This paper presents a scheme named code hopping (CodeHop) for gaussian wiretap channels based on nonsystematic low-density parity-check (LDPC) codes. Different from traditional communications, in the CodeHop scheme, the legitimate receiver (Bob) rapidly switches the parity-check matrix upon each correctly received source message block. Given an authenticated public feedback channel, the transmi...

We extend the framework for studying the stopping redundancy of a linear block code by introducing and analyzing the stopping redundancy hierarchy. The stopping redundancy hierarchy of a code represents a measure of the trade-off between performance and complexity of iteratively decoding a code used over the binary erasure channel. It is defined as an ordered list of positive integers in which ...

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...

A code symbol of a linear code is said to have locality r if this symbol could be recovered by at most r other code symbols. An (n, k, r) locally repairable code (LRC) with all symbol locality is a linear code with length n, dimension k, and locality r for all symbols. Recently, there are lots of studies on the bounds and constructions of LRCs, most of which are essentially based on the generat...

We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of one’s of the parity-check matrix of the codes presented is typically higher than the number of one’s of the parity-check matrix of low-density paritycheck (LDPC) codes. But, still lower than those of the parity-check matrix of classical block c...

Low-Density Parity Check (LDPC) codes are linear block codes which perform closer to Shannon‟s limit. It is defined by the parity check matrix (PCM) which contains only a few ones in comparison to the number of zeros (sparsity). Stochastic based computation is a method to design lowprecision digital circuits. In stochastic computing, probabilities are encoded by random sequences of bits. In thi...

The problem of fast evaluation of a matrix-vector product over GF (2) is considered. The problem is reduced to erasure decoding of a linear error-correcting code. A large set of redundant parity check equations for this code is generated. The multiplication algorithm is derived by tracking the execution of the message-passing algorithm on the obtained set of parity check equations. The obtained...