Abstract: Two different ways of obtaining generalized low-density parity-check codes are considered. Lower bounds on the minimum distance, stopping distance, and pseudodistance are derived for these codes using graph based analysis. These bounds are generalizations of Tanner’s bit-oriented and parity-oriented bound for simple LDPC codes. The new bounds are useful in predicting the performance o...

We generalize Sudan’s list decoding algorithm without multiplicity to evaluation codes coming from arbitrary order domains. The number of correctable errors by the proposed method is larger than the original list decoding without multiplicity.

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We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.

Two decoding procedures combined with a beliefpropagation (BP) decoding algorithm for low-density parity-check codes over the binary erasure channel are presented. These algorithms continue a decoding procedure after the BP decoding algorithm terminates. We derive a condition that our decoding algorithms can correct an erased bit which is uncorrectable by the BP decoding algorithm. We show by s...

Although evidence suggests that individual differences in reading and mathematics skills are correlated, this relationship has typically only been studied in relation to word decoding or global measures of reading. It is unclear whether mathematics is differentially related to word decoding and reading comprehension. The current study examined these relationships at both a phenotypic and etiolo...

The previous are identical to the expressions (2) and (3). Thus the n 1 columns do consist of two repetitions of 2”-r-level Gray code. Now if we combine the first two columns again, we reduce each 2”-‘-level Gray code into two 2n-2-level Gray codes, or, the complete array into four 2”-2-level Gray codes. This can continue until we have only m columns, which would be 2n-m repetitions of 2”‘-leve...

Given an algebraic geometry code CL(D,αP ), the GuruswamiSudan algorithm produces a list of all codewords in CL(D,αP ) within a specified distance of a received word. The initialization step in the algorithm involves parameter choices that bound the degree of the interpolating polynomial and hence the length of the list of codewords generated. In this paper, we use simple properties of discrimi...