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We solve the problem of designing powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather…
Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity…
We propose an approximation of maximum-likelihood detection in ISI channels based on linear programming or message passing. We convert the detection problem into a binary decoding problem, which can be easily combined with LDPC decoding. We…
In this paper, we develop an efficient decoder via the proximal alternating direction method of multipliers (proximal-ADMM) technique for nonbinary linear block codes in the Galois field. Its main contents are as follows: first, exploiting…
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of…
An efficient decoding algorithm for horizontally u-interleaved LRPC codes is proposed and analyzed. Upper bounds on the decoding failure rate and the computational complexity of the algorithm are derived. It is shown that interleaving…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
Low Rank Parity Check (LRPC) codes form a class of rank-metric error-correcting codes that was purposely introduced to design public-key encryption schemes. An LRPC code is defined from a parity check matrix whose entries belong to a…
Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and…
This paper proposes two approaches for reducing the impact of the error floor phenomenon when decoding quantum low-density parity-check codes with belief propagation based algorithms. First, a low-complexity syndrome-based linear…
Raptor codes have been widely used in many multimedia broadcast/multicast applications. However, our understanding of Raptor codes is still incomplete due to the insufficient amount of theoretical work on the performance analysis of Raptor…
The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary…
This paper considers the average complexity of maximum likelihood (ML) decoding of convolutional codes. ML decoding can be modeled as finding the most probable path taken through a Markov graph. Integrated with the Viterbi algorithm (VA),…
This paper studies maximum likelihood(ML) decoding in error-correcting codes as rational maps and proposes an approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion, which will be denoted by $p$ in the…
In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the…
In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
This paper considers the joint-decoding (JD) problem for finite-state channels (FSCs) and low-density parity-check (LDPC) codes. In the first part, the linear-programming (LP) decoder for binary linear codes is extended to JD of…
The Learning Parity with Noise (LPN) problem underlines several classic cryptographic primitives. Researchers have attempted to demonstrate the algorithmic hardness of this problem by finding reductions from the decoding problem of linear…
In this study, an optimization model for offline scheduling policy of low-density parity-check (LDPC) codes is proposed to improve the decoding efficiency of the belief propagation (BP). The optimization model uses the number of messages…