Regular partitionsDedekind eta-functionModular formsWe give a complete characterisation of the parity of b(8)(n), the number of 8-regular partitions of n. Namely, we prove that b(8)(n) is odd precisely when 2(4a+7 )has the form p4(a+1)m(2) with p prime and p m.doi:10.1007/s11139-023-00784-4Cherubini, GiacomoCharles Universit...
Parity games play a central role in model checking and satisfiability checking. Solving parity games is computationally expensive, among others due to the
On the other hand, Player 1's goal is to exhaust the resources by making the cost unbounded. Note that Player 1's objective is not an ω-regular property, and in general, Player 1 needs infinite memory to win such games. However, cost-parity games enjoy some nice properties: Player 0...
The (n, n − 1) code with the preceding parity check matrix is called a parity check code (or even weight code). A codeword of this code is a binary vector x such that (2.70)HxT =x1 + x2+⋯+xn =0. So the sum of the n symbols of a codeword is zero under mod...
2.1 Parity Games A parity game G = (V0, V1, E, λ) consists of a directed graph (V, E) where V = V0 ∪ V1 is partitioned into vertices, or positions, of Player 0 and 1, and a priority function λ : V → N. We only consider finite parity games and define the size of ...
the plurality of possible bit degree distributions, wherein the selected bit degree distribution has a best performance threshold among the plurality of possible bit degree distributions; decomposing a parity check matrix that corresponds to a GRS-based regular LDPC code into a plurality of partial-...
R. Narayanan, “Memory-efficient sum-product decoding of LDPC codes,” IEEE Trans. Comm., vol. 52, No. 8, pp. 1225-1230, Aug. 2004. B. Gocal, “Bitonic sorting on Bene networks”, in Proceedings of the 10th International Parallel Processing Symposium (Apr. 15-19, 1996). IPPS. ...
1. An error correction decoder for block serial pipelined layered decoding of block codes, the error correction decoder comprising: a primary memory and a secondary memory each capable of storing log-likelihood ratios (LLRs) for at least one of a plurality of iterations of an iterative decoding...
1. A method for encoding variable sized data using a low-density parity-check (LDPC) code, and transporting the encoded variable sized data in modulated symbols, the method comprising: calculating a minimum number of modulated symbols capable of transmitting a data packet; selecting a codeword si...
Certain aspects of the present disclosure generally relate to techniques for puncturing of structured low density parity check (LDPC) codes. A method for wireless communications by