Low density parity check codes over groups and rings
نویسندگان
چکیده
The role of low density parity check principles in the design of group codes for coded modulation is examined. In this context, the structure of linear codes over certain rings Zm and Gm is discussed, and LDPC codes over these ring structures are designed.
منابع مشابه
On Belief Propagation Decoding of LDPC Codes over Groups
We introduce a wide class of LDPC codes, large enough to include LDPC codes over finite fields, rings or groups as well as some non-linear codes. This class is defined by an extension of the parity-check equations involved in the code’s definition. A belief propagation decoding procedure with the same complexity as for the decoding of LDPC codes over finite fields is presented for theses new pa...
متن کاملImproving the Rao-Nam secret key cryptosystem using regular EDF-QC-LDPC codes
This paper proposes an efficient joint secret key encryption-channel coding cryptosystem, based on regular Extended Difference Family Quasi-Cyclic Low-Density Parity-Check codes. The key length of the proposed cryptosystem decreases up to 85 percent using a new efficient compression algorithm. Cryptanalytic methods show that the improved cryptosystem has a significant security advantage over Ra...
متن کاملStructured LDPC Codes over Integer Residue Rings
This paper presents a new class of low-density parity-check (LDPC) codes over Z2a represented by regular, structured Tanner graphs. These graphs are constructed using Latin squares defined over a multiplicative group of a Galois ring, rather than a finite field. Our approach yields codes for a wide range of code rates and more importantly, codes whose minimum pseudocodeword weights equal their ...
متن کاملAlgebraic constructions of LDPC codes with no short cycles
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...
متن کاملA New Construction for LDPC Codes using Permutation Polynomials over Integer Rings
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudorandom nature, and the new codes are quasi-cyclic. Graph isomorphisms and automorphisms are identified and used in an efficient search for good codes. Graphs with girth as large as 12 wer...
متن کامل