The construction of LDPC codes based on the subspaces of singular linear space over finite field

2016 ◽  
Vol 08 (04) ◽  
pp. 1650073
Author(s):  
Congcong Wang ◽  
Yingying Zhang ◽  
Zhuoqun Li ◽  
Xiaona Zhang ◽  
You Gao
Keyword(s):  
Finite Field ◽  
Linear Space ◽  
Prime Power ◽  
Ldpc Codes

Let [Formula: see text] be a finite field with [Formula: see text] elements, where [Formula: see text] is a prime power. [Formula: see text] denotes the [Formula: see text]-dimensional row linear space over [Formula: see text]. In this paper, we construct a series of LDPC codes based on the subspaces of singular linear space over [Formula: see text], and calculate their parameters.

scholarly journals Decoding of NB-LDPC codes over Subfields

2020 ◽  
Author(s):  
V B Wijekoon ◽  
Emanuele Viterbo ◽  
Yi Hong
Keyword(s):  
Finite Field ◽  
Ldpc Codes ◽  
The Novel ◽  
Decoding Complexity ◽  
Novel Method ◽  
Graph Expansions

<div>In this paper, we present a novel method to expand a graph over a finite field into a larger one over one of </div><div>the original field’s subfields. This allows a number of different graph expansions for any given graph. </div><div>These expansions can be used in various applications, and we focus specifically on the case of decoding </div><div>NB-LDPC codes. Using the novel expanded graphs, it is possible to reduce decoding complexity of NB-</div><div>LDPC codes significantly with minimal performance losses.</div>

Projective Geometries that are Disjoint Unions of Caps

1980 ◽  
Vol 32 (6) ◽  
pp. 1299-1305 ◽  
Author(s):  
Barbu C. Kestenband
Keyword(s):  
Finite Field ◽  
Projective Geometry ◽  
Prime Power ◽  
Disjoint Union ◽  
Hermitian Matrices ◽  
Incidence Relation ◽  
Projective Geometries ◽  
Image Position ◽  
Natural Way ◽  
Square Matrix

We show that any PG(2n, q2) is a disjoint union of (q2n+1 − 1)/ (q − 1) caps, each cap consisting of (q2n+1 + 1)/(q + 1) points. Furthermore, these caps constitute the “large points” of a PG(2n, q), with the incidence relation defined in a natural way.A square matrix H = (hij) over the finite field GF(q2), q a prime power, is said to be Hermitian if hijq = hij for all i, j [1, p. 1161]. In particular, hii ∈ GF(q). If if is Hermitian, so is p(H), where p(x) is any polynomial with coefficients in GF(q).Given a Desarguesian Projective Geometry PG(2n, q2), n > 0, we denote its points by column vectors:All Hermitian matrices in this paper will be 2n + 1 by 2n + 1, n > 0.

Fault tolerant bit parallel finite field multipliers using LDPC codes

2008 ◽  
Author(s):  
J. Mathew ◽  
J. Singh ◽  
A. M. Jabir ◽  
M. Hosseinabady ◽  
D. K. Pradhan
Keyword(s):  
Finite Field ◽  
Fault Tolerant ◽  
Ldpc Codes

CONSTRUCTION OF m-METRIC ARRAY CODES DETECTING AND CORRECTING CT-BURST ARRAY ERRORS

2008 ◽  
Vol 01 (04) ◽  
pp. 589-617 ◽  
Author(s):  
Sapna Jain ◽  
Seul Hee Choi
Keyword(s):  
Finite Field ◽  
Error Correction ◽  
Linear Space ◽  
Lower Bounds ◽  
Array Codes ◽  
Hamming Metric ◽  
Array Errors

In [11], the first author introduced the notion of CT bursts in the space Mat m×s(Fq), the linear space of all m × s matrices with entries from a finite field Fq, endowed with a non-Hamming metric [16] and obtained some lower bounds for CT burst array error correction. In this paper, we first obtain various construction bounds on the parameters of m-metric array codes [16] for the detection and correction of CT burst array errors and then construct the array codes meeting these bounds.

QE rings in characteristic pn

1983 ◽  
Vol 48 (1) ◽  
pp. 140-162 ◽  
Author(s):  
Chantal Berline ◽  
Gregory Cherlin
Keyword(s):  
Finite Field ◽  
Jacobson Radical ◽  
Prime Power ◽  
Galois Field ◽  
Power Characteristic ◽  
Witt Ring ◽  
Boolean Power ◽  
Three Components

AbstractWe show that all QE rings of prime power characteristic are constructed in a straightforward way out of three components: a filtered Boolean power of a finite field, a nilpotent Jacobson radical, and the ring Zp. or the Witt ring W2(F4) (which is the characteristic four analogue of the Galois field with four elements).

Performance of Non-Binary LDPC Codes for Next Generation Mobile Systems

2010 ◽  
Vol 56 (2) ◽  
pp. 111-116 ◽  
Author(s):  
Henryk Gierszal ◽  
Witold Hołubowicz ◽  
Łukasz Kiedrowski ◽  
Adam Flizikowski
Keyword(s):  
Finite Field ◽  
System Performance ◽  
Ldpc Codes ◽  
Transmission System ◽  
Mobile Systems ◽  
Mobile System ◽  
Next Generation ◽  
Single Carrier ◽  
New Family ◽  
The Future

Performance of Non-Binary LDPC Codes for Next Generation Mobile SystemsA new family of non-binary LDPC is presented that are based on a finite field GF(64). They may be successfully implemented in single-carrier and OFDM transmission system. Results prove that DAVINCI codes allow for improving the system performance and may be considered to be applied in the future mobile system.

Quasi-regular semilattices in singular linear spaces

2016 ◽  
Vol 08 (01) ◽  
pp. 1650005
Author(s):  
Baohuan Zhang ◽  
Yujun Liu ◽  
Zengti Li
Keyword(s):  
Finite Field ◽  
Linear Space ◽  
Fixed Integer ◽  
Linear Spaces ◽  
Partially Ordered ◽  
Type Formula ◽  
Singular Linear Spaces

Let [Formula: see text] denote the [Formula: see text]-dimensional singular linear space over a finite field [Formula: see text]. For a fixed integer [Formula: see text], denote by [Formula: see text] the set of all subspaces of type [Formula: see text], where [Formula: see text]. Partially ordered by ordinary inclusion, one family of quasi-regular semilattices is obtained. Moreover, we compute its all parameters.

Zeros of random polynomials over finite fields

1992 ◽  
Vol 111 (2) ◽  
pp. 193-197 ◽  
Author(s):  
R. W. K. Odoni
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Prime Power ◽  
Random Polynomials ◽  
Polynomials Over Finite Fields ◽  
Image Position

Let be the finite field with q elements (q a prime power), let r 1 and let X1, , Xr be independent indeterminates over . We choose an arbitrary and a d 1 and consider

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