Non-Binary LDPC Codes for Magnetic Recording Channels: Error Floor Analysis and Optimized Code Design

LOCO Codes: Lexicographically-Ordered Constrained Codes

“…It is of course possible to protect all the bits of the LDPC code, but our method limits the rate loss. Our demonstration uses a modified version of the PR system described in [9], and a spatially-coupled (SC) LDPC code constructed as in [27]. 3) We prove that the inherent symmetry of LOCO codes makes balancing easy.…”

“…PR channel: We use the PR channel described in [9]. The MR channel effects are inter-symbol interference (intrinsic memory), jitter, and electronic noise.…”

“…The MR channel effects are inter-symbol interference (intrinsic memory), jitter, and electronic noise. The channel density [9], [29], which is the ratio of the read-head pulse duration at half the amplitudes to the bit duration, is swept to generate the plots. The signal-to-noise ratio (SNR) is 13.00 dB.…”

“…Constrained codes were used to extend the life of MR systems employing peak detection, and they continue to be used in modern MR systems [5], [6] to improve the performance of sequence detection on partial response (PR) channels such as extended PR4 (EPR4 and E 2 PR4) channels [7], [8]. PR channels with equalization targets that follow the channel impulse response [9] require forbidden patterns to be symmetric. Moreover, constrained codes improve the performance on low resolution media by preventing short pulses, which might be missed when reading [10].…”

“…From Table IV, the C-LOCO code C c 90,1 has rate 0.6923 and adder size 63 bits. The same rate is achieved in [26] for an RLL code with d = 1 at code (resp., message) length 13 (resp., 9) bits. However, the technique in [26] is based on lookup tables; thus, the complexity of the encoding and decoding is governed by lookup tables of size 2 9 × 13 = 6656 bits.…”