Experimental Comparison of Pulse Code Modulation Codes for Magnetic Recording

Abstract

The bit error probability (BEP) versus signal-to-noise ratio (SNR) was experimentally determined for Non-Return-to-Zero-Level (NRZ-L), Bi-Phase-Level (BIΦ/-L), Delay Modulation (DM) and Miller Squared (M²) codes for a bandpass channel. This was done by passing the data through a 400 Hz to 500 kHz Bessel bandpass filter and linearly adding noise. The power spectral density of the noise was shaped to match the noise out of an analog magnetic tape recorder running at 30 inches per second (in./s). This provided a simulation of an optimum wideband 2.0 MHz tape recorder running at 30 in./s (no flutter, tape dropouts, etc.). The bit rate, pattern, and code to be tested were then selected. The SNR was varied until the bit error probability was approximately 10⁻⁶ With a commercial Pulse Code Modulation (PCM) bit synchronizer with a "good" dc restorer and a pseudo-random pattern at 1.0 megabits per second (Mb/s) (33.3 kilobits per inch (kb/in.) equivalent packing density), NRZ-L had a 4 dB SNR advantage over DM and a 14 dB advantage over BIΦ/-L for a BEP of 10⁻⁶ through the bandpass channel. At 1.5 Mb/s, NRZL had a 6 dB advantage over DM and a 10⁻⁶ BEP was not achievable with BIΦ/-L coding. For a synchronizer with no dc restoration NRZ-L had only a 1 dB advantage over DM at 1.0 Mb/s and also only a 1 dB advantage at 1.5 Mb/s. M² gave the same results as DM for pseudo-random data. However, M² was relatively insensitive to patterns while DM and NRZ-L required a higher SNR with a "good" dc restorer and lost synchronization completely with no dc restorer for worst case 16-bit repeating patterns.