Low Density Parity Check (LDPC) codes have enjoyed increasing interest during recent years. In general these are described in the terminology of sparse bipartite graphs containing no 4 -cycles, but an alternative way to deal with them are a particular class of incidence structures, namely partial linear spaces. This paper shows how to obtain a large class of partial linear spaces from inversive...

This paper presents a new approach to decode turbo codes using a nonbinary belief propagation decoder. The proposed approach can be decomposed into two main steps. First, a nonbinary Tanner graph representation of the turbo code is derived by clustering the binary parity-check matrix of the turbo code. Then, a group belief propagation decoder runs several iterations on the obtained nonbinary Ta...

It is known that any linear code allows for a decoding strategy that treats errors and erasures separately over an error-erasure channel. In particular, a carefully designed paritycheck matrix makes efficient erasure correction possible through iterative decoding while instantly providing the necessary paritycheck equations for independent error correction on demand. The separating redundancy o...

A specific LDPC check matrix structure is used to form multi-channel alternative signal to solve the problem that traditional block codes inhibiting PAPR scheme is not suitable for a large number of sub-carriers and LDPC code is applied to the field of optimization of peak-to-average ratio. A rapid construction method of LDPC check matrix and fast encoding process using matrix are analyzed in d...

—High-speed, high-reliability requirements and strict power limitation of near-earth communications yield that the channel coding must have high coding gain and lower error floor. In this paper, an irregular quasi-cyclic low-density paritycheck (QC-LDPC) code for specific use in near-earth communications is proposed. In order to eliminate the impact of short-cycles and further improve the perf...

Based on the construction of linear codes recently proposed by Niederriter and Xing, a corresponding generator matrix is derived. The duality operator and the propagation operator of these extended linear codes are studied. A sufficient and necessary condition under which these two operators are commutative is obtained. This commutative property is found useful for constructing the correspondin...

An (n, k) linear code C of length n over GF(q) = Fq, a Galios field of order q, where q is a prime, is a fc-dimensional linear subspace of F"q, where F"q denotes the space of all n-tuples over GF(q). A generator matrix G of this code is a k x n matrix whose rows form a basis of C. The parity-check matrix H of this code is an(n — fc) x n matrix such that Hv = 0 for all vectors veC. The row space...

In this paper, we incorporate the layered structure with low-density parity-check codes (LDPC) to develop a quasi-block diagonal LDPC space-time structure. The lower triangular structure of the parity check matrix introduces correlation between layers. In addition, each layer, as a part of the whole codeword, can be decoded while taking information from other undetected layers to improve the de...

We describe an operation to dynamically adapt the structure of the Tanner graph used during iterative decoding. Codes on graphs– most importantly, low-density parity-check (LDPC) codes–exploit randomness in the structure of the code. Our approach is to introduce a similar degree of controlled randomness into the operation of the messagepassing decoder, to improve the performance of iterative de...

This paper introduces different construction techniques of parity-check matrix H for irregular LowDensity Parity-Check (LDPC) codes. The first one is the proposed Accurate Random Construction Technique (ARCT) which is an improvement of the Random Construction Technique (RCT) to satisfy an accurate profile. The second technique, Speed Up Technique (SUT), improves the performance of irregular LDP...