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Trellis based detection with pattern dependent noise prediction (PDNP) has become standard practice in the HDD industry. In a typical single-track signal processing scheme, the received samples from the read head are first filtered by a linear equalizer with a 1D partial response (PR). The linear filter output flows into a trellis-based (e.g. BCJR) detector that employs a super-trellis based on the PR mask ISI channel and a 1D pattern dependent noise prediction (1D PDNP) algorithm. The effective channel model has a media noise term which models signal dependent noise due to, e.g., magnetic grains intersected by bit boundaries. The media noise can influence two or more bit readback values. The trellis detector sends soft estimates of the coded bits to a channel decoder, which outputs estimates of the user information bits. There are two problems with traditional PDNP. First, when the number of tracks Nt simultaneously processed is greater than one, e.g. in two-dimensional magnetic recording (TDMR), the number of trellis states can become impractically large; this is the state explosion problem. Second, the relatively simple autoregressive noise model and linear prediction used in PDNP is somewhat restrictive and may not accurately represent the media noise, especially at high storage densities; this is the modeling problem. To address the state explosion problem, we separate the ISI detection and media noise prediction into two separate detectors and use the turbo-principle to exchange information between them, thus avoiding use of a super-trellis. To address the modeling problem, we design and train deep neural network (DNN) based media noise predictors. As DNN models are much more general than autoregressive models, they give a more accurate model of magnetic media noise than PDNP; this more accurate modeling results in reduced detector BERs compared to PDNP.
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The Geometry of Community Detection via the MMSE Matrix
The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow for variability in the sizes and behaviors of the different communities, and thus better reflect the behaviors observed in real-world networks. Our results show that the ability to detect communities can be described succinctly in terms of a matrix of effective signal-to-noise ratios that provides a geometrical representation of the relationships between the different communities. This characterization follows from a matrix version of the I-MMSE relationship and generalizes the concept of an effective scalar signal-to-noise ratio introduced in previous work. We provide explicit formulas for the asymptotic per-node mutual information and upper bounds on the minimum mean-squared error. The theoretical results are supported by numerical simulations.
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- Award ID(s):
- 1750362
- PAR ID:
- 10139964
- Date Published:
- Journal Name:
- 2019 IEEE International Symposium on Information Theory (ISIT)
- Page Range / eLocation ID:
- 400 to 404
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ISIT.2019.8849594
