Sliding-Window Digital Fountain Codes for Streaming of Multimedia Contents Matta C.O. Bogino, Pasquale Cataldi, Marco Grangetto, Enrico Magli, Gabriella Olmo. IEEE International Symposium on Circuits and Systems (ISCAS), 2007.

Outline Introduction Proposed Method Performance Analysis Conclusions Future Works

Introduction Luby Transform (LT) Codes: –Encoding process For the i th encoding symbol (packet), select degree d i by Soliton distribution Choose d i source data Perform XOR on chosen data –Decoding process Decode degree-one encoded symbols Remove degree-one edges iteratively … x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 y1y1 y2y2 y3y3 y4y4 y5y5 x1x3x1x3 x2x2 x2x5x2x5 x3x5x6x3x5x6 Degree123…k probabilityΩ1Ω1 Ω2Ω2 Ω3Ω3 …ΩkΩk x4x4

Introduction Digital Fountain (DF): –Decoder can recover original data from enough number of received encoded packets. Any subset of the encoded packets. –Receive n = (1 +  ) · k encoded packets can recover k original data. ε: code overhead. –Digital Fountain Codes are potentially (asymptotically) optimal. for k → ∞, such that ε→ 0

Introduction I II PP played! queued I II PPPPP P PPPPPPPPP P discarded! Many applications require short data block length: – k ↓, such that ε ↑, overhead↑ –k ↑, such that ε ↓, overhead↓ Video streaming:

Introduction Sliding Fountain (SF): –Use a windowing approach to partition the information data (original source data). –Encoder chooses source data among those in a sliding window. Sliding window moves following the chronological order of the video stream. –Provides a rough temporal ordering of the received packets. Avoiding expired information to be processed.

Proposed Method Sliding Windows:

Proposed Method Sliding Windows: A GBDCEHJIKFL data streaming (chronological order) A GMBDCEHJIKNPOQFLR A DGBDCEEGFHHJIKFIL A GBDCEHJIKFL

Proposed Method Sliding Windows: –Number of windows that consider a particular symbol: w / s window movementwindow length overlap region A GMBDCEHJIKNPOQFLR w = 6 s = 2

Proposed Method overlap region window movement A B C D E F G H I J K L A B C D E F D E F G H I G H I J K L A B C D E F C D E F G H E F G H I J G H I J K L s = 3 s = 2 w = 6 Sliding Windows: –The overlap strategy permits to virtually extend the window length. s↓, such that (w – s) ↑, virtual block length↑, ε ( overhead ) ↓.

Proposed Method Total overhead: –The total overhead of the SF code is equal to traditional DF. –Conventional DF encoder: –SF encoder: Each source data is processed in w/s windows. The number of source data as virtually enlarged: The number of encoded packets can be generated, on average, for every virtual source data:

Proposed Method Why more efficient? –The number of encoded symbols can be generated from each window of SF: –The number of encoded packets that generates in every window of SF code is smaller than traditional DF code in order to recover the whole information. < Number of encoded packets generates per window (SF code) Number of encoded packets generates per window (DF code) Total number of windows in DF code: N f = k / w

Proposed Method Why more efficient? –The number of encoded packets that generates in every window of SF system is smaller than traditional DF code in order to recover the whole information DF Code: SF Code:

Proposed Method SF decoder: –A conventional DF decoder, does not require to know windowing is being used. Two decoding cases: –All the symbols of the window have been solved. Usually there are not enough encoded symbols to recover all the window source data. –There are still unsolved equations. Decoder requires a suitable amount of memory to store all the unsolved equations. Would be solved using the new incoming symbols. –window overlap.

Performance Analysis Using LT Codes to analyze on varying: –Window speed. –Total overhead of the code. LT Codes: –Robust Soliton distribution: Constant: δ & c were set empirically. Performed on an personal computer. –Intel Pentium 4 processor 1.7 GHz –512 MB of Ram –Linux OS

Performance Analysis

Undecoded Symbols as a function of the Received Overhead

Performance Analysis Simulation Failure Probability as a function of the Received Overhead

Performance Analysis Encoding Times as a function of the Received Overhead

Performance Analysis Decoding Times as a function of the Received Overhead

Performance Analysis Peak of Memory Usage as a function of the Received Overhead

Conclusions Presented an innovative Sliding Fountains (SF) transmission scheme. The window sliding through the data stream and leaving some overlap between successive steps. –Permits to virtually enlarge block length to obtain higher code efficiency. Keeping the overhead constant, SF approach allows to achieve an undecoded symbol rate lower of 10 5 than traditional ones.

Conclusions Time complexity: –SF encoding process is less complex. –An increasing of decoding complexity with low values of ε, where traditional systems cannot work properly. SF system needs a lower amount of memory with respect of a traditional one.

Future Works The system parameters can be tuned in order to transmit multimedia contents over critical channels. SF scheme can be further modified so that an Unequal Error Protection (UEP) can be performed.