Chapter 3 Proposed UEP Method
3.3. RD Optimized Channel Rate Allocation
Channel rate allocation method is used to determine the amount of FEC assigned to each SG. To utilize FEC efficiently, a rate-distortion optimized algorithm is proposed here and the symbols used are summarized in Table 3.1
protection level for frame n in SG s sth SG group of frame n
Total size for frame n in SG s The source size for frame n in SG s SG number in frame
Macroblock for frame n in pixel j N The total size for GOP
Number of frames in GOP Number of SGs in frame The maximum bit rate
summation diction for entire GOP Distortion for SG group in frame n SG s Distortion for macroblock n in pixel j
Summation bit rate for entire GOP
Table 3.1 The symbol table for rate distortion estimation
Since our algorithm organizes SG by grouping together macroblocks that have similar impact factors, we use the same protection level for all the macroblocks belonging to the same SG. Let denote the protection level assigned to , the sth SG of frame n, and , denote the parameters of the RS code associated with this protection
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level. Since the RS block length is usually determined based on the end-to-end system delay constraints, we assume it is constant (say N) over the entire GOP. So, we have
for all the possible n and s in a GOP.
In order to take into account the importance of each SG, more RS packets (i.e., higher protection level) are allocated to SGs carrying important information and less to the rest. Our channel rate allocation strategy is to optimize the code rates { / } for each SG in order to minimize the distortion for a given overall transmission rate. Here we present a rate-distortion optimized solution that seeks the best protection level for each SG. Our objective is to seek for the vector of RS coding parameters,
, … , , … , , … , that minimizes the expected end-to-end distortion of the corresponding GOP, where s is the desired number of SGs for each frame and is the number of frames in a GOP. The expected distortion of a GOP is given by.
(17)
where ∑ for all the macroblocks belonging to ,
and the . However, since has protection level , , the packet loss rate p in the equations (7) must be substituted with below:
1 (18)
where is the probability that is not correctly decoded by the RS decoder, and is the actual channel loss probability. The channel rate allocation problem is formulated as:
min (19)
where (20)
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The above constrained minimization problems (19) and (20) are naturally recast in the standard Lagrange formulation as:
(21)
By appropriately choosing Lagrange multiplier λ , the above problem (19) can be solved within a convex-hull approximation by solving (21). The search for an appropriate choice of λ can be carried out by the bisection algorithm or a fast convex search technique which is not discussed here. The optimal K then leads to the optimal rate distribution between source and FEC rates.
To solve this equation, we had adopted dynamic program (DP) with the conditions in equation (22) and (23). Equation (22) means that K of slice i must be less than or equal to that of slice j with i < j, assuming that slices are numbered in a descending orders of their important. Since the lost important SG will cause high distortion than the others, we assign more protection (i.e., smaller k) to important SG. Equation (23) means that earlier frames in GOP are more important than the later ones, so we assign more protection on earlier fame in GOP. For the first SG, it calculates J is calculated for all the combination of K. Then for rest of SGs only the J for possible combinations of K that meet the according to condition.
, 1~
, 1~
(22) (23)
To analysis the perForemance of dynamic program, we had use Foreman, Coastguard and Stefan for getting running results. The Table 3.2 shows the execution time for calculating all the combination of K with 105 frames and 6 slices.
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Foreman Coastguard Stefan
Execution time (s) 116.466 116.640 127.809
Table 3.2 Execute time for Lagrange
When video stream transfer over error-prone wireless network, it will cause packet loss. As discuss earlier, the 802.11a standard had defined eight PHY modes. Assume the sender can receive Signal to Noise Ratio (SNR) from receiver, it can use SNR to determine the status of the network and then select the best modulation for transmitting video data. In [23,24], it will calculate the packet loss rate according by SNR and data rate. We calculated all eight PHY modes and use the packet loss rate for calculate the minimum J. After all combination has been calculated, it can decide which PHY mode has the best K combination. The calculation for bit packet loss rate was shown below where s is SNR value and M is M-ary (M=4, 16, and 64) which depend on Quadrature Amplitude Modulation (QAM):
1 · (24)
where is defiend as follow:
1 1 √ (25)
where √ is defined as follow:
√ 2 · 1 1
√ · 3
1· (26)
The Q is defended as
1
√2 (27)
The 4-ary QAM and Quadrature Phase Shift Keying (QPSK) modulation are identical.
For Binary Phase Shift Keying (BPSK) modulation, the bit error probability is defined
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as follow:
√2 (28)
For calculate minimum J for all the combination of K, we will calculate all the combination of the modulation and use the one with the minimum J:
min 1 8 (29)
These can be calculated from the corresponding packet size and BER. Since equations (24)(28) are calculated probability for bits, we have to summation them together so we can have packet loss rate for bytes where L is the length of bytes:
1 1 (30)
The probability that the packet with L-byte data payload is successfully transmitted within the R retransmission limit under PHY mode m, we replace as
, where i is the number of modulation mode:
, 1 1 (31)
1 , 1 , (32)
where , is the ACK packet error probability, , is the data packet error probability. For calculate Ji, we use replace , as which is calculate by
, and the maximum data rate for each modulation: as :
1 ,
(33)
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