Name
Title | ||
|---|---|---|
Low Complexity Encoder for Generalized Quasi-Cyclic Codes Coming from Finite Geometries |
Abstract | ||
|---|---|---|
We define generalized quasi-cyclic (GQC) codes as linear codes with nontrivial automorphism groups. Therefore, GQC codes, unlike quasi-cyclic codes, can include many important codes such as Hermitian and projective geometry (PG) codes; this capability is important in practical applications. Further, we propose the echelon canonical form algorithm for computing Gröbner bases from their parity check matrices. Consequently, by applying Gröbner base theory, GQC codes can be systematically encoded and implemented with simple feedback shift registers. Our algorithm is based on Gaussian elimination and requires a sufficiently small number of finite-field operations, which is related to the third power of code-length. In order to demonstrate our encoder's efficiency, we prove that the number of circuit elements in the encoder architecture is proportional to the code-length for finite geometry (FG) LDPC codes (a class of GQC codes). We show that the hardware complexity of a serial-in-serial-out encoder architecture for FG-LDPC codes is related to the linear order of the code-length; less than 2n adder and 2n memory elements are required to encode a binary codeword of length n. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1109/ICC.2009.5199152 | Dresden |
Keywords | DocType | ISSN |
Gaussian processes,binary codes,codecs,cyclic codes,parity check codes,shift registers,FG-LDPC codes,GQC codes,Gaussian elimination,Grobner base theory,Grobner bases,Hermitian codes,binary codeword,echelon canonical,finite geometries,finite geometry,finite-field operations,generalized quasicyclic codes,hardware complexity,linear codes,low complexity encoder,nontrivial automorphism groups,parity check matrices,projective geometry codes,serial-in-serial-out encoder architecture,simple feedback shift registers | Conference | 1938-1883 E-ISBN : 978-1-4244-3435-0 |
ISBN | Citations | PageRank |
978-1-4244-3435-0 | 1 | 0.43 |
References | Authors | |
12 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vo Tam Van | 1 | 18 | 2.65 |
| Hajime Matsui | 2 | 18 | 8.14 |
| Seiichi Mita | 3 | 316 | 38.88 |