# Addendum

## A. Loss Independence

We expand on the results presented in **Table 1** in **Section
3.1** of our paper to show further evidence of loss independence among
a set of simultaneous receivers. The results were presented during my
talk at MobiCom 2005 but were not included in time for the camera-ready
due date.
We ran a broadcast experiment involving six simultaneous 802.11a
receivers at a bit rate of 48 Mbps. The six receivers are distributed
at various locations near the sender. The sender broadcasted 100,000
1500-byte UDP frames, each uniquely numbered, at saturation rate.

We then take each pairwise combination of the six receivers and for
each receiver pair, we computed the frame loss rates (FLR) at the
individual receivers (R1 and R2), and the simultaneous loss rate at both
receivers (i.e., the rate at which both receivers observe a loss for the
same UDP frame). In contrast to **Table 1**, which presented the results
for one receiver pair, we plot the results for a total of 6 choose 2 =
15 receiver-pair combinations to test for loss independence.

This scatter plot (click to see full res.) plots the individual FLR
(the circles and triangles, on the y-axis) vs. the simultaneous FLR
(x-axis) for each pairwise combination of receivers. Note that there are
a total of 15 circles and 15 triangles. The plot shows that the
individual FLR are greater than the simultaneous FLR, which suggests
losses are not totally correlated between the two receivers within each
pair.

To test independence, we plot the product of the individual FLRs
(star) vs. simultaneous FLR. The plot shows that the product value lie
roughly on the *y=x* line, which suggest that the product of losses
are roughly equivalent to the joint loss probability (simultaneous
losses). Thus, our results suggests a high degree of loss independence
among receivers in our experiments.

Note that the same experiments and analysis are used to generate the
results in **Table 1** in **Section 3.1**. In fact, the values of
three of the points in the scatter plot appear in **Table 1**.

## B. Related Work

The idea of extending frame combining to spatial domain was also
proposed by Liang and Chakraborty in the following references:
Liang, Y., and Chakraborty, S.S. ARQ and packet combining with
post-reception selection diversity. In IEEE VTC, vol. 3, pp. 26-29,
(September 2004).

Chakraborty, S.S., Liinaharja, M., and Ruttik, K. Diversity and packet
combining in Rayleigh fading channels. In IEE Proc. Communications,
vol. 152, no. 3, pp. 353-356, (June 2005).

# Errata

1. Caption for **Figure 10** should read: Trace-driven simulation of
`p_f` and `\Delta`` for various values of ``N_B` in
the `HIVAR MRD-R1` experiments.

For feedback and questions, please email the contact author Allen Miu at
*aklmiu [at] mit [dot] edu*.