Generalized Threshold Decoding of Convolutional Codes

It is shown that any rate l/b systematic convolutional code over GF(p) can be decoded up to its minimum distance with respect to the decoding constraint length by a one-step threshold decoder. It is further shown that this decoding method can be generalized in a natural way to allow “decoding” of a received sequence in its unquantized analog form

SOME RESULTS ON THE BEST MATCH PROBLEM

The best-match problem is concerned with the complexity of finding the best match between a randomly chosen query word and the members of a randomly chosen set of data words. Of principal interest is whether it is possible to significantly reduce the search time required, as compared to exhaustive comparison, by use of memory redundancy (file structure). Minskv and Papert conjecture that the speed-up values of large memory redundancies is very small, and for large data sets with long word lengths there are no practical alternatives to large searches that inspect large parts of memory . For this report we present two algorithms that do yield significant speed-up, although at the cost of large memory redundancies. (Whether these algorithms constitute counterexamples to the Minskv-Papert conjecture depends on one\u27s interpretation of their term “large memory redundancies .) The algorithms are subjected to statistical analysis and time-memory trade-off curves are given

DUAL-MODE SEQUENTIAL LOGIC FOR FUNCTION INDEPENDENT FAULT-TESTING

This paper presents a method of using hardware redundancy to ease the problem of fault testing in sequential logic networks. Sequential logic networks are constructed using two kinds of dual-mode logic gates, one of which is specifically required to initialize a feedback loop to some logic value. Initially, it is shown that these networks can be tested for all single stuck-at-faults with six function-independent tests. Next, this method is generalized to detect large classes of multiple faults with six function-independent tests. In both cases, the network must have the proper number of extra inputs

SOME RESULTS ON THE DISTANCE PROPERTIES OF CONVOLUTIONAL CODES

Rate 1/2 binary convolutional codes are analyzed and a lower bound on free distance in terms of the minimum distances of two associated cyclic codes ìs derived. Next, the complexity of computing the free distance is discussed and a counterexample to a conjecture on the relationship of row distance to free distance for systematic codes Ìs presented. Finally, an improved Gilbert bound for definite decoding is derived

A Note on the Free Distance of a Convolutional Code

A counterexample to a conjecture on the number of constraint lengths required to achieve the free distance of a rate l/n systematic convolutional code is presented

An Optimum Symbol-by Symbol decoding rule for linear codes

A decoding rule is presented which minimizes the probability of symbol error over a time-discrete memoryless channel for any linear error-correcting code when the code words are equiprobable. The complexity of this rule varies inversely with code rate, making the technique particularly attractive to high rate codes. Examples are given for both block and convolutional codes

Generalized Finite-Geometry Codes

A technique is presented for constructing cyclic codes that retain many of the combinatorial properties of finite-geometry codes, but are often superior to geometry codes. It is shown that L-step orthogonalization is applicable to certain subclasses of these codes

Decoding by Sequential Code Reduction

A general decoding method for cyclic codes is presented which gives promise of substantially reducing the complexity of decoders at the cost of a modest increase in decoding time (or delay). Significant reductions in decoder complexity for binary cyclic finite-geometry codes are demonstrated, and two decoding options for the Golay code are presented

On APP Decoding

In this paper we show that APP decoding for a linear code C is optimum not for C, but for a minimum-distance-2 code which contains C as a subcode when the codewords of are transmitted with equal probability. However, APP decoding is shown to be a symptotically optimum for C for high SNR when C is a binary one-step orthogonolizable code with equiprobable codewords transmitted over the AWGN channel

Transcription-dependent spatial arrangements of CFTR and adjacent genes in human cell nuclei

We investigated in different human cell types nuclear positioning and transcriptional regulation of the functionally unrelated genes GASZ, CFTR, and CORTBP2, mapping to adjacent loci on human chromosome 7q31. When inactive, GASZ, CFTR, and CORTBP2 preferentially associated with the nuclear periphery and with perinuclear heterochromatin, whereas in their actively transcribed states the gene loci preferentially associated with euchromatin in the nuclear interior. Adjacent genes associated simultaneously with these distinct chromatin fractions localizing at different nuclear regions, in accordance with their individual transcriptional regulation. Although the nuclear localization of CFTR changed after altering its transcription levels, the transcriptional status of CFTR was not changed by driving this gene into a different nuclear environment. This implied that the transcriptional activity affected the nuclear positioning, and not vice versa. Together, the results show that small chromosomal subregions can display highly flexible nuclear organizations that are regulated at the level of individual genes in a transcription-dependent manner