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)

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Introduction

Capacity of the channel C = max

p(x) I(X; Y )

bits/channel use Rate distortion function R(D) = min

p(ˆ v|v):E[d(V, ˆ V )]≤D

I(V ; ˆ V ) 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

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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) D ≥ ∆2 2πe(1 + P

N )

1 2

Not known if achievable, and even if so, it needs infinite delay and complexity

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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

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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 15 20 25 30 35 40 45 −40 −35 −30 −25 −20 −15 −10 Average SNR (dB) Average distortion (dB) SK mapping Hybrid scheme Shannon and ZZ LB

N=2 N=3 N=7 N=9 N=8 N=6 N=5 N=4

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Ziv-Zakai Bound

A generalized information measure. If φ(·) is convex and lim

t→0 tφ(1/t) = 0, it satisfies data processing inequality

Iφ(X; Y ) = f(x, y)φ f(x)f(y) f(x, y)

• dxdy

Shannon bound obtained for α = 1 Better bounds than Shannon bound for the bandwidth matched case Rα(D) = inf Iα(V, ˆ V ) ≤ sup Iα(X; Y ) = Cα

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