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Abstract

Decoders minimizing the Euclidean distance between the received word and the candidate codewords are known to be optimal for channels suffering from Gaussian noise. However, when the stored or transmitted signals are also corrupted by an unknown offset, other decoders may perform better. In particular, applying the Euclidean distance on normalized words makes the decoding result independent of the offset. The use of this distance measure calls for alternative code design criteria in order to get good performance in the presence of both noise and offset. In this context, various adapted versions of classical binary block codes are proposed, such as (i) cosets of linear codes, (ii) (unions of) constant weight codes, and (iii) unordered codes. It is shown that considerable performance improvements can be achieved, particularly when the offset is large compared to the noise.

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... A novel decoding algorithm for the concatenated scheme is proposed, aiming to exploit its error correction potential better. The concatenation is between a Reed-Solomon (RS) code and a certain coset of a block code proposed in [66]. The modified Pearson distance detection is used to decode the inner code. ...
... For the noisy channels with unknown offset, we design a concatenated code. A Reed-Solomon (RS) code [69] and a certain coset of a binary block code proposed in [66] are used as outer and inner codes, respectively. The two codes are chosen according to a rule that the inner code is of a short length. ...
... Binary block codes proposed in [66] work well with the modified Pearson distance based decoding criterion (2.39), which guarantees immunity to channel offset mismatch. Note that for any binary linear block code S containing the all-one vector, the minimum δ P distance is zero since δ P (0, 1) = 0. ...
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