Algorithm 1 The CS-DDSG algorithm

Input:

The probability of selecting source nodes: P1;

The probability of forwarding: P2;

The number of measurements: M;

Output:

Measurement vector: y;

Measurement matrix: Φ;

Stage 1:

1: for i = 1:N

2: S(i).id = [i];

3: S(i).data = xi;

4: end for

Stage 2:

5: Nodes select themselves with the probability p1 and broadcast their packets;

6: N2 = 0;

7: for i = 1:N·p1

8: for j = 1:N

9: if node i receives the broadcasting data from node j

10: S(j).id = [j,i];

11: S(j).data = xj + xi;

12: N2 = N2 + 1;

13: end if

14: end for

15: end for

Stage 3:

16: The receiving nodes in Stage 2 forward their update packets with probability p2.

17: N3 = N2p2;

18: for loop = 1:max

19: if N3 ≤ 1

20: break

21: end if

22: if node j forwards its packets

23: for i = 1: N

24: if node i has not received a packet and hears node j

25: S(i).id = [i,j];

26: S(i).data = xi + xj;

27: N3 = N3 + 1;

28: end if

29: end for

30: end if

31: The reception nodes in the stage 3 forwarding their packets with probability p2.

32: end for

Stage 4:

33: The mobile sink queries M nodes to generate Φ and Y .

34: Φ = zeros (M, N)

35: if node ik are queried

36: Ωk = S(ik).id;

37: Φ(k, Ωk) = 1;

38: end if

39: Return Φ and Y.