Related papers: Asymptotically MDS Array BP-XOR Codes
The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with {\em bounded complexity}, per information bit, of encoding and decoding. It also…
We present a new decoder for the surface code, which combines the accuracy of the tensor-network decoders with the efficiency and parallelism of the belief-propagation algorithm. Our main idea is to replace the expensive tensor-network…
MDS array codes are widely used in storage systems to protect data against erasures. We address the \emph{rebuilding ratio} problem, namely, in the case of erasures, what is the the fraction of the remaining information that needs to be…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with…
In this paper we introduce a lowest density MDS array code which is applied to a Smart Meter network to introduce reliability. By treating the network as distributed storage with multiple sources, information can be exchanged between the…
Segmentation-based image coding methods provide high compression ratios when compared with traditional image coding approaches like the transform and sub band coding for low bit-rate compression applications. In this paper, a…
We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to…
In this paper, we propose a new decoder, called the Multiple-Bases Belief-Propagation List Decoder (MBBP-LD), for Quantum Low-Density Parity-Check (QLDPC) codes. It extends the Multiple-Bases Belief-Propagation (MBBP) framework, originally…
Quantum low-density parity-check (LDPC) codes are a promising family of quantum error-correcting codes for fault tolerant quantum computing with low overhead. Decoding quantum LDPC codes on quantum erasure channels has received more…
Codes based on sparse matrices have good performance and can be efficiently decoded by belief-propagation (BP). Decoding binary stabilizer codes needs a quaternary BP for (additive) codes over GF(4), which has a higher check-node complexity…
The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root…
This paper proposes a quasi-belief propagation decoder for BCH codes that systematically integrates domain knowledge--specifically, channel noise variance, the cyclic property of the codes, and the deliberate redundancy in their…
A technique of lossless compression via substring enumeration (CSE) attains compression ratios as well as popular lossless compressors for one-dimensional (1D) sources. The CSE utilizes a probabilistic model built from the circular string…
This paper proposes a belief propagation (BP) message passing algorithm based joint multiple symbol differential detection (MSDD) and channel decoding scheme for noncoherent differential ultra-wideband impulse radio (UWB-IR) systems. MSDD…
Assuming iterative decoding for binary erasure channels (BECs), a novel tree-based technique for upper bounding the bit error rates (BERs) of arbitrary, finite low-density parity-check (LDPC) codes is provided and the resulting bound can be…
We present two sequences of ensembles of non-systematic irregular repeat-accumulate codes which asymptotically (as their block length tends to infinity) achieve capacity on the binary erasure channel (BEC) with bounded complexity per…
This paper presents an enhanced belief propagation (BP) decoding algorithm and a reinforcement learning-based BP decoding algorithm for polar codes. The enhanced BP algorithm weighs each Processing Element (PE) input based on their signals…
Rank metric codes and constant-dimension codes (CDCs) have been considered for error control in random network coding. Since decoder errors are more detrimental to system performance than decoder failures, in this paper we investigate the…
We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric…