1. Improving Loss Resilience with Multi- Radio Diversity in Wireless Networks by Allen Miu, Hari Balakrishnan and C.E. Koksal Appeared in ACM MOBICOM 2005, was considered as a candidate for the best paper award.

2. What is the paper about? The paper looks at multi-radio diversity and uses the fact that the fading experienced at the different radios are different to improve performance in WLANs. The major contribution of this paper is that it proposes a new technique called “Frame Combining” using which, it tries to combine two frames received by the two radios, in error, to reconstruct the transmitted frame. The effort is “thorough”; the authors do an implementation of their proposed approach, provide some analytical insights and also do simulations to study the problem deeper.

3. What did I learn from this paper? Obtained insights into how much, and why, multi-radio diversity can help improve performance. How does any kind of diversity affect “rate control” ? (to some degree) Some interesting interactions between the physical, MAC and network layers which I will highlight in the presentation.

4. What I will do I will not present 100% of the paper -- time constraints. I will go over it as thoroughly as I can in the rest of the time. You should read the paper and get back to me if you have comments/questions.

5. The MRD System The idea is to use multiple radios or multiple APs in a wireless LAN to simultaneously receive transmitted frames. Why does this help ? -- The radios are not spatially collocated. Thus, the wireless channel to the two radios differ (path diversity) –Thus the errors experienced at one radio, would differ from that at the other. So, you would get two copies of a transmitted frame, but possibly at errors at different locations. –Of course, if one of the frames is error free, that can be delivered to the IP layer (selection diversity). –If not, can we combine the corrupted frames ?

6. A High level view Note: Unless I state otherwise, all figures that I have are from the paper itself. Of the two APs, one is called an active AP -- it is in communication with the client. The others passively listen and try to gather frames.

7. What are the challenges ? How does this frame combining (done at a layer that sits above the MAC) interact with the 802.11 MAC and the PHY layer ? –Specifically, the frame combining make take some time, and so how can you acknowledge and provide retransmissions of “reconstructed” or “salvaged” frames ? –How does this frame recombining work with the auto rate control ? –How are the bit errors distributed ? Can frames even be salvaged and if so how ? The paper tries to address these questions while proposing a new technique for frame combining.

8. Frame Combining The idea is simple. Divide each frame into N B blocks, each of fixed size (the last block may possibly have fewer bits). Let us say we want to see if we can reconstruct the frame from two copies that are received. –Clearly if any of the copies is ok (CRC is ok), then, the packet is successful. We look at those blocks that differ -- as an example, the i th block of the first copy might differ from that of the second copy. Assemble a combined frame with different possibilities --choosing different blocks from either of the copies. If CRC passes, then a success.

9. More about frame combining What should the block size be ? Note that the previous combining method is simple, but its running time is exponential in terms of the number of differing blocks . If you have two copies, then you need about 2  CRC check operations. So, clearly you want to keep  small; which means that you may want to reduce the total number of blocks i.e., increase B, the number of bits per block. However, if you do this, then, the possibility of successfully recombining reduces (Why ?).

10. Analyzing Frame Combining Let the frame combining failure probability be p f. Let there be a bit error model characterized by “bursts” of “b” bit errors. p f is the fraction of frames that cannot be corrected with combining out of those that could not be corrected by the soft selection. The assumption made is that the loss rates observed at the two receivers are independent of each other. -- The paper corroborates this claim by experimental results. The errors are clustered and occur with a periodicity.

11. Bit Errors The authors claim that the error pattern is in line with what is used. QAM-64 modulation on OFDM with a rate 2/3 code. With QAM-64, you transmit 6 bits/symbol. This means, that for each transmission on 50 OFDM carriers, you have ~ 50 x 6 = 300 bits. Since you use a rate 2/3 code, you decode 3 symbols at a given time -- each carrier carries 3 symbols. Thus, you have approximately 900 bit transmission patterns on the different carriers that repeat. Since each carrier is likely to experience similar fades periodically (static), the error distribution repeats about 1000 s.

12. Assumptions made for computing p f In order to compute the frame combining failure probability p f, the authors make the following assumptions: The burst of errors is of fixed to “b” bits. The number of bits per block “B” is much larger than b and thus: – the probability that two blocks have errors that overlap is negligible. –they ignore the possibility that the block can spread over more than one block -- i.e., the errors are completely contained within a block. –the number of burst errors that a block can hold are not fixed. Note that given that b ~ 300 bits and a block is more than say 200 bytes, these are reasonable assumptions.

13. Notations and some details D b,i -- number of b-bit sequences with errors in a given frame received at receiver R i. N 1 and N 2 represent the sets of blocks that contain errors in frames received at receivers 1 and 2. Note that two receivers are considered. Then, the intersection of the two sets N 1 and N 2 represent those blocks that have errors in both frames. Now, if this intersection ( N 1  N 2 ), contains no errors, then, it means that the frame can be decoded.

14. Computing p f First, assume that bit error sequences (b bits in error) occur uniformly over the frame. Let frame 1 have d 1 errors and frame 2 have d 2 errors. Then, Why is this true ?

15. This is similar to the problem wherein we have N B buckets, and d 1 balls; we put the balls (probably more than N B ) into those N B buckets. We want to compute the number of ways in which we can put balls into these buckets. Note that some buckets may have multiple balls and so we can have empty buckets.

16. So, we have the first N B buckets, and in addition have (d 1 - 1) dummy buckets. Note that there is at least one bucket which contains balls (all balls). If a ball falls into a non-empty bucket, we put the ball into one of the dummy buckets. Thus, the total ways we can do what we want is to choose d 1 buckets out of the N B + d 1 -1 buckets.

17. Given this.... We remove the conditioning to get: where: Note : This is an upper bound on the frame combining failure probability.

18. Looking at p f Note that if the burst error size is small, errors are more uniform, and even for large N B, probability of combining successfully is small. With bursty errors (as observed), p f gets lower with N B. But beyond a certain point, increasing N B does not help much.

19. What does this mean? It is necessary to keep N B small, so as to reduce complexity. So, N B can be set to a small value (6-10) and still performance is ok.

20. We will continue with this paper next Tuesday. In the meantime, please read it and come. Thursday, Eric Law will present a paper from INFOCOM 2006.