Related papers: Convolutional codes from unit schemes
We define the bidirectional distance profile (BDP) of a convolutional code as the minimum of the distance profiles of the code and its corresponding "reverse" code. We present tables of codes with the optimum BDP (OBDP), which minimize the…
Low decoding latency and complexity are two important requirements of channel codes used in many applications, like machine-to-machine communications. In this paper, we show how these requirements can be fulfilled by using some special…
This paper provides a construction of non-binary LDPC convolutional codes, which generalizes the work of Robinson and Bernstein. The sets of integers forming an $(n-1,w)$-difference triangle set are used as supports of the columns of rate…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit…
A lower bound on minimum distance of convolutional polar codes is provided. The bound is obtained from the minimum weight of generalized cosets of the codes generated by bottom rows of the polarizing matrix. Moreover, a construction of…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
Density evolution for protograph Low-Density Parity-Check (LDPC) codes is considered, and it is shown that the message-error rate falls double-exponentially with iterations whenever the degree-2 subgraph of the protograph is cycle-free and…
There exists a large literature of construction of convolutional codes with maximal or near maximal free distance. Much less is known about constructions of convolutional codes having optimal or near optimal column distances. In this paper,…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
A single source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the symbols received at their incoming edges on their…
This paper presents a design technique for obtaining regular time-invariant low-density parity-check convolutional (RTI-LDPCC) codes with low complexity and good performance. We start from previous approaches which unwrap a low-density…
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic…
Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration…
In the search for highly efficient decoders for short LDPC codes approaching maximum likelihood performance, a relayed decoding strategy, specifically activating the ordered statistics decoding process upon failure of a neural min-sum…
Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…
This paper addresses the construction of observable convolutional codes that exhibit good performance with the available decoding algorithms for erasure channels. Our construction is based on the use of input/state/output (I/S/O)…