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Linear Programming Case Study - Maximizing Audio Quality

  1. 1. Maximizing Audio Quality (A Linear programming Problem) Team Members: • Shailendra Shankar Gautam • Abhay Kumar • Ankit Katiyar • Dharm Jaiswal • Sharad Srivastava - 12810075 12810001 12810010 12810029 12810076
  2. 2. Problems  Current Internet still provides best efforts service  No Guarantee of performance for real time multimedia application  Multimedia typically uses UDP  Not reliable  No congestion control  Multimedia traffic is normally subject to  Restricted available bandwidth  Delay, Delay jitter  Loss of packets
  3. 3. Control Mechanisms  Mechanisms which  Dynamically adapt the behavior of the audio application to maximize the audio quality under the constraints of • Restricted bandwidth • Delay • Packet Loss • Jitter present in the network at that point of time
  4. 4. Audio Compression Techniques (codecs)  Current codecs have a diverse range in terms of degree of compression (bitrates) and underlying technologies  Thus the quality of an IP telephony call is highly dependent on the codecs and their reaction to available bandwidth, link delays and packet loss.
  5. 5. Mean Opinion Score (MOS)  Described in ITU recommendation P.800  Formal subjective measure if voice quality  Real number – Between 1 to 5  Toll Quality – Quality with MOS between 4 and 4.3  Communication Quality – Between 3.5 and 4  Lower bound for acceptability of a speech – 3.5  MOS has been determined for every codec under the ideal condition of no loss.
  6. 6. Examples of codecs Codec Technology Bitrate (ms) MOS PCM µ-law Waveform 64 4.3 G.721 Waveform 32 4.0 GSM fullrate RPE-LTP 13 3.7 G.728 LD-CELP 8 4.0 G.723.1 MP-MLQ CELP 5.6 3.9
  7. 7. Bandwidth Constraint  End to End available bandwidth – the maximum rate that the path can provide to a flow  Depends upon the utilization of various links in the path in presence of cross traffic  Less than or equal to capacity of the path – The maximum rate a path can provide to a flow, wwhen there is no other traffic in the path
  8. 8. Bandwidth Constraint (contd..)  In underutilized network we can use high bitrate codecs  which will consume more bandwidth  but will generate high quality  But switch to low bitrate codecs when available bandwidth gets tighter  It is possible to mix multiple codecs in a certain ratio for bandwidth optimization ensuring that the audio quality provided is optimum for the user.
  9. 9. Delay Constraint  Delay of the path  Propagation delay of individual links  Queuing delay at individual hops/routers  Delay inherent to the codec T(codec) = T(enc.) + T(dec.) + T(LA)  Total delay must be under the constraint of tolerable Mouth-to-Ear (M2E) delay  The time that elapses between the moment the talker utters the words and the moment the listener hears them  Must be under 400 ms (ITU recommendation G.114 & G.131)
  10. 10. The LP Problem Maximizes the audio quality under the constraint of available bandwidth and link delay Maximizes MOS (z) = c1x1 + c2x2 + ….. + cnxn Subject to; b1x1 + b2x2 + ….. + bnxn <= B /*bandwidth constraint*/ d1x1 + d2x2 + ….. + dnxn <= D /*delay constraint*/ c1x1 + c2x2 + ….. + cnxn <= 4.3 /*max possible MOS attainable by codec*/ c1x1 + c2x2 + ….. + cnxn >= 3.5 /*lower bound of acceptable MOS score*/ x1 + x2 + ….. + xn= 1 /*total of all percentage*/
  11. 11. The LP Problem (contd..) Where x1, x2 ….., xn = percentage of each codec in transmission mixing c1, c2 ….., cn = MOS value for each codec b1, b2 ….., bn = bitrates for each codec d1, d2 ….., dn = (packet size in bytes)*(encoding/decoding delay to create/decode 1 byte) B = Available bandwidth D = 400 ms (link one way delay)
  12. 12. Implementation Codec Bitrate (kbps) MOS Delay for Packet 1 byte size (ms) (bytes) PCM µ-law 64 4.3 0.50 200 G.721 32 4.0 1.00 200 GSM fullrate 13 3.7 2.42 198 G.728 8 4.0 2.50 200 G.723.1 5.6 3.9 6.00 210 The delay values for each codec has been determined based on existing literature and experiment.
  13. 13. Implementation (contd..) The formulation of this particular linear programming problem is thus: Maximizes MOS (z) = 4.3x1 + 4.0x2 + 3.7x3 + 4.0x4 + 3.9x5 Subject to; 64x1 + 32x2 + 13x3 + 8x4 + 5.6x5 <= B 0.1x1 + 0.2x2 + 0.48x3 + 0.5x4 + 1.26x5 <= D 4.3x1 + 4x2 + 3.7x3 + 4x4 + 3.9x5 <= 4.3 4.3x1 + 4x2 + 3.7x3 + 4x4 + 3.9x5 >= 3.5 x1 + x2 + x3 + x4 + x5 = 1 Xi >= 0 where i = 1,2,3,4,5
  14. 14. Solution High bandwidth availability (500) and low delay (40)
  15. 15. Solution High bandwidth availability (500) and low delay (40)
  16. 16. Result Sr. No. Network Condition Available 1 way bandwidth delay (ms) Solution Optimum MOS value 1 High available bw/Low Delay 500 40 X1=1, X2=0, X3=0, X4=0, X5=0 4.30 2 High available bw/High Delay 100 150 X1=1, X2=0, X3=0, X4=0, X5=0 4.30 3 Med available bandwidth/High delay 50 140 X1=0.75, X2=0, X3=0, X4=0.25, X5=0 4.225 4 Low available bw/Low Delay 30 40 X1=0.39, X2=0, X3=0.61, X4=0, X5=0 4.11 5 Low available bw/High Delay 30 150 X1=0.083, X2=0.722, X3=0, X4=0.194, X5=0 4.025 6 Very Low available bw/High delay 20 150 Infeasible!! -
  17. 17. Thank You!! 

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