1. Error Control Code Combining Techniques in Cluster-based Cooperative Wireless Networks
Su Yi
Babak Azimi-Sadjad
Shivkumar Kalyanaraman
Vijaynarayan Subramanian
Presenter: Jayasri Akella
11/24/2018
Rensselaer Polytechnic Institute

2. Rensselaer Polytechnic Institute
Outline
Introduction and Related work
Performance Analysis for Link Layer Cooperation
Simulations
Conclusions and Future Work
11/24/2018
Rensselaer Polytechnic Institute

3. Rensselaer Polytechnic Institute
Introduction
Objective: to improve the overall channel quality/ throughput for each transmitter/receiver pair
Method: link layer cooperation scheme for multi-hop wireless networks and sensor networks
Advantage: extract diversity gain out of the redundancy inherently present in all broadcast network transmission
It is widely accepted that wireless ad hoc networks are under physical constraint of wireless nature, such as coarse communication environment, interference of neighboring nodes etc, which is not seen in wired networks. Consequently the performance of the networks is very dependent on the link performance.
To this end, we intend to find ways to improve the overall channel quality/ throughput for each transmitter/receiver pair.
The basic idea is using a link layer cooperation scheme for multi-hop wireless ad hoc networks.
The Advantage is to extract diversity gain out of the redundancy inherently present in all broadcast network transmission.
This is especially suitable for a recourse-constraint environment, such as an energy-constraint sensor network or in a battle field.
11/24/2018
Rensselaer Polytechnic Institute

4. Physical Layer Cooperation
Previous Work:
Physical Layer Cooperation
The information source reaches the first relay cluster.
The nodes in the relay cluster share their information for diversity gain. Then they relay the information to the next cluster.
The next cluster has a reliable channel with the destination node, hence there is no need of physical layer cooperation. A single node can relay the information to the final destination node.
This is an example of how physical layer cooperation takes place. The cluster-by-cluster relaying achieves a MIMO type diversity gain.
With a similar network setting, we use cooperation in link layer, as to avoid the complexity involved in physical layer cooperation.
11/24/2018
Rensselaer Polytechnic Institute

5. Link Layer Cooperation
Stage 1: Cluster head decides if cooperation is necessary
Stage 2: FEC and Code combining among cluster nodes
Stage 3: Use ARQ or transmit diversity if else fail
11/24/2018
Rensselaer Polytechnic Institute

6. Code Combining Procedure
Info pkt
Encoded pkt
Wireless
channel
Received pkt
Viterbi decoder
Estimate of info pkt
11/24/2018
Rensselaer Polytechnic Institute

7. Code Combining Technique
Combine L repeated packets encoded with a code of rate R
Thus obtain a lower rate R/L and more powerful
Viterbi (maximum-likelihood) decoding
The decoding function:
An alternate way is:
where weight for the i th channel
Don’t need to explain all the variables
r – received sequence, vm – codeword indexed by m, we find the optimal codeword among vm
pi - BER for the i th channel
N – pre-combined codeword length
dmi – number of bit disagreements for the i th codeword
11/24/2018
Rensselaer Polytechnic Institute

8. Code Combining with Convolutional Codes: An Example
A (3,1,2) code with an information sequence h =3
001 S 3 S 3 1 1 1 1 1 1 S 1 S 1 1 S 1 1 1 1 1 1
We first assume there is no code combining. This slide represent the Viterbi decoding algorithm for non-combining.
The trellis diagram is actually a state machine, with the state S0,S1,S2,S3 representing different states of the register.
Red numbers are the outputs for each branch. r is the received sequence.
The decoding algorithm finds the optimal path given the received sequence.
(the following is for your understanding only, no need to elaborate):
This code is (n,k,m)=(3,1,2)
X-axis represents time units. The first m=2 time units correspond to the encoder’s departure from state S0, and the last m=2 time units correspond to the encoder’s return to state S0. There are 2^k=2 branches leaving and entering each state. The upper branch leaving each state at time unit i represents the input bit ui=1, and the lower branch represents ui=0. Each branch is labeled with the n=3 corresponding outputs vi, and each of the 2^h=32 codewords of length N=n(h+m)=15 (no combining) is represented by a unique path through the trellis.
Why not use block codes? Block codes are efficient with large blocks. But large block codes increase the complexity of maximum likelihood decoding greatly. S 2 S 2 S 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
000
000
000
000
000 S S S S S S
r = ( 000 , , , , )
11/24/2018
Rensselaer Polytechnic Institute

9. Code Combining with Convolutional Codes: An Example
A (3,1,2) code with an information sequence h =3
Cooperative nodes L=3
Weight for each channel is w1, w2, w3
If w1=w2=w3, the all zero path is chosen.
If w1=1, w2=2, w3=3, then the highlighted path is chosen. S 3 S 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 S 1 S 1 1 1 1 S 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
This slide represents the decoding for combined convolutional codes. The structure (state diagram) is same as the non-combining case, thus the decoding complexity is the same. The only difference is the metric for each branch (since we have more outputs – the black bits).
w1 w2 w3 1 1 1 1 S 2 S 2 S 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 S S S S S S
r = ( , , , , )
11/24/2018
Rensselaer Polytechnic Institute

10. Code Combining with Convolutional Codes in a Uniform Channel Condition
Bit-error prob of the non-combined code:
Bit-error prob of the L-repeated code:
p – BER for wireless channel
- coefficient of power term in B(X), the bit weight enumerating function (WEF) of the convolutional code
- minimum free distance
If we roughly consider each cluster node has same SNR, this means the channel condition is uniform.
11/24/2018
Rensselaer Polytechnic Institute

11. Code Combining with Different Channel Conditions
Bit-error prob of the L-repeated code:
where
is the coefficient in the generating function of r.v. S:
S is a weighted sum of the received sequence
In reality, each node will have different SNR. That is because of the different distance between the node and the sender, different path condition, interference and so on.
11/24/2018
Rensselaer Polytechnic Institute

12. Rensselaer Polytechnic Institute
Simulations
A simple network topology
L = 4
50 or 100 m
250 m
Sender
Cluster head
Since we are more concerned with link performance, we use a single hop network scenario. Results for multi-hop networks will be easily extended.
Sender wants to send packets to the receiver, as the cluster head in the cluster.
Rayleigh fading channel. Nodes (1~4) are randomly (evenly and independently) distributed in cluster with radius of 50m or 100m. Results are averaged among all distributions.
11/24/2018
Rensselaer Polytechnic Institute

13. Link Layer Decoding Performance
Transmission power is proportional to SNR, so we use SNR as a measure of the power (to avoid real numbers used in different energy models). SNR is the SNR measured at the receiving cluster head.
3 levels of transmission power are used, 4dB, 6dB, and 8dB. For each power level, two levels of intra-cluster power (left plot) or two levels of cluster radius (right plot) are used.
L=1 means no cooperation, the traditional node-to-node transmission.
Decoded bit-error rate Pb vs. number of cooperative nodes L. PL is the amount of power deduction of the intra-cluster transmission upon the inter-cluster transmission.
Decoded bit-error rate Pb vs. number of cooperative nodes L with different cluster radius. Smaller cluster radius has a better performance.
11/24/2018
Rensselaer Polytechnic Institute

14. Rensselaer Polytechnic Institute
Energy Consumption
In left plot, again, we use SNR as a measure of the transmission power.
In right plot, the total energy consumption of both sender and the cluster nodes is considered. (If asked: receiving energy, computation energy etc are not considered yet, since they are generally much less compared with transmission energy. )
SNR vs. number of cooperative nodes L. With a fixed objective Pb, the required SNR decreases with the increase of the cluster size L.
Aggregate energy consumption vs. number of cooperative nodes or packet repeats L. A decoded bit-error rate Pb=10-7 is fixed.
11/24/2018
Rensselaer Polytechnic Institute

15. Conclusion and Future Work
Cooperation architecture is effective in improving the link performance and reducing the energy consumption
Less power leads to less interference among nodes, thus can improve the capacity of the wireless networks.
Future work on designs which explicitly exploit physical layer, data link layer, and network layer cooperation among nodes
These designs include:
cooperation-intended cluster-based routing
medium access issues in the intra-cluster communications
network performance from all aspects
more information theoretic analysis of the coding technique and network capacity.
11/24/2018
Rensselaer Polytechnic Institute

16. Rensselaer Polytechnic Institute
Thank you!
For more information:
11/24/2018
Rensselaer Polytechnic Institute