Analysis of error sequences for PRML and EPRML signaling performed over Lorentzian channel

On codes that avoid specified differences

“…The superscript then represents the column indexes (modulo the period) in which the pattern cannot appear. For example, 101; 010 means that these triples do not appear in any three consecutive columns, and 10 (0) ; 01 (1) means that 10 does not appear in columns [i; i + 1] for even i and 01 does not appear in columns [i; i + 1] for odd i.…”

“…Several of these constraints have appeared in the magnetic recording literature. O = f00 (1) ; 11 (1) g is referred to as the biphase constraint [30], O = f1010;0101g as the MTR constraint [5], and O = f1010 (1) ; 0101 (1) g as the TMTR constraint [6].…”

“…At high signal-to-noise ratios (SNRs), the probability of a bit error for this detector is well approximated, e.g., [12], by Pr(bit error) e P (e) wgt(e)Q d e (e) 2 (1) where wgt(e) is the number of 61s in e, and…”

“…where the parameter measures the density of the recording. It was shown in [1] that for x = (1; 1; 01; 01) and 1:5 2:75, a target response and a density range of practical interest, the minimum effective distance difference pattern is contained in the set D = f000(+0) k 00; 000 + (0+) k 000g where ( 1 ) k denotes k 1 repetitions of ( 1 ), and we use a shorthand notation to represent the ternary difference patterns, i.e., +00 is used to denote +1, 0, 01. The bit-error probability is well approximated over this range of densities by taking k = 1, i.e., D = f000 + 000; 000 + 0 + 000g:…”

“…The error probability of many magnetic-recording systems may be characterized in terms of the differences between the sequences that may be recorded [1]- [3]. In fact, the bit-error rate (BER) is often dominated by a small set of potential difference patterns.…”