Delay limited Joint Source-Channel Coding Morteza Varasteh Imperial - PowerPoint PPT Presentation

Delay limited Joint Source-Channel Coding Morteza Varasteh Imperial College London (ICL) M. Varasteh (ICL) Delay limited Joint Source-Channel Coding 1 / 6

Introduction Capacity of the channel C = max p ( x ) I ( X ; Y ) bits/channel use Rate distortion function I ( V ; ˆ R ( D ) = min V ) v | v ): E [ d ( V, ˆ p (ˆ V )] ≤ D Shannon’s source-channel separation theorem It is shown capacity C or rate distortion function R ( D ) can be achieved Infinite delay and infinite complexity. Optimal performance theoretically attainable (OPTA) mR ( D ) ≤ nC M. Varasteh (ICL) Delay limited Joint Source-Channel Coding 2 / 6

Uniform Source over AWGN Channel Gaussian source/ channel: uncoded is optimal for bandwidth matched case Banwidth compression 2:1 (2 source samples over 1 channel use) Shannon lower bound for this system model (For the uniform source being spread over ∆ and AWGN channel) ∆ 2 D ≥ 1 2 πe (1 + P N ) 2 Not known if achievable, and even if so, it needs infinite delay and complexity M. Varasteh (ICL) Delay limited Joint Source-Channel Coding 3 / 6

Hybrid Scheme First sample is quantized then scaled, second sample is scaled, and both are superimposed Transmission is considered with a noise gap d to increase the resistance of TX M. Varasteh (ICL) Delay limited Joint Source-Channel Coding 4 / 6

Hybrid Scheme There is a gap of 2.07 db between the achievablilty and Shannon bound Scheme performs better than Shannon-Kotel’nikov mapping −10 N=2 −15 N=3 N=4 Average distortion (dB) N=5 N=6 −20 N=7 N=8 −25 −30 N=9 −35 SK mapping Hybrid scheme Shannon and ZZ LB −40 10 15 20 25 30 35 40 45 Average SNR (dB) M. Varasteh (ICL) Delay limited Joint Source-Channel Coding 5 / 6

Ziv-Zakai Bound A generalized information measure. If φ ( · ) is convex and t → 0 tφ (1 /t ) = 0 , it satisfies data processing inequality lim � f ( x ) f ( y ) � � � I φ ( X ; Y ) = f ( x, y ) φ dxdy f ( x, y ) Shannon bound obtained for α = 1 Better bounds than Shannon bound for the bandwidth matched case R α ( D ) = inf I α ( V, ˆ V ) ≤ sup I α ( X ; Y ) = C α M. Varasteh (ICL) Delay limited Joint Source-Channel Coding 6 / 6