Related papers: Sub-Block Rearranged Staircase Codes
In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications, the data to be transmitted may lie (or can be well approximated) in a…
Families of generalized spatially-coupled low-density parity-check (GSC-LDPC) code ensembles can be formed by terminating protograph-based generalized LDPC convolutional (GLDPCC) codes. It has previously been shown that ensembles of…
We consider a special family of SC-LDPC codes, that is, time-invariant LDPCC codes, which are known in the literature for a long time. Codes of this kind are usually designed by starting from QC block codes, and applying suitable unwrapping…
This paper presents a construction for high-rate MDS codes that enable bandwidth-efficient repair of a single node. Such MDS codes are also referred to as the minimum storage regenerating (MSR) codes in the distributed storage literature.…
This paper presents a new class of spatially coupled turbo-like codes (SC-TCs), namely half spatially coupled braided convolutional codes (HSC-BCCs) and half spatially coupled parallel concatenated codes (HSC-PCCs). Different from the…
Reliability is an important requirement for both communication and storage systems. Due to continuous scale down of technology multiple adjacent bits error probability increases. The data may be corrupted due soft errors. Error correction…
Belief propagation applied to iterative decoding and sparse recovery through approximate message passing (AMP) are two research areas that have seen monumental progress in recent decades. Inspired by these advances, this article introduces…
We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless,…
In a distributed storage network, reliability and bandwidth optimization can be provided by regenerating codes. Recently table based regenerating codes viz. DRESS (Distributed Replication-based Exact Simple Storage) codes has been proposed…
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
We propose a new partial decoding algorithm for $m$-interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m+1}}$ at all code rates $R$, in time polynomial in the code…
Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes…
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in…
Low-density parity-check (LDPC) codes together with belief propagation (BP) decoding yield exceptional error correction capabilities in the large block length regime. Yet, there remains a gap between BP decoding and maximum likelihood…
We propose a new low-density parity-check code construction scheme based on 2-lifts. The proposed codes have an advantage of admitting efficient hardware implementations. With the motivation of designing codes with low error floors, we…
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
A linear error correcting code is a subspace of a finite-dimensional space over a finite field with a fixed coordinate system. Such a code is said to be locally recoverable with locality $r$ if, for every coordinate, its value at a codeword…