Abstract: The present invention provides a high-speed decoder for decoding signals encoded into Nordstrom-Robinson 16,256,6 non-linear code. The novel decoder receives a transmitted encoded signal in the form of a multi-dimensional vector to be decoded. The decoder comprises a plurality of computing elements coupled to the input encoded signals and produces modified multi-dimensional vectors and subcode values which are decoded in a plurality of subcode decoders to produce intermediate inner product values and information words associated with the intermediate inner product values. The intermediate inner product values are compared in comparator means to provide the maximum intermediate inner product value and its associated information which is indicative of the best mathematical estimate of the encoded signal being decoded.

Abstract: Described is a novel technique and associated arrangement for determining the noise-free value of a system parameter (e.g., head position in a disk drive) which is time variable and (usually) has a noise component as detected. The technique involves processing the (as detected) noise-including value and passing it through "Second Order/Summing" filter means.For instance, the technique is described as particularly useful with the "track-following servo" (part of the transducer positioning means) in a high density disk file (where track density is higher than usual) to secure superior head-displacement error values which are more noise-free. Thus, (see FIG. 4), a pair of first values V.sub.a, V.sub.b are secured by detecting motor current sense voltage V.sub.i, integrating it with respect to time and passing the result through a pair of novel "second order filter" means--one hand-pass (F.sub.1) the other low-pass (F.sub.2); while also securing a third value V.sub.