SNR Definition for Magnetic Recording Channels with Transition Noise

This letter proposes a new signal to noise ratio (SNR) definition for magnetic recording channels with both additive and medium noise components. The proposed SNR is a generalized version of o b N E / , the information bit energy to noise spectral height ratio, widely used in average power constrained communication channels with additive white noise. The goal is to facilitate comparison of efficiencies of read channels that may operate at different symbol densities due to varying code rates. Revised on April 19, 2000 This work is supported in part by NSIC and NSF under Grant No. CCR-9805195. Correspondence to: Prof. Jaekyun Moon Department of Electrical and Computer Engineering University of Minnesota 200 Union St. S.E. Minneapolis, MN 55455 TEL: 612-625-7322 FAX: 612-625-4583 e-mail: [email protected] SNR definition for magnetic recording with transition noise 1 SNR Definition for Magnetic Recording Channels with Transition Noise Jaekyun Moon CDSLab, University of Minnesota October 6, 1999 Abstract -This letter proposes a new signal to noise ratio (SNR) definition for magnetic recording channels with both additive and medium noise components. The proposed SNR is a generalized version of o b N E / , the information bit energy to noise spectral height ratio, widely used in average power constrained communication channels with additive white noise. The goal is to facilitate comparison of efficiencies of read channels that may operate at different symbol densities due to varying code rates. SNR Definitions for Additive Noise Channels We wish to define the signal to noise ratio (SNR) in such a way that we can compare efficiencies of different codes/detectors running at different symbol densities based on the SNR required to meet a fixed BER target. As such, the SNR definition should be free of the symbol density. However, the statistical properties of medium noise depend on the written pattern as well as the symbol (or written bit) density, and defining an SNR to meet this goal is not a trivial matter. Let us first review SNR definitions for additive noise channels. In communication channels with additive white noise (AWN) and an average transmitter power constraint, the o b N E / ratio, the information bit energy to noise spectral height ratio, serves this purpose. It is well known that the error probability of such systems is mainly determined by the ratio T N P N rE N E o s o b o s com / (1)This letter proposes a new signal to noise ratio (SNR) definition for magnetic recording channels with both additive and medium noise components. The proposed SNR is a generalized version of o b N E / , the information bit energy to noise spectral height ratio, widely used in average power constrained communication channels with additive white noise. The goal is to facilitate comparison of efficiencies of read channels that may operate at different symbol densities due to varying code rates. SNR Definitions for Additive Noise Channels We wish to define the signal to noise ratio (SNR) in such a way that we can compare efficiencies of different codes/detectors running at different symbol densities based on the SNR required to meet a fixed BER target. As such, the SNR definition should be free of the symbol density. However, the statistical properties of medium noise depend on the written pattern as well as the symbol (or written bit) density, and defining an SNR to meet this goal is not a trivial matter. Let us first review SNR definitions for additive noise channels. In communication channels with additive white noise (AWN) and an average transmitter power constraint, the o b N E / ratio, the information bit energy to noise spectral height ratio, serves this purpose. It is well known that the error probability of such systems is mainly determined by the ratio T N P N rE N E o s o b o s com / (1) where s E is the symbol energy, r is the code rate, and s P denotes the average transmitter power. This ratio is sometimes referred to as the detection SNR. The penalty associated with the code rate loss is apparent in (1). For magnetic recording channels with AWN, o t N E / , the isolated transition pulse energy to noise spectral height ratio, can serve this function as discussed in [1]. A magnetic recording channel can be viewed as the “h(t)-constrained” channel, where h(t) is the channel’s response to a single transition; there is no average or peak power constraint here, but for a given head/medium interface h(t) is fixed and coding and signal processing engineers must live with it. At low to medium recording densities, where single errors are more likely than multiple errors, the detection SNR of an optimal sequence detector is given by SNR definition for magnetic recording with transition noise 2 o d o mag N E T N dt T t h t h T