Hybrid Codes and the Point-to-Point Channel Paul Cuff Curt Schieler.

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Presentation transcript:

Hybrid Codes and the Point-to-Point Channel Paul Cuff Curt Schieler

Source-Channel Coding p(y|x) fg Correlation between S and Ŝ: Achieved with separately designed encoder and decoder.

Video Transmission (example) p(y|x) f

Systematic Transmission (example) Digital Hybrid Analog Relay Transmission

Copy-Robust Documents (example) A document gets printed with redundancy. Photocopy noise removed by photocopier.

Connection to General Point-to-Point Channel Setting p(y|x) fg

Digital Watermark (example) Media is modified to include extra information Scoundrel may try to delete the watermark – Channel input (X) is modified media – Ŝ is additional information (digital tag)

Define Empirical Coordination p(y|x) fg is achievable if: Empirical distribution:

Separation Method Index Channel Achieves product distributions: such that

A Better Idea (Hybrid Codes) Channel

Hybrid Codes Digital – Source is compressed and coded in blocks Analog – Channel input and reconstruction depend letter- by-letter on the source and channel output Hybrid Codes take advantage of correlation in network setting (i.e. interference channel) – [Minero, Lim, Kim – Allerton 2010, ISIT 2011]

Achievable Inner Bound is achievable if Source Channel Markov Chain Function (analog encoding) Function( analog decoding) Digital Decoding

Binary Example Source is Bern(p) Binary symmetric channel (Ɛ) Require reconstruction to equal channel input – i.e. X = Ŝ(systematic transmission) Minimize Hamming distortion If p=.5: D = Ɛ (Optimal) If p>0 and Ɛ>0 : D > 0 (Suboptimal)

State Amplification Channel State is known to the encoder Two objectives – Transmit a message – Help decoder estimate state p(y|x,s) fg [Kim, Sutivong, Cover – ‘08][Choudhuri, Kim, Mitra – ‘10, ‘11] No loss of generality

Causal Achievable Region is achievable iff Source Channel Markov Chain Function (analog encoding) Function( analog decoding) Digital Decoding

Strictly-Causal Achievable Region is achievable iff Source Channel Markov Chain Function (analog encoding) Function( analog decoding) Digital Decoding