Equivalent Results: A methodology to measure the effects of high-speed compression

For signal processing engineers that design DSP systems with high-speed A/D and D/A converters, compression has not really been an available option for reducing bandwidth and storage bottlenecks. After all, at sample rates above 20 Msamp/sec, no useful compression algorithms exist. Available algorithms for speech, audio, and video come with significant drawbacks that preclude their use at sample rates above 10 Msamp/sec. For instance, a radar engineer can't apply the frequency response of human hearing (an integral part of the MP3 audio compression algorithm's psychoacoustic models) to her radar signals. Similarly, a wireless hardware engineer can't divide his W-CDMA or WiMax signal into 10-msec blocks, just so speech compression can be used.

If compression is really going to be useful for engineers using high-speed DSP, wouldn't the compression be restricted to some kind of lossless compression, such as WinZIP? And if not, wouldn't lossy compression be a non-starter for such high-speed signals? This article introduces a new concept for high-speed signal processing: equivalent results using high-speed compression. By using the concept of equivalent results, we discover answers to these questions concerning the effects of high-speed compression.

Motivation: Compression's benefits
Thanks to consumer electronic products introduced since 2000, the concept of equivalent results is already in the engineering consciousness. When MP3 audio was first introduced in the 1990s, many people were skeptical at first: how could a compression algorithm throw away 9 out of 10 bits (10:1 compression) without significantly affecting audio quality? But given the success of Apple Computer's iPod and iTunes, and many other MP3 players, the market has already decided that for audio, equivalent results at 10: 1 compression means "the audio quality is good enough for my listening expectations." Most consumers would rather carry more songs around with them than drag around uncompressed audio files, despite the "better" quality of uncompressed audio. For MP3 audio consumers, equivalent results means "sounds good enough to me, compared to the original."

Similarly, digital video disks (DVDs) use a video compression algorithm called MPEG (Motion Picture Experts Group) that compresses video by 20:1. Given the widespread adoption of DVD technology, most people now agree that the quality of MPEG compression is "good enough for my viewing tastes." Again, the benefit of fitting a long-form movie on a single DVD outweighs the need to store the video in its pristine, uncompressed format.

How do I measure equivalent results for high-speed signals?
Let's now describes how equivalent results are measured. Fig 1 shows a generic DSP system that processes samples from an A/D converter or other source of sampled data. We'd like to compare the performance of that DSP system with an alternate system that uses compression to achieve better performance (cheaper, faster, smaller, etc.), just as MP3 systems use audio compression to reduce the cost and increase the convenience of listening to music.

1. Equivalent results block diagram.

All DSP systems have at least two or three system metrics. Often these metrics are imposed by industry standards, but such system metrics may also come from a marketing requirements document or product specification. Examples of system metrics include signal-to-noise ratio (SNR), bit error rate (BER), signal spectrum, out-of-band signal rejection ratio, rise time/fall time, jitter, etc. The important thing for equivalent results is that the system metrics are measurable and quantifiable. Once we've identified our system's relevant metrics, determining equivalent results is as simple as comparing the system metrics of the original DSP system without compression to the improved (cheaper, faster, smaller) DSP system that benefits from compression.

Most compression algorithms are lossy, so the samples after compression differ in some way from the original samples that were compressed. Examples of lossy compression algorithms include MP3 and Windows Media Audio (WMA) for audio samples, linear predictive coding (LPC) and adaptive differential pulse code modulation (ADPCM) for speech samples, Joint Photographic Experts Group (JPEG) for digital cameras, and MPEG and H.264 for video. For these speech, audio, and video compression algorithms, equivalent results means "humans don't notice a difference." As most of us have experienced, the benefits of compression (reduced storage and bandwidth requirements) are compelling enough to overcome our suspicions about compressed audio or image quality. We like what we hear and see, so these lossy compression methods for speech, music, photos, and video are acceptable.

An important point about Fig 1 is that the amount of compression used in a high-speed DSP system is adjustable. MP3 audio and JPEG image compression algorithms offer a variety of compressed bit rates. For example, we might use 192 kbps for classical music on our MP3 player but can live with 128 kbps for hard rock. We might want 3:1 compression for a family portrait on our digital camera but can live with 8:1 compression for everyday snapshots. By adjusting the amount of compression, users can trade off a signal's bit rate and its quality. In mathematical terms, users are selecting an operating point on their signal's rate-distortion curve, which is unique for each unique signal. Just as the amount of acceptable audio compression depends on the kind of audio being compressed, the amount of compression that generates equivalent results varies from signal to signal.

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