Related papers: Construction Methods Based on Minimum Weight Distr…
Polar codes are the first class of channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels with efficient encoding and decoding algorithms. But the weight spectrum of Polar codes is relatively poor…
Post-processing of the raw bits produced by a true random number generator (TRNG) is always necessary when the entropy per bit is insufficient for security applications. In this paper, we derive a tight bound on the output min-entropy of…
In this paper, we consider the update bandwidth in distributed storage systems~(DSSs). The update bandwidth, which measures the transmission efficiency of the update process in DSSs, is defined as the total amount of data symbols…
We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator ($\cM$), rather than on the weight enumerator ($\cW$)…
Recent advances in machine translation (MT) have shown that Minimum Bayes Risk (MBR) decoding can be a powerful alternative to beam search decoding, especially when combined with neural-based utility functions. However, the performance of…
Optimization results are one method for understanding neural computation from Nature's perspective and for defining the physical limits on neuron-like engineering. Earlier work looks at individual properties or performance criteria and…
Maximum distance separable (MDS) codes are widely used in distributed storage systems as they provide optimal fault tolerance for a given amount of storage overhead. The seminal work of Dimakis~\emph{et al.} first established a lower bound…
In this paper, we propose an enhanced quasi-maximum likelihood (EQML) decoder for LDPC codes with short block lengths. After the failure of the conventional belief propagation (BP) decoding, the proposed EQML decoder selects unreliable…
Minimum Bayes risk (MBR) decoding outputs the hypothesis with the highest expected utility over the model distribution for some utility function. It has been shown to improve accuracy over beam search in conditional language generation…
Regenerating codes are efficient methods for distributed storage in storage networks, where node failures are common. They guarantee low cost data reconstruction and repair through accessing only a predefined number of arbitrarily chosen…
Designing large coupling memory quasi-cyclic spatially-coupled LDPC (QC-SC-LDPC) codes with low error floors requires eliminating specific harmful substructures (e.g., short cycles) induced by edge spreading and lifting. Building on our…
Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…
In this paper we study the iterative decoding threshold performance of non-binary spatially-coupled low-density parity-check (NB-SC-LDPC) code ensembles for both the binary erasure channel (BEC) and the binary-input additive white Gaussian…
Due to their provably capacity-achieving performance, polar codes have attracted a lot of research interest recently. For a good error-correcting performance, list successive-cancellation decoding (LSCD) with large list size is used to…
Designing good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be non-zero, has found many recent applications, including in distributed…
This paper introduces techniques to construct binary polar source/channel codes based on the bit error probability of successive-cancellation decoding. The polarization lemma is reconstructed based on the bit error probability and then…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5th generation (5G) wireless standard. Most polar code research examines the original Arikan polar…
We address the use of maximum distance separable (MDS) codes for distributed storage (DS) to enable efficient content delivery in wireless networks. Content is stored in a number of the mobile devices and can be retrieved from them using…
This paper first presents a new approach to evaluating the descriptive complexity of finite-length binary sequences. Specifically, we investigate the sequence-wise recovery behavior induced by polar compression and successive cancellation…