On the dimensions of certain LDPC codes based on q-regular bipartite graphs
نویسندگان
چکیده
An explicit construction of a family of binary LDPC codes called LU(3, q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The proof involves the geometry of a 4-dimensional symplectic vector space and the action of the symplectic group and its subgroups.
منابع مشابه
q - regular bipartite graphs
An explicit construction of a family of binary LDPC codes called LU(3, q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The proof involves the geometry of a 4-dimensional symplectic vector space and the action of the symplectic group and its subgroups.
متن کاملThe dimensions of LU(3, q) codes
A family of LDPC codes, called LU(3, q) codes, has been constructed from q-regular bipartite graphs. Recently, P. Sin and Q. Xiang determined the dimensions of these codes in the case that q is a power of an odd prime. They also obtained a lower bound for the dimension of an LU(3, q) code when q is a power of 2. In this paper we prove that this lower bound is the exact dimension of the LU(3, q)...
متن کاملRecent Developments in Low-Density Parity-Check Codes
In this paper we prove two results related to low-density parity-check (LDPC) codes. The first is to show that the generating function attached to the pseudo-codewords of an LDPC code is a rational function, answering a question raised in [6]. The combinatorial information of its numerator and denominator is also discussed. The second concerns an infinite family of q-regular bipartite graphs wi...
متن کاملExplicit Construction of Families of LDPC Codes with Girth at Least Six
LDPC codes are serious contenders to Turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m ≥ 2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m, q) on 2qm vertices, which has girth at least 2dm/2e+ 4. We regard these graphs as Tanner graphs of binar...
متن کاملOn the Tanner Graph Cycle Distribution of Random LDPC, Random Protograph-Based LDPC, and Random Quasi-Cyclic LDPC Code Ensembles
Random bipartite graphs, random lifts of bipartite protographs, and random cyclic lifts of bipartite protographs are used to represent random low-density parity-check (LDPC) codes, randomly constructed protograph-based LDPC codes, and random quasi-cyclic (QC) LDPC codes, respectively. In this paper, we study the distribution of cycles of different length in all these three categories of graphs....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 52 شماره
صفحات -
تاریخ انتشار 2006