scispace - formally typeset
Search or ask a question
Author

B. Ammar

Bio: B. Ammar is an academic researcher from Lancaster University. The author has contributed to research in topics: Block code & Linear code. The author has an hindex of 5, co-authored 9 publications receiving 294 citations.

Papers
More filters
Journal ArticleDOI
TL;DR: This correspondence presents a method for constructing structured regular low-density parity-check codes based on a special type of combinatoric designs, known as balance incomplete block designs, which have girths at least 6 and perform well with iterative decoding.
Abstract: This correspondence presents a method for constructing structured regular low-density parity-check (LDPC) codes based on a special type of combinatoric designs, known as balance incomplete block designs. Codes constructed by this method have girths at least 6 and they perform well with iterative decoding. Furthermore, several classes of these codes are quasi-cyclic and hence their encoding can be implemented with simple feedback shift registers.

159 citations

Journal ArticleDOI
TL;DR: A new family of so-called reducible rank codes which are a generalization of rank product codes is presented, which includes maximal rank distance (MRD) codes for lengths n>N in the field F/sub N/.
Abstract: We present a new family of so-called reducible rank codes which are a generalization of rank product codes . This family includes maximal rank distance (MRD) codes for lengths n>N in the field F/sub N/. We give methods for encoding and decoding reducible rank codes. A public key cryptosystem based on these codes and on the idea of a column scrambler is proposed. The column scrambler "mixes" columns of a generator (parity-check) matrix of a code. It makes the system more resistant to structural attacks such as Gibson's attacks. Possible attacks on the system are thoroughly studied. The system is found to be secure against known attacks for public keys of about 16 kbits and greater.

77 citations

Proceedings ArticleDOI
30 Jun 2002
TL;DR: This paper presents a method for constructing low density parity check (LDPC) codes based on a special type of combinatoric designs, known as the balanced incomplete block designs (BIBDs), which perform well with iterative decoding.
Abstract: This paper presents a method for constructing low density parity check (LDPC) codes based on a special type of combinatoric designs, known as the balanced incomplete block designs (BIBDs). Several classes of BIBDs suitable for constructing LDPC codes are presented. Codes constructed based on these classes of BIBDs perform well with iterative decoding.

24 citations

Journal ArticleDOI
27 Dec 2005
TL;DR: In this article, two classes of well-structured binary low-density parity check codes (LDPC) are described and compared with known random LDPC codes, in order to assess their relative achievable performance/complexity trade-offs.
Abstract: Two classes of well-structured binary low-density parity check codes (LDPC) are described. The first class is based on a branch of combinatorial mathematics, known as the balanced incomplete block design (BIBD). Construction of three types of codes derived from BIBD designs is illustrated in addition to a family of LDPC codes constructed by decomposition of incidence matrices of the proposed BIBD designs. The decomposition technique reduces the density of the parity check matrix and hence reduces the number of short cycles, which generally lead to better performing LDPC codes. The second class of well-structured LDPC codes, Vandermonde or array LDPC codes, are defined by a small number of parameters and cover a large set of code lengths and rates with different column weights. The presented LDPC codes are quasi-cyclic with no cycles of length four; hence simple encoding while maintaining good performance is achieved. Furthermore, the codes are compared with known random LDPC codes, in order to assess their relative achievable performance/complexity trade-offs. It is shown that well-structured LDPC codes perform very similar to the known random LDPC codes.

10 citations


Cited by
More filters
Journal ArticleDOI
TL;DR: It is shown that the encoding complexity of a QC-LDPC code is linearly proportional to the number of parity bits of the code for serial encoding, and to the length of thecode for high-speed parallel encoding.
Abstract: Efficient Encoding of Quasi-Cyclic Low-Density Parity-Check Codes Quasi-cyclic (QC) low-density parity-check (LDPC) codes form an important subclass of LDPC codes. These codes have encoding advantage over other types of LDPC codes. This paper addresses the issue of efficient encoding of QC-LDPC codes. Two methods are presented to find the generator matrices of QC-LDPC codes in systematic-circulant form from their parity-check matrices given in circulant form. Based on the systematic-circulation form of the generator matrix of a QC-LDPC code, various types of encoding circuits using simple shift registers are devised. It is shown that the encoding complexity of a QC-LDPC code is linearly proportional to the number of parity bits of the code for serial encoding, and to the length of the code for high-speed parallel encoding.

559 citations

Journal ArticleDOI
TL;DR: Finite fields can be successfully used to construct algebraic low-density parity-check (LDPC) codes for iterative soft-decision decoding and these codes are quasi-cyclic (QC) and perform very well over the additive white Gaussian noise, binary random, and burst erasure channels with iterative decoding.
Abstract: In the late 1950s and early 1960s, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for hard-decision algebraic decoding, such as Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes. This paper shows that finite fields can also be successfully used to construct algebraic low-density parity-check (LDPC) codes for iterative soft-decision decoding. Methods of construction are presented. LDPC codes constructed by these methods are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN), binary random, and burst erasure channels with iterative decoding in terms of bit-error probability, block-error probability, error-floor, and rate of decoding convergence, collectively. Particularly, they have low error floors. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.

272 citations

Journal ArticleDOI
TL;DR: New algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented and most of the codes constructed can be either put in cyclic or quasi-cyclic form and hence their encoding can be implemented with linear shift registers.
Abstract: New algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented. The new construction methods result in a class of multistep majority-logic decodable codes and three classes of low-density parity-check (LDPC) codes. Decoding methods for the class of majority-logic decodable codes, and a class of codes that perform well with iterative decoding in spite of having many cycles of length 4 in their Tanner graphs, are presented. Most of the codes constructed can be either put in cyclic or quasi-cyclic form and hence their encoding can be implemented with linear shift registers.

196 citations

Journal ArticleDOI
TL;DR: This correspondence presents a method for constructing structured regular low-density parity-check codes based on a special type of combinatoric designs, known as balance incomplete block designs, which have girths at least 6 and perform well with iterative decoding.
Abstract: This correspondence presents a method for constructing structured regular low-density parity-check (LDPC) codes based on a special type of combinatoric designs, known as balance incomplete block designs. Codes constructed by this method have girths at least 6 and they perform well with iterative decoding. Furthermore, several classes of these codes are quasi-cyclic and hence their encoding can be implemented with simple feedback shift registers.

159 citations

Journal ArticleDOI
TL;DR: Two algebraic methods for systematic construction of structured regular and irregular low-density parity-check (LDPC) codes with girth of at least six and good minimum distances are presented, based on geometry decomposition and a masking technique.
Abstract: Two algebraic methods for systematic construction of structured regular and irregular low-density parity-check (LDPC) codes with girth of at least six and good minimum distances are presented. These two methods are based on geometry decomposition and a masking technique. Numerical results show that the codes constructed by these methods perform close to the Shannon limit and as well as random-like LDPC codes. Furthermore, they have low error floors and their iterative decoding converges very fast. The masking technique greatly simplifies the random-like construction of irregular LDPC codes designed on the basis of the degree distributions of their code graphs

159 citations