Yasunari MAEDA (Kitami Institute of Technology)

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Presentation transcript:

A Note on Theoretical Limit of Type-I Hybrid Selective-repeat ARQ with Finite Receiver Buffer Yasunari MAEDA (Kitami Institute of Technology) Hideki YOSHIDA (Kitami Institute of Technology) Toshiyasu MATSUSHIMA (Waseda University)

Topics 1. Introduction 2. Preparations 3. Modeling 4. Proposed algorithm 5. Experiments 6. Conclusion

1. Introduction overview of type-I hybrid selective-repeat ARQ codeword received block binary symmetric channel transmitter receiver feedback channel noiseless acknowledgement symbol ACK (a positive acknowledgement symbol) no bit error or correctable bit errors in the received block NAK (a negative acknowledgement symbol) uncorrectable bit errors in the received block

× 1. Introduction △ × undetectable errors △ buffer over flow example of operation in type-I hybrid selective-repeat ARQ 7 6 2 5 4 3 1 × △ × undetectable errors  △ buffer over flow ○ round-trip delay D=3 transmitter receiver receiver buffer size of time 10 9 8 ACK NAK C=4 ○ delivered to the user

1. Introduction overview of Markov decision processes reward transition probability action set of states state state set of actions a probability of an event that a state transition from state to state is occurred when action is selected at state a true parameter of transition probability (known) a reward of a state transition from state to state under the condition that action is selected at state target : to maximize total rewards

1. Introduction the theoretical limit of throughput of type-I hybrid Selective-repeat ARQ the theoretical limit of throughput with infinite receiver buffer many previous research the theoretical limit of throughput with finite receiver buffer our research In previous research many type-I hybrid selective-repeat ARQ methods with finite receiver buffer are proposed. But the throughput of the proposed methods can not be compared with the limit with finite receiver buffer. We study the theoretical limit of throughput of type-I hybrid selective-repeat ARQ with finite receiver buffer.

2. Preparations(1/4) a codeword which a transmitter wants to send a set of codewords a positive acknowledgement symbol a negative acknowledgement symbol an acknowledgement symbol received by the transmitter at time the minimum number of a codeword whose ACK symbol is not received yet at time the number of codeword which is transmitted at time the size of finite receiver buffer a round-trip delay (The transmitter receives the acknowledgement symbol for at time .)

2. Preparations(2/4) (1) (2) (3) (actions in MDP) a state at time in Markov decision processes(MDP) (1) where, represents a situation of the receiver buffer. (2) represents codeword already sent by the transmitter. (3) (actions in MDP)

 2. Preparations(3/4) a bit error rate of a BSC(binary symmetric channel) the probability of an event that a receiver sends back ACK symbol a parameter which dominates the true parameter which is known (4) (5) assumptions (n,k) linear code is used, feedback channel is noiseless, where, the maximum number of correctable bit errors the number of bit errors in the received block the maximum number of detectable bit errors

2. Preparations(4/4) (6) operations from time to time (after deciding action at time ) Transmitter receives an acknowledgement symbol at time . ( is for codeword sent at time ) (2) State at time and are computed by using state at time , action at time and acknowledgement symbol at time . (3) Reward at time is computed by using state at time , action at time and state at time . ACK symbol is received and some codewords are sent to the user ; else . (6) (4) Action at time is decided.

3. Modeling(1/2) modeling to solve periods MDP problem utility function (7) where, decision function which returns the number of codeword to send by using the state and time reward after time eqs.(7) is equal to the number of codewords which are delivered to the user.

3. Modeling(2/2) expected utility function (8) where, is first state and known. expected value for the number of codewords which are delivered to the user In order to compute the theoretical limit with finite receiver buffer, we have to maximize the expected utility.

 4. Proposed algorithm compute the maximum of eqs.(8) by using dynamic programming method (9) where, is the maximum of expected utility after time . (Expected utility is equal to the expected value for the number of codewords which are delivered to the user.) the theoretical limit of throughput with finite receiver buffer

5. Experiments(1/2) conditions a round-trip delay D=4 size of receiver buffer C=4, C=8 number of sending codewrods T=1000 bit error rate 0.001, 0.01 using (255,115)BCH code,3 conditions , , :the maximum number of correctable bit errors :the maximum number of detectable bit errors ISR : theoretical limit with infinite receiver buffer( ) PRO : proposed theoretical limit with finite receiver buffer WEL : an averaged throughput of 1000 times simulations by Weldon’s method (Weldon’s method is one of typical selective-repeat ARQ methods. And we apply Weldon’s method to type-I hybrid for the experiments.)

 5. Experiments(2/2) The differences between ISR and WEL are big, but the differences between PRO and WEL are small. case of bit error rate 0.001 0.01 ISR 0.997737 0.530352 PRO 0.997708 0.449197 WEL 0.997663 0.425040 The performance of WEL is close to the theoretical limit with finite receiver buffer. Our proposed theoretical limit with finite receiver buffer is useful to investigate the performance of previous methods.

6. Conclusion We applied Markov decision processes to type-I hybrid selective-repeat ARQ with finite receiver buffer. We proposed the algorithm which computes the theoretical limit of throughput of type-I hybrid selective-repeat ARQ with finite receiver buffer. The theoretical limit of throughput computed by our proposed algorithm is useful to investigate the performance of previous type-I hybrid selective-repeat ARQ methods with finite receiver buffer. As further works, we want to study the relationship of throughput and decoding error probability.