# A relay-assisted distributed source coding problem

## Summary (1 min read)

### Remark:

- For any arbitrarily small positive real number and all n sufficiently large, X n can be encoded at location-a at the rate H(X|Y) bits per sample, and decoded at location-b with a probability which can be made smaller than .
- The converse to the Slepian-Wolf coding theorem proves that the lower bound R a ≥ H(X|Y) cannot be improved.
- The cutset bound (3.5) in Section III-A proves that the lower bound R b ≥ H(X|Z) cannot be improved.

### B. Special cases in which the cutset bounds are tight

- Thus for any arbitrarily small positive real number and all n sufficiently large, X n can be encoded at location-a at the rate H(X|Y, Z) bits per sample, and decoded at location-b with a probability which can be made smaller than .
- The authors shall call this relay-assisted distributed source coding strategy as relay decode and re-encode.
- The operation at the intermediate location-b is to simply forward the message from location-a to location-c without any processing.
- The authors shall call this relay-assisted distributed source coding strategy as relay forward.
- The operation at the intermediate location-b is to (i) encode its observations to be reproduced at location-c and (ii) forward the message from location-a to location-c without any processing.

### is, the auxiliary random variables U, V satisfy the following two Markov chains: U-X-(Y, Z) and V-(U, Y)-(X, Z). Then all rate-pairs

- EQUATION are operationally admissible for relay-assisted distributed source coding and cover all the four previously discussed special cases.
- The authors first show that all the four previously discussed special cases are covered by Theorem 1.
- The authors now sketch the proof that all rate-pairs (R a , R b ) satisfying (4.7) and (4.8) are operationally admissible for relayassisted distributed source coding.
- The encoder also randomly partitions the tuple of codewords C u into nonoverlapping bins.

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### Cites background from "A relay-assisted distributed source..."

...F (X1, X2, X3) = X1 was considered in [7]....

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##### References

45,034 citations

### "A relay-assisted distributed source..." refers background or methods in this paper

...P(E3 | E2) ↓ 0 as n ↑ ∞ by the Markov lemma [10] because U–X–Y is a Markov chain....

[...]

...This follows from the coding theorem due to Slepian and Wolf [10] with Xn as the source of information to be encoded at location-a and Yn as the sideinformation available to a decoder at location-b....

[...]

...5h2(p) where h2(α) := −α log2(α) − (1 − α) log2(1 − α), α ∈ [0, 1] is the binary entropy function [10]....

[...]

...The Slepian-Wolf coding theorem with Yn as the source of information available at location-b and Zn as the sideinformation available to a decoder at location-c shows that, for any arbitrarily small positive real number and all n sufficiently large, Yn can be encoded at location-b at the rate H(Y |Z) bits per sample, and decoded at locationc with a probability which can be made smaller than ....

[...]

...The Slepian-Wolf coding theorem applied a second time with Xn as the source of information available at location-a and (Yn,Zn) as the side-information available to a decoder at location-c shows that, for any arbitrarily small positive real number and all n sufficiently large, Xn can be encoded at location-a at the rate H(X|Y,Z) bits per sample, and decoded at location-c with a probability which can be made smaller than ....

[...]

3,404 citations

563 citations

### "A relay-assisted distributed source..." refers background in this paper

...Beginning the late 90’s, the construction of practical distributed source codes for emerging wireless sensor network applications [2] received...

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468 citations