LDPC codes from Singer cycles
نویسندگان
چکیده
منابع مشابه
LDPC codes from Singer cycles
The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes—characterised by admitting a sparse parity check matrix—with good correction capabilities. In the present paper the orbits of subspaces of a finite projectiv...
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Low-Density Parity-Check convolutional codes (LDPCccs) are very interesting for practical error-correction coding in wireless transmission as they have excellent performance and at the same time they allow for variable block size with low complexity encoding and decoding. As for all LDPC codes that are decoded by the sub-optimal (but highly efficient) Sum Product Algorithm, the cycles in the co...
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An algebraic group ring method for constructing codes with no short cycles in the check matrix is derived. It is shown that the matrix of a group ring element has no short cycles if and only if the collection of group differences of this element has no repeats. When applied to elements in the group ring with small support this gives a general method for constructing and analysing low density pa...
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Simple cycles are the easiest cycles to reveal in Low-Density Parity Check (LDPC) codes. All minimum matrices of simple cycles with the same length will be equivalent after row or column permutations .In this paper,we analysis the structure of simple cycles and show all figures of minimal matrices of simple cycles. Firstly, we introduce a more general definition of cycle and investigate simple ...
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Small loops in the graphical representations of lowdensity parity-check codes are hypothesised to be detrimental to the code’s performance. In this paper we demonstrate a procedure for removing such loops from the graphs. An algorithm based on the code’s adjacency matrix is used to locate any unwanted loops, and then certain edges are exchanged within the graph to eliminate those loops (without...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2009.01.013