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Minimum Pearson Distance Detection Using Mass-Centered Codewords in the Presence of Unknown Varying Offset

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Abstract

We consider the transmission and storage of data that use coded binary symbols over a channel, where a Pearsondistance-based detector is used for achieving resilience against additive noise, unknown channel gain, and varying offset. We study Minimum Pearson Distance (MPD) detection in conjunction with a set, S, of codewords satisfying a center-of-mass constraint. We investigate the properties of the codewords in S, compute the size of S, and derive its redundancy for asymptotically large values of the codeword length n. The redundancy of S is approximately 3/2 log2 n + α where α = log2 √π/24 =-1.467. for n odd and α =-0.467. for n even. We describe a simple encoding algorithm whose redundancy equals 2 log2 n + o(log n). We also compute the word error rate of the MPD detector when the channel is corrupted with additive Gaussian noise.

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... Then, the re-scaled signal, brought into its standard range, can be forwarded to the final detection/decoding system, where the distance properties of the code can be optimally utilized by applying, for example, the Chase algorithm [58]. A detection scheme for channels with gain and such varying offset is investigated in [59,60], where, for the binary case, minimum Pearson distance based detection is used in conjunction with mass-centered codewords. ...
... Here, we consider the situation in which the offset varies linearly within a codeword, where the slope of the offset, represented by the parameter c, is unknown. A detection scheme for channels with gain and such varying offset is investigated in [59], where, for the binary case, MPD detection is used in conjunction with mass-centered codewords, in such a way that the system is insensitive to both gain and varying offset, i.e., it is (a, b, c)-immune. However, this scheme is very expensive in terms of redundancy. ...
... Another example of constrained code techniques is advocated in [59] with a less redundant option that also guarantees (a, b, c)-immunity. The Pearson distance offers immunity to gain and non-varying offset mismatch [49], and an MPD decoder chooses among all candidate codewordsx ∈ S the codeword x o whose Pearson distance to the received vector r is smallest. ...
... discussed in [9], memory cells of nonvolatile data storage products that are closer to warmer spots lose their data charge more rapidly than memory cells closer to colder spots, so that offset loss is not constant within a codeword [4]. Evidently, the (varying) offset cannot be considered to be equal for all symbols in a codeword, and alternative detection methods have been sought for. ...
... The quest for advanced detection techniques that are immune to unknown, first-order, offset variation is not new. Skachek and Immink [9] introduced mass centered codewords whose detection is independent of both unknown base offset and offset's slew rate. They concluded that the redundancy of their scheme is prohibitively large for many applications. ...
... They introduced Pearson-distance-based detection in conjunction with a difference operator and a pair-constrained code. Their adopted code has significantly less redundancy than the previously proposed mass-centered codes [9]. However, it requires a 3 dB higher noise margin, which makes it less suitable for noise-dominant channels. ...
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... Here, we consider the situation in which the offset varies linearly within a codeword, where the slope of the offset, represented by the parameter c, is unknown. A detection scheme for channels with scaling and such varying offset is investigated in [4], where, for the binary case, MPD detection is used in conjunction with mass-centered codewords, in such a way that the system is insensitive to both scaling and varying offset, i.e., it is (a, b, c)-immune. However, this scheme is very expensive in terms of redundancy. ...
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... The error performance of the MPD detector with the employment of mass-centered codes is insensitive to scaling and varying offset mismatch, i.e., (a, b, c)-immune. However, the redundancy is O(log n) [4]. In this paper, we will propose a less redundant scheme that also guarantees (a, b, c)-immunity. ...
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... Most of the literature related to CS codes is restricted to the design and analysis of fixed-length codes [1], [9]- [11]. However it has been shown that simple, variable-length CS codes can have higher maximum possible code rates and lower implementation complexity than fixed-length codes [2]- [4], [12]- [16]. ...
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... The authors assume that the offset is constant (uniform) for all symbols in the codeword. In [10], it is assumed that the offset varies linearly over the codeword symbols, where the slope of the offset is unknown. The error performance of Pearson-distance-based detectors is intrinsically resistant to both offset and gain mismatch. ...
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