding buffer size K_max is set to an initial value K_mιtιal. Next, at step 302, the number of packets in both the queueing buffer and the coding buffer respectively are measured in T time slots. Different averages may be used, as will be described in more detail below.

In step 304, K_max is updated using an algorithm depending on the averages measured in step 302, again as will be described in more detail below. At step 306, a determination is made whether there is convergence. If there is no convergence the process returns to step 302, whereas if there is convergence, the process stops and the updated value for K_maxis being used.

In the example embodiment, the operating size of the coding buffer K_max determines how efficient channel utilization is, and also how large the delay overhead is due to network coding. When K_max gets smaller, the delay overhead due to network coding lowers and transmission delay decreases. But, the channel may not be efficiently utilized and packets suffer more delay from the increased queueing delay. Conversely, when K_max gets larger, the queueing delay decreases as a result of efficient channel utilization. But, the delay overhead due to network coding rises and packets suffer more delay from the increased transmission delay. Both queueing and transmission delays are non-linear with respect to K_max, and there exists an optimal operating point for K_max where the total delay is minimized.

The optimal K_max depends on channel conditions, packet arrival statistics and the coding/broadcasting mechanism used. Taking all these factors into account, the optimal

K_max in the example embodiment occurs when the average occupancy of the queueing buffer B is equal to that of the coding buffer B_c . The following iterative procedure allows the system to adapt the two buffer sizes and arrive at the optimal values in one embodiment:

1. Start with an arbitrary value (K,_nrtιaι) of K_max.

2. Compute B_q and B_c the average buffer occupancies for both buffers.

3. Update K_max to be a linear combination of both average buffer occupancies used, i.e. [cB_q

where c is some constant in between 0 and 1. 4. Repeat to Step 2.

When K_max is continually updated, the above procedure is also robust in that it can adapt to changes in arrival traffic and channel conditions automatically.

Example measurement procedures of buffer occupancy are listed as below. Note that this list is non-exhaustive.

Simple average - count the total buffer occupancy over a period and compute its mean.

Running average - continually compute the average buffer occupancy. Moving average - compute the average buffer occupancy over a sliding window.

Weighted moving average - buffer occupancy is viewed as a time-series. The mean is computed over a weighted average of the series over a sliding window where the weights are heavier on recent points. Exponential average - buffer occupancy is viewed as a time-series. The mean is computed over a weighted average of the series where the weights decay exponentially over time.

Exponential moving average - a combination of the (3) and (5). There is a sliding window where the average is computed with exponentially decaying weights.

Example formulas for the various K_max updates are listed as below. Note that this list is non-exhaustive.

Simple update - /C_max <- [cB_q

where 0<c<1 is some constant. Weighted update - The last few values of K_max are stored. The new K_max is then a weighted combination of the stored values and [cB_q

Exponential update - K_max <- (i-α)κ_max +α[cB_g

where α is a tunable parameter.

Average update - K_max <- +(i-c)B_c], where n is the iteration

number.

The above estimation and update procedures can either be done periodically at fixed time intervals or on every repeatable event, e.g. clearing of the coding buffer.

Fig. 4 shows that either full feedback or limited feedback modes can be applied.

In full feedback mode, all receivers send back their receiving status after every slot. In limited feedback mode, receivers only report to BS at some predetermined time. This time, called feedback interval, depends on the overall system state. As an example, BS can set the next feedback interval to be equal to the maximum number of packets still not being decoded by the receivers.

In the example illustrated in Fig. 4, at step 400 the system determines whether it has been set to operate in full feedback mode (or limited feedback mode). If yes, the feedback interval /b/_πte/va/ is set to 1 , and returned for use in the operation of the transmitter as illustrated for example above with reference to Fig. 2. If not, i.e. the system is set to limited feedback mode, fb_mtervaι is calculated in step 404, as a function of the system state. Details of the calculation in an example embodiment will be described below. The calculated value for fb,_ntervaι is then returned.

The ranking of packet combinations specified (compare step 206, Fig. 2) uses knowledge of the state of R receivers. This feedback information can be sent at the end of every time slot (i.e. full feedback mode). However, the amount of feedback and computation can be reduced if after receiving the feedback from all R users in a particular slot, the Base Station (BS) calculates K₁₁ - the number of undecoded packets in the coding buffer, and instructs the receivers to only send the next feedback after the next K₁₁ time slots. When doing this, BS can rank coded combinations by either assuming the most recent feedback state information or estimating the state information.

Fig. 5 depicts the operation of the receiver in the example embodiment. Similar to the operation of the transmitter, this is based on batches.

More particular, at step 500, it is determined whether there is start of a new batch. If yes, the receiving database is initiated in step 502, and a combination received from the transmitter at step 504. At step 506, it is determined whether the receipt was successful. If yes, the receiver performs decoding of packets at step 508, followed by updating the receiving database at step 510.

If the receipt was not successful, the process proceeds to step 512. In step 512, the receiver either determines the relevant feedback interval, using the same process as described above with reference to Fig. 3, or the feedback interval is received from BS.

In step 514, it is determined whether feedback is to be sent in this time slot, and if yes, the feedback is sent in step 516. If not, the process proceeds to step 518.

In step 518, it is determined whether all packets in the batch have been decoded. The number of packets in each batch can be determined from the header of each transmission.

If all packets in the batch have been decoded, the process returns to step 500. If not, the process returns to step 504. In the example embodiment, the transmitter repeatedly broadcasts network- coded packets to the receiving nodes until all receiving nodes have received and decoded all packets. In every round of broadcast, the transmitter selects some packets from the coding buffer according to a selection algorithm and combines them using network coding into a single coded packet. The resultant coded packet is then broadcasted to ail receiving nodes. Nodes that correctly receive the coded packet attempt to decode immediately. The transmitter then begins a new round of broadcast.

The packet selection algorithm in the example embodiment selects packets based on combinations. There are a total of 2^K -1 packet combinations for a batch of K packets, e.g. {p_Λ, p₃} and (P₁, p₂} are two different combinations of packets P₁, p₂ and p₃. Each combination has a priority value that is tied to delay performance.

The selection algorithm in the example embodiment runs as follows:

1) Combinations are sorted according to priority.

2) The combination with the highest priority will be picked.

One special case of the algorithm is when all but one receiving node has received and decoded all packets in the coding buffer. Packets will then be sent directly in unicast mode to the last receiving node in a highest priority-first manner without any network coding being performed. This is regardless of how the priority is computed and whether step 3) is performed.

Priority is computed based on the current delay of the packets in each combination ς and how many packets can ς decode if correctly received Sometimes, receiving a combination can result in more than 1 packet being decoded. For example, a node has already received coded packets as combinations p_tθ p₃ and p₂θ p₃. Based on current information, there is no way to decode any of those three packets. However, upon receiving any one of the three packets {p,}, {p₂} or {p₃} from the transmitter, the receiving node can simultaneously decode p,, p₂ and p₃. This is also true if e.g. the transmitter sends combination p_!©2 p₂. Combination ς is a binary vector of length K in which packet / is included in that combination if its /-th element equals 1. Denote by D^ς) the set of packets which ς can decode for a node r. Then the priority of ς is

where d_p is the current delay of packet p and c_r is the channel quality of receiver r.

The set D^ ς) can be computed based on the state of receiver r. Upon reception of a new combination, every receiver attempts to decode it using the Gauss-Jordan elimination method [5]. This facilitates immediate decoding whenever possible. Let E_r be the reduced echelon matrix produced from the Gauss-Jordan elimination after each decoding attempt. The matrix E_r describes the state of receiver r. If r has not received any coded or uncoded packet p, then row p of the matrix E_r consists of all zeros, vice versa. If r has received packet p, then element (p, p) of the matrix E_r is 1 and the other elements of the row p are zeros, vice versa. The positions of the rest of the rows indicate packets that the receiver has received but has yet to decode. The way to test the condition of the first summation in Eqn. 1 in the example embodiment is as follows. A packet p is in DX ς) if the combination ς increases the rank of E_r and a new combination ς'= ς + p (i.e., includes packets p and that of the combination ς) does not increases the rank further.

The matrix E_r may be large with a large K_max. In order to reduce the size of each feedback and simplify computation at the transmitter, a receiver can send a binary matrix of the same dimension of the matrix E_r instead as feedback, in an example emboidment. It is a binary summary of the matrix E_r where a '1' denotes a non-zero element in of E_r the same position, vice versa.

As shown in Fig. 6, the example embodiment can provide a significant performance improvement against a single buffer system which uses the existing ARQ scheme [4] that is designed for achieving low-delays. Bad users with c = 0.5 suffer more in terms of delay in the ARQ scheme (c is a measure of channel quality and is between 0 and 1, where a larger value indicates better channel quality). As a result, the system- wide performance is much higher.

A performance improvement can still be observed (especially at high loads) in an alternative embodiment , where the packet selection algorithm is omitted. In this case, all

K packets are always combined using random linear coding (RLC). This is illustrated in

Fig. 7. The results illustrate improvement due to the dual queue system and an iterative procedure for the optimal K_max in such an embodiment.

As can be observed in Fig. 8, the degrade in performance with limited feedback against that of per slot feedback in different embodiments is somewhat negligible for low arrival rates but noticeable at high loads. The maximum difference in average delay is about ^"0.5 slots at arrival rate = 0.3 and is in any event small compared to the existing ARQ scheme in Fig. 6.

One special case in one embodiment of the algorithm is when all but one receiving node has received and decoded all packets in the coding buffer. Packets will then be sent directly to the last receiving node in a highest priority-first manner without any network coding being performed. The delay gain in this special case is shown in Figs. 9 and 10, which uses the worst-case selection method as reference: select all packets at every round up till the last node, leading to the maximum delay. As can be seen from Figs. 9 and 10, the gain is always positive for all channel conditions and is most significant when the difference in the channel conditions between the receiving nodes is the largest.

In Figs. 11 and 12, two different embodiments are being compared: the case with a static K_max and the case with an optimal K_max obtained using the iterative procedure described above. When K_max is either too large or too small, the average packet delay is not at optimum. The iterative procedure described above in one embodiment is able to continually determine the best K_max for different traffic and channel conditions.

The method and system of the example embodiment can be implemented on a computer system 800, schematically shown in Figure 8. It may be implemented as software, such as a computer program being executed within the computer system 800, and instructing the computer system 800 to conduct the method of the example embodiment.

The computer system 800 comprises a computer module 802, input modules such as a keyboard 804 and mouse 806 and a plurality of output devices such as a display 808, and printer 810.

The ^"computer module 802 is connected to a computer network 812 via a suitable transceiver device 814, to enable access to e.g. the Internet or other network systems such as Local Area Network (LAN) or Wide Area Network (WAN).

The computer module 802 in the example includes a processor 818, a Random Access Memory (RAM) 820 and a Read Only Memory (ROM) 822. The computer module 802 also includes a number of Input/Output (I/O) interfaces, for example I/O interface 824 to the display 808, and I/O interface 826 to the keyboard 804.

The components of the computer module 802 typically communicate via an interconnected bus 828 and in a manner known to the person skilled in the relevant art. The application program is typically supplied to the user of the computer system 800 encoded on a data storage medium such as a CD-ROM or flash memory carrier and read utilising a corresponding data storage medium drive of a data storage device 830. The application program is read and controlled in its execution by the processor 818. Intermediate storage of program data maybe accomplished using RAM 820.

Embodiments of the present invention introduce an effective DQDC mechanism that can achieve the inherent throughput gain of network coding while ensuring the delay performance of all users is also improved. The proposed DQDC mechanism in example embodiments consists of: i) a method of organizing packets at the transmitter into queueing buffer and coding buffer in tandem to restrict the number of packets being processed each time ii) an efficient algorithm that determines what packets should be coded for each transmission/broadcast and iii) an iterative procedure to determine the optimal parameter for (i). Embodiments of the present invention can have of the following features:

A dual-buffering system at the transmitter (broadcast station) side consisting of a queueing buffer followed by a coding buffer.

The coding buffer has a maximum operating size of K_max. This is a parameter which can be tuned dynamically for optimum performance.

Network coding can only be carried out over packets in the coding buffer. A packet is excluded from coding if it has been successfully decoded by all receiving nodes (receivers).

Newly arriving packets will be first stored in the queueing buffer and not allowed to enter the coding buffer.

Whenever the coding buffer is empty, it will be filled up as much as possible using packets from the queueing buffer. If there are not enough packets in the queueing buffer to fully fill up the coding buffer, the transmitter simply uses all the packets available in the queueing buffer.

An iterative procedure to determine the optimum value of parameter K_max.

Figure 13 shows a flow chart illustrating a method of linear network coding according to an example embodiment. At step 1302, incoming packets are buffered, in a first buffer. At step 1304, a batch of packets is moved from the first buffer into a second buffer having a maximum operating size, K_max. At step 1306, linear coding is applied on the batch of packets in the second buffer. At step 1308, the coded packets are transmitted to receivers of the network. At step 1310, the second buffer is flushed once all receivers have decoded the batch of packets. At step 1312, the second buffer is refilled with a new batch of packets from the first buffer.

Industrial Application

Embodiments of the present invention can be applied for reliable downlink transfers. Some examples of potential applications are:

Digital Video Broadcast (DVB) - achieving higher quality with lower bandwidth requirement, e.g. Mediacorp MobileTV or other channels (currently only channels 5 and 8 are available).

Wireless LAN Multicasts / Broadcasts, e.g.

High quality video conferencing on individual terminals (Both video and voice). Wireless HD-TV in homes and buildings - no more wired TV points.

Wireless audio systems - common components in the audio channels can be broadcasted to wireless speakers.

Large file dissemination.

Wireless Sensor networks. Reprogramming nodes on-the-fly.

Information / control parameter downloads from the sink to nodes.

Multicasts and broadcasts in Cellular Networks.

It will be appreciated by a person skilled in the art that numerous variations and/or modifications may be made to the present invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects to be illustrative and not restrictive.

References

[1] R. Ahlswede, Ning Cai, S. R. Li, and R. W. Yeung, "Network Information Flow," IEEE Transactions on Information Theory, 46: 1204 — 1216, July 2000.

[2] R. Koetter and M. Medard, "Beyond Routing: An Algebraic Approach to

Network Coding," IEEE Transactions on Information Theory, 11 :782 — 795, October 2003.

[3] A. Eryilmaz, A. Ozdaglar, and M. Medard, "On Delay Performance Gains From Network Coding," in Proceedings of the Conference on Information Sciences and Systems (CISS'06), March 2006. [4] J. K. Sundararajan, D. Shah, and M. Medard, "ARQ for Network Coding," in Proceedings of the IEEE International Symposium on Information Theory (ISIT 2008), July 2008.

[5] R. K. Jain and S. R. K. Iyengar, Advanced Engineering Mathematics. Alpha Science Int'l Ltd, September 2007.

Claims

1. A method of linear network coding in a lossy network with link-by-link feedback, the method comprising the steps of: buffering incoming packets in a first buffer; moving a batch of packets from the first buffer into a second buffer having a maximum operating size, K_max; applying linear coding on the batch of packets in the second buffer; transmitting the coded packets to receivers of the network; flushing the second buffer once all receivers have decoded the batch of packets; and refilling the second buffer with a new batch of packets from the first buffer.

2. The method as claimed in claim 1 , further comprising dynamically adjusting K_max based on respective occupancies of the first and second buffers.

3. The method as claimed in claim 2, wherein K_max is adjusted based on respective averages of the occupancies of the first and second buffer.

4. The method as claimed in claim 3, wherein the respective averages comprise one of a group consisting of a mean over a period of time, a running average, a moving average over a sliding time window; and a weighted moving average.

5. The method as claimed in any one of the preceding claims, wherein applying the linear coding comprises applying a selection algorithm based on combinations of the packets in the second buffer.

6. The method as claimed in claim 5, wherein the selection algorithm comprises sorting the combinations according to priority.

7. The method as claimed in claim 6, wherein the priority is based on a current delay of the packets in each combination and a number of packets that can be decoded if each combination is received.

8. The method as claimed in any one of claims 5 to 7, further comprising, when all but one of the receivers have decoded all packets in the batch, transmitting remaining packets without coding in a highest priority first order to said one of the receivers.

9. The method as claimed in any one of the preceding claims, further comprising controlling in which time slots feedback from the receivers is to be provided to the transmitter.

10. The method as claimed in claim 10, wherein said controlling comprises determining, after feedback from the receivers has been received in one time slot, the number of packets, K_u, that have not been decoded by all receivers, and instructing the receivers to only sent feedback after the next K_u time slots.

11 A system for linear network coding in a lossy network with link-by-link feedback, the system comprising: a first buffer for buffering incoming packets; means for moving a batch of packets from the first buffer into a second buffer having a maximum operating size, K_max; means for applying linear coding on the batch of packets in the second buffer; means for transmitting the coded packets to receivers of the network; means for flushing the second buffer once all receivers have decoded the batch of packets; and means for refilling the second buffer with a new batch of packets from the first buffer.

12. The system as claimed in claim 11 , further comprising means for dynamically adjusting K_max based on respective occupancies of the first and second buffers.

13. The system as claimed in claim 12, wherein K_max is adjusted based on respective averages of the occupancies of the first and second buffer.

14. The system as claimed in claim 13, wherein the respective averages comprise one of a group consisting of a mean over a period of time, a running average, a moving average over a sliding time window; and a weighted moving average.

15. The system as claimed in any one of claims 11 to 14, wherein the means for applying the linear coding applies a selection algorithm based on combinations of the packets in the second buffer.

16. The system as claimed in claim 15, wherein the selection algorithm comprises sorting the combinations according to priority.

17. The system as claimed in claim 16, wherein the priority is based on a current delay of the packets in each combination and a number of packets that can be decoded if each combination is received.

18. The system as claimed in any one of claims 15 to 17, wherein, when all but one of the receivers have decoded all packets in the batch, the means for transmitting transmits remaining packets without coding in a highest priority first order to said one of the receivers.

19. The system as claimed in any one of claims 11 to 18, further comprising means for controlling in which time slots feedback from the receivers is to be provided to the transmitter.

20. The system as claimed in claim 19, wherein said means for controlling determines, after feedback from the receivers has been received in one time slot, the number of packets, K_u, that have not been decoded by all receivers, and instructing the receivers to only sent feedback after the next K_u time slots.

21. A data storage medium having computer code means for instructing a computing device to execute a method of linear network coding in a lossy network with link-by-link feedback, the method comprising the steps of: buffering incoming packets in a first buffer; moving a batch of packets from the first buffer into a second buffer having a maximum operating size, K_max; applying linear coding on the batch of packets in the second buffer; transmitting the coded packets to receivers of the network; flushing the second buffer once all receivers have decoded the batch of packets; and refilling the second buffer with a new batch of packets from the first buffer.