# Wireless communications outage

For communication systems, there is usually a target minimum rate $$R$$ bits per second. An outage occurs if the actual rate ever falls below $$R$$. Since $$\frac{1}{2}\text{log}_2(1+\text{SNR})$$, sometimes outage is also talked about in terms of $$\text{SNR}$$ and received signal power needing to be greater than some threshold $$P$$.

My question is: Say I have a very small packet of five symbols, and during the second symbol I experience an outage. The other four symbols received power was all greater than $$P$$. Does this mean that my entire packet was unable to be decoded?

EDIT:

For example, if I use the encoding scheme where: 0 = 00000, 1 = 11111, then I have 1 bit per 5 channel uses. So I can use the formula: $$\frac{1}{2}\text{log}_2(1+\text{SNR})=\frac{1}{5}$$ bits per channel use, and can solve for the required $$\text{SNR}=0.3195$$. Does this mean that all five symbols should have $$\text{SNR}\geq0.3195$$ in order to successfully receive the single bit?

• Making sure I understand your formula - it looks like the Shannon channel capacity equation C = B log2(1 +SNR). Where does the 1/2 come in in your use? From the capacity formula this is suggesting your channel bandwidth is 1/2 and the bound on the achievable error free rate in that case is 1/5 bits per second? – Dan Boschen Dec 12 '19 at 15:47
• But to your final question: No. The simple counter example is to consider one bit with significantly less SNR (and clearly be in error) while at least three of the bits are significantly higher SNR (and clearly error free). – Dan Boschen Dec 12 '19 at 15:53
• I'm reading out of this book Equation 5.7 web.stanford.edu/~dntse/Chapters_PDF/… – Engineer Dec 12 '19 at 16:16