Wednesday, February 17, 2010

PPM Explained

Math is hard, and lots of people are bad at it. They find it intimidating and frustrating. I include myself. It's a shame really since math is one of the few things which can contain actual, unadulterated, indisputable, non-partisan truth. To that point, despite those good qualities, it can be hard to understand. In that category PPM is so complicated that it's nearly impossible to explain to a layperson at all.

What's changed is how listening is tracked. So lets start there. In PPM a signal is embedded in the radio stations broadcast. But what kind of signal? How is it embedded? the signal is called a watermark. It is a sub-audible signal in the audio. It's not in the carrier wave, it's not RDS. It's actually in the audio. Arbitron actually has a device in the transmission chain that embeds a station identification code into the audio at each individual radio station.

Watermarking isn't exactly inaudible. I've done a few controlled tests to see if I can hear a supposedly inaudible watermark. Interestingly, I can detect it by ear, but only when comparing to source audio (about 70% of the time.) The watermark is a modification of the source audio that either adds to or changes existing audio. Watermarks are measured in three very specific ways. Robustness, Perceptibility and Capacity. These first two exist in total opposition. RBR reported that this had even come into play with PPM deployment. I quote:
"Anecdotal reports from radio broadcasters say that Arbitron lowered the watermarking energy in response to complaints about the watermarking being audible in certain circumstances."
A digital watermark is called robust with if it is detectable in the marked audio even if degraded by a number of transformations. Perceptibility is more binary. Since a watermark you can find by ear is useless we have a mushy adjective called "non-intrusive." Some watermarks are truly imperceptible, but the best ones are perceptible but non-intrusive. Capacity is how much data you can put in it.There are three primary ways to embed water marks. They can be used in tandem: Spread Spectrum, Amplitude Modulation, and Quantization. You probably figured out by the quote that PPM includes some Amplitude modulation. The PPM system takes 10 audio bands between 1 and 3 kHz. In the image above I've increased the amplitude of that region so you can see all ten peaks. But to reduce perceptibility, all 10 bands don't run full-tilt all the time. Each channel will have 4 frequencies within it. The identifying data will only be injected in one of them at any time, and only then if the energy (amplitude) of the channel is great enough to render the injected watermark imperceptible. This is of course patented.

Each of the four "injectable" frequencies represents 2 bits of data. I don't know the refresh rate but 500 ms rate was suggested and seems reasonable. This would produce a total of 40 bits per second or 2,400 bits per minute to encode a watermark. RBR suggested A unique ID might only consist of 50 bits. I think it could be done with less. There are only 14,000 stations in the US. Error rates will eat into this but multiple IDs per minute should be common. Compare that to a diary-based system.