A class of geometrically structured quasi-cyclic low-density paritycheck codes with a cylinder structure graph and girth 12 is considered. The parity-check matrix of such a code consists of blocks of zeros and circulant permutation matrices. A class of convolutional codes is assigned to these codes. The convolutional form generator matrix of these codes is obtained by elementary row and column ...

Various space time code (STC) designs have been proposed to obtain full diversity at full rate in multiple-input multiple-output (MIMO) channels for uncoded systems. However, commercial wireless systems typically employ powerful channel codes such as turbo codes and low density parity check (LDPC) codes together with an STC. For these applications, an STC optimized for uncoded systems may not p...

This paper investigates the design of channel-optimized scalar quantizers with erasure correcting codes over binary symmetric channels (BSC). A new scalar quantizer with uniform decoder and channel-optimized encoder aided by erasure correcting code is proposed. The lower bound for performance of the new quantizer with complemented natural code (CNC) index assignment is given. Then, in order to ...

We develop methods for analyzing and constructing combined modulation/error-correctiong codes (ECC codes), in particular codes that employ some form of reversed concatenation and whose ECC decoding scheme requires easy access to soft information (e.g., turbo codes, low-density parity-check (LDPC) codes or parity codes). We expand on earlier work of Immink and Wijngaarden and also of Fan, in whi...

the paper presents lower and upper bounds on the number of parity check digits required for a linear code that detects solid bursts of length $b$ or less and simultaneously any $e$ or less random errors. an example of such a code is also provided. further, codes capable of detecting and simultaneously correcting such errors have also been dealt with.

A) , (L J regular QC-LDPC code of length N is defined by a parity-check matrix L L p I p I p I p I p I p I p I p I p I H     (1) where 1 1    J j , 1 1    L l and   l j p I , represents the p p  circulant permutation matrix obtained by cyclically right-shifting the p p  identity matrix   0 I by l j p , positions, with. / L N p  For a specific QC-LDPC code we define the correspo...

Low-density parity-check (LDPC) code is linear-block error-correcting code defined by sparse parity-check matrix. It is decoded using the massage-passing algorithm, and in many cases, capable of outperforming turbo code. This paper presents a class of low-density parity-check (LDPC) codes showing good performance with low encoding complexity. The code is constructed using difference families fr...

In this paper, we suggest a new technique for LDPC parity-check matrix (H-matrix) generation and a corresponding decoding process. The key idea is to construct LDPC H-matrix by using a convolutional encoder. It is easy to have many different coderates from a mother code with convolutional codes. However, it is difficult to have many different coderates with LDPC codes. Constructing LDPC Hmatrix...

A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with column weight 2 and row weight v. In this report, we give an ontology-based approach to the optimization for this class of codes. All possible inter-connected cycle patterns that lead to low symbol-weight codewords are identified to put together the ontology. The optimization goal is to improve the distance property o...

We consider the decoding of convolutional codes using an error trellis constructed based on a submatrix of a given check matrix. In the proposed method, the syndromesubsequence computed using the remaining submatrix is utilized as auxiliary information for decoding. Then the ML error path is correctly decoded using the degenerate error trellis. We also show that the decoding complexity of the p...