HYBRID ARQ IN WIRELESS NETWORKS Emina Soljanin Mathematical - PowerPoint PPT Presentation

HYBRID ARQ IN WIRELESS NETWORKS Emina Soljanin Mathematical Sciences Research Center, Bell Labs March 19, 2003

HYBRID ARQ IN WIRELESS NETWORKS Emina Soljanin Mathematical Sciences Research Center, Bell Labs March 19, 2003 R. Liu and P. Spasojevic WINLAB

HYBRID ARQ IN WIRELESS NETWORKS Emina Soljanin Mathematical Sciences Research Center, Bell Labs March 19, 2003 R. Liu and P. Spasojevic WINLAB

ACKNOWLEDGEMENTS 1 Alexei Ashikhmin Jaehyiong Kim Sudhir Ramakrishna Adriaan van Wijngaarden

AUTOMATIC REPEAT REQUEST 2 • The receiving end detects frame errors and requests retransmissions. • P e is the frame error rate, the average number of transmissions is 1 1 · (1 − P e ) + · · · + n · P n − 1 (1 − P e ) + · · · = e 1 − P e

AUTOMATIC REPEAT REQUEST 2 • The receiving end detects frame errors and requests retransmissions. • P e is the frame error rate, the average number of transmissions is 1 1 · (1 − P e ) + · · · + n · P n − 1 (1 − P e ) + · · · = e 1 − P e • Hybrid ARQ uses a code that can correct some frame errors.

AUTOMATIC REPEAT REQUEST 2 • The receiving end detects frame errors and requests retransmissions. • P e is the frame error rate, the average number of transmissions is 1 1 · (1 − P e ) + · · · + n · P n − 1 (1 − P e ) + · · · = e 1 − P e • Hybrid ARQ uses a code that can correct some frame errors. • In HARQ schemes – the average number of transmissions is reduced, but – each transmission carries redundant information.

THROUGHPUT IN HYBRID ARQ 3 BPSK, AWGN, BCH Coded 1 uncoded 0.8 0.6 0.4 0.2 0 -6 -4 -2 0 2 4 6 8 10 E s /N 0 [dB]

THROUGHPUT IN HYBRID ARQ 3 BPSK, AWGN, BCH Coded 1 1 uncoded 0.8 0.8 [255,247,3] 0.6 0.6 0.4 0.4 0.2 0.2 0 0 -6 -6 -4 -4 -2 -2 0 0 2 2 4 4 6 6 8 8 10 10 E s /N 0 [dB]

THROUGHPUT IN HYBRID ARQ 3 BPSK, AWGN, BCH Coded 1 1 1 uncoded 0.8 0.8 0.8 [255,247,3] [255,215,11] 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 -6 -6 -6 -4 -4 -4 -2 -2 -2 0 0 0 2 2 2 4 4 4 6 6 6 8 8 8 10 10 10 E s /N 0 [dB]

THROUGHPUT IN HYBRID ARQ 3 BPSK, AWGN, BCH Coded 1 1 1 1 uncoded 0.8 0.8 0.8 0.8 [255,247,3] [255,215,11] [255,177,23] 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0 0 0 0 -6 -6 -6 -6 -4 -4 -4 -4 -2 -2 -2 -2 0 0 0 0 2 2 2 2 4 4 4 4 6 6 6 6 8 8 8 8 10 10 10 10 E s /N 0 [dB]

THROUGHPUT IN HYBRID ARQ 3 BPSK, AWGN, BCH Coded 1 1 1 1 1 cutoff rate uncoded 0.8 0.8 0.8 0.8 0.8 [255,247,3] [255,215,11] [255,177,23] 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 -6 -6 -6 -6 -6 -4 -4 -4 -4 -4 -2 -2 -2 -2 -2 0 0 0 0 0 2 2 2 2 2 4 4 4 4 4 6 6 6 6 6 8 8 8 8 8 10 10 10 10 10 E s /N 0 [dB]

THROUGHPUT IN HYBRID ARQ 3 BPSK, AWGN, BCH Coded 1 1 1 1 1 1 capacity cutoff rate uncoded 0.8 0.8 0.8 0.8 0.8 0.8 [255,247,3] [255,215,11] [255,177,23] 0.6 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 0 -6 -6 -6 -6 -6 -6 -4 -4 -4 -4 -4 -4 -2 -2 -2 -2 -2 -2 0 0 0 0 0 0 2 2 2 2 2 2 4 4 4 4 4 4 6 6 6 6 6 6 8 8 8 8 8 8 10 10 10 10 10 10 E s /N 0 [dB]

TYPE II HYBRID ARQ 4 Incremental Redundancy • Information bits are encoded by a (low rate) mother code. • Information and a selected number of parity bits are transmitted.

TYPE II HYBRID ARQ 4 Incremental Redundancy • Information bits are encoded by a (low rate) mother code. • Information and a selected number of parity bits are transmitted. • If a retransmission is not successful: – transmitter sends additional selected parity bits – receiver puts together the new bits and those previously received. • Each retransmission produces a codeword of a stronger code. • Family of codes obtained by puncturing of the mother code.

INCREMENTAL REDUNDANCY 5 A Rate 1 / 5 Mother Code at the transmitter

INCREMENTAL REDUNDANCY 5 A Rate 1 / 5 Mother Code at the transmitter transmission # 1 at the receiver

INCREMENTAL REDUNDANCY 5 A Rate 1 / 5 Mother Code at the transmitter transmission # 1 transmission # 2 at the receiver

INCREMENTAL REDUNDANCY 5 A Rate 1 / 5 Mother Code at the transmitter transmission # 1 transmission # 2 transmission # 3 at the receiver

INCREMENTAL REDUNDANCY 5 A Rate 1 / 5 Mother Code at the transmitter transmission # 1 transmission # 2 transmission # 3 transmission # 4 at the receiver

THROUGHPUT IN HYBRID ARQ 6 HARQ Scheme based on Turbo codes in AWGN Channel 1 0.9 0.8 0.7 0.6 Throughput 0.5 0.4 0.3 0.2 Throughout of new puncturing scheme 0.1 Throughout of standard BPSK Capacity Cutoff Rate 0 −8 −6 −4 −2 0 2 4 6 8 10 Es/N0 (dB)

RANDOMLY PUNCTURED CODES 7 • The mother code is an ( n, k ) rate R turbo code. • Each bit is punctured independently with probability λ .

RANDOMLY PUNCTURED CODES 7 • The mother code is an ( n, k ) rate R turbo code. • Each bit is punctured independently with probability λ . • The expected rate of the punctured code is R/ (1 − λ ) . • For large n we have turbo code puncturing device n bits ( 1 − λ ) n bits k bits

A FAMILY OF RANDOMLY PUNCTURED CODES 8 Rate Compatible Puncturing • The mother code is an ( n, k ) rate R turbo code. • λ j for j = 1 , 2 , . . . , m are puncturing rates, λ j > λ k for j < k . • If the i -th bit is punctured in the k -th code and j < k , then it was punctured in the j -th code.

A FAMILY OF RANDOMLY PUNCTURED CODES 8 Rate Compatible Puncturing • The mother code is an ( n, k ) rate R turbo code. • λ j for j = 1 , 2 , . . . , m are puncturing rates, λ j > λ k for j < k . • If the i -th bit is punctured in the k -th code and j < k , then it was punctured in the j -th code. • θ i for i = 1 , 2 , . . . , n are uniformly distributed over [0 , 1] . • If θ i < λ l , then the i -th bit is punctured in the l -th code.

MEMORYLESS CHANNEL MODEL 9 • Binary input alphabet { 0 , 1 } and output alphabet Y . • Constant in time with transition probabilities W ( b | 0) and W ( b | 1) , b ∈ Y .

MEMORYLESS CHANNEL MODEL 9 • Binary input alphabet { 0 , 1 } and output alphabet Y . • Constant in time with transition probabilities W ( b | 0) and W ( b | 1) , b ∈ Y . • Time varying with transition probabilities at time i W i ( b | 0) and W i ( b | 1) , b ∈ Y . • W i ( ·| 0) and W i ( ·| 1) are known at the receiver.

PERFORMANCE MEASURE 10 Time Invariant Channel • Sequence x ∈ C ⊆ { 0 , 1 } n is transmitted, and x ′ decoded. • Sequences x and x ′ are at Hamming distance d .

PERFORMANCE MEASURE 10 Time Invariant Channel • Sequence x ∈ C ⊆ { 0 , 1 } n is transmitted, and x ′ decoded. • Sequences x and x ′ are at Hamming distance d . • The probability of error P e ( x , x ′ ) can be bounded as P e ( x , x ′ ) ≤ γ d = exp {− dα } , where γ is the Bhattacharyya noise parameter: � � γ = W ( b | x = 0) W ( b | x = 1) b ∈Y

PERFORMANCE MEASURE 10 Time Invariant Channel • Sequence x ∈ C ⊆ { 0 , 1 } n is transmitted, and x ′ decoded. • Sequences x and x ′ are at Hamming distance d . • The probability of error P e ( x , x ′ ) can be bounded as P e ( x , x ′ ) ≤ γ d = exp {− dα } , where γ is the Bhattacharyya noise parameter: � � γ = W ( b | x = 0) W ( b | x = 1) b ∈Y and α = − log γ is the Bhattacharyya distance.

PERFORMANCE MEASURE 11 • An ( n, k ) binary linear code C with A d codewords of weight d .

PERFORMANCE MEASURE 11 • An ( n, k ) binary linear code C with A d codewords of weight d . • The union-Bhattacharyya bound on word error probability: n � P C A d e − αd . W ≤ d =1

PERFORMANCE MEASURE 11 • An ( n, k ) binary linear code C with A d codewords of weight d . • The union-Bhattacharyya bound on word error probability: n � P C A d e − αd . W ≤ d =1 • Weight distribution A d for a turbo code?

PERFORMANCE MEASURE 11 • An ( n, k ) binary linear code C with A d codewords of weight d . • The union-Bhattacharyya bound on word error probability: n � P C A d e − αd . W ≤ d =1 • Weight distribution A d for a turbo code? • Consider a set of codes [ C ] corresponding to all interleavers. [ C ]( n ) • Use the average A instead of A d for large n . d

TURBO CODE ENSEMBLES 12 A Coding Theorem by Jin and McEliece • There is an ensemble distance parameter c [ C ] s.t. for large n 0 [ C ]( n ) dc [ C ] � � A ≤ exp for large enough d. d 0

TURBO CODE ENSEMBLES 12 A Coding Theorem by Jin and McEliece • There is an ensemble distance parameter c [ C ] s.t. for large n 0 [ C ]( n ) dc [ C ] � � A ≤ exp for large enough d. d 0 • For a channel whose Bhattacharyya distance α > c [ C ] 0 , we have [ C ]( n ) = O ( n − β ) . P W • c [ C ] is the ensemble noise threshold. 0

PUNCTUREDTURBO CODE ENSEMBLES 13 ITW, April 2003 • c [ C P ] is the punctured ensemble noise threshold: 0 [ C P ]( n ) dc [ C P ] � � A ≤ exp for large enough n and d. d 0