Explicit Construction of Multiple Access Channel Resolvability Codes - PowerPoint PPT Presentation

Explicit Construction of Multiple Access Channel Resolvability Codes from Source Resolvability Codes Rumia Sultana R´ emi A. Chou Wichita State University 2020 IEEE International Symposium on Information Theory 1/29

Outline Introduction and Model • Coding Scheme • Coding Scheme Analysis • 2/29

Channel Resolvability Problem (P2P) [Han-Verdú 93] Channel Resolvability Problem (P2P) [ Han-Verd´ u’93 ] S ~ Unif � ( ) N � 1: N X ~ q ENC X f ( ) S � i 1 N q q Y X | Y X | � 1: N 1: N Y Y p � q 1: N 1: N Y Y ? � � p q 1: N 1: N Y Y • ( ) denotes the uniform distribution over . � � • P2P channel ( X , q Y | X , Y ) ( � , , � ) • P2P Channel . • Unif ( S ) denotes the uniform distribution over S | 3/29 3

Channel Resolvability (MAC) [ Steinberg’98 ] Channel Resolvability (MAC) [Steinberg’98] S ~ Unif � ฀ ( ) S ~ Unif � ฀ ( ) 1 1 2 2 N � ENC ENC 1: N 1: N ( X , Y ) ~ q XY f ( S ) f ( S ) � i 1 1, N 1 2, N 2 q q Z XY | Z XY | � 1: N 1: N Z Z � q p 1: N 1: N Z Z ? � p � q 1: N 1: N z z • and are uniformly distributed sequences. • DMMAC ( X × Y , q Z | XY , Z ) 1 2 � ( , , ) � � � • DMMAC . • S 1 and S 2 are uniformly distributed sequences | 4 4/29

Applications • Strong secrecy MAC-WT [ Pierrot-Bloch’11 ], [ Yassaee-Aref’10 ] • Cooperative jamming [ Pierrot-Bloch’11 ] • Semantic security for MAC-WT [ Frey-Bjelakovic-Stanczak’17 ] • Strong coordination in networks [ Bloch-Kliewer’13 ] 5/29

Related Works (Non-exhaustive) P2P Resolvability • Existence results ⇒ [ Han-Verdu’93 ] • Explicit and low-complexity code constructions ⇒ Polar codes for resolvability over BSC and DMC [ Bloch-Luzzi-Kliewer’12 ], [ Chou-Bloch-Kliewer’18 ] ⇒ Injective group homomorphisms for resolvability over BSC [ Hayashi-Matsumoto’16 ] • Non-explicit, linear coding ⇒ Resolvability over DMC [ Amjad-Kramer’15 ] 6/29

Related Works MAC Resolvability • Existence results ⇒ MAC [ Steinberg’98 ] ⇒ MAC resolvability region [ Frey-Bjelakovic-Stanczak’17 ] • Explicit low-complexity coding scheme ⇒ Symmetric MAC [ Chou-Bloch-Kliewer’14 ] − Invertible extractors − Injective group homomorphisms • Explicit low-complexity coding scheme ⇒ Polar codes for arbitrary MAC [ Sultana-Chou’19 ] 7/29

This Work • Explicit and low-complexity codes for MAC resolvability ⇒ Arbitrary DMMAC ⇒ Input alphabets are binary • Coding scheme ideas ⇒ Reduce MAC resolvability coding problem to a simpler source resolvability coding problem ⇒ Randomness recycling with distributed hashing coupled with block-Markov encoding ⇒ Source resolvability codes used in a black box manner 8/29

Outline Introduction and Model • Coding Scheme • Coding Scheme Analysis • 9/29

Reduction of the MAC Resolvability Region to a Simpler Region To achieve the MAC resolvability region R q Z , it is sufficient to achieve regions of the form R X , Y for some fixed distribution p X p Y     ( R 1 , R 2 ) : I ( XY ; Z ) < R 1 + R 2 ,     R X , Y � I ( X ; Z ) < R 1 ,       I ( Y ; Z ) < R 2 10/29

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