相关论文: Error-correcting codes on scale-free networks
Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…
In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated…
A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The…
A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates. We show that any {\em zero-error} $2$-query locally correctable code…
As a special case of sparse code multiple access (SCMA), low-density signatures based code-division multiple access (LDS-CDMA) was widely believed to have worse error rate performance compared to SCMA. With the aid of Eisenstein numbers, we…
We explain an algorithm that approximately but efficiently assesses particular parity-check error-correcting codes of large, but finite, blocklength. This algorithm is based on the ``renormalization-group'' approach from physics: the idea…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of K\"otter and Kschischang. A large class of constant-dimension subspace codes is…
Power-law scaling, a central concept in critical phenomena, is found to be useful in deep learning, where optimized test errors on handwritten digit examples converge as a power-law to zero with database size. For rapid decision making with…
This paper studies several properties of channel codes that approach the fundamental limits of a given (discrete or Gaussian) memoryless channel with a non-vanishing probability of error. The output distribution induced by an…
Shannon's analysis of the fundamental capacity limits for memoryless communication channels has been refined over time. In this paper, the maximum volume $M_\avg^*(n,\epsilon)$ of length-$n$ codes subject to an average decoding error…
Recently there have been a tremendous interest in models of networks with a power-law distribution of degree -- so called "scale-free networks." It has been observed that such networks, normally, have extremely short path-lengths, scaling…
We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…
Variable-length block-coding schemes are investigated for discrete memoryless channels with ideal feedback under cost constraints. Upper and lower bounds are found for the minimum achievable probability of decoding error $P_{e,\min}$ as a…
We study improved degree distribution for Luby Transform (LT) codes which exhibits improved bit error rate performance particularly in low overhead regions. We construct the degree distribution by modifying Robust Soliton distribution. The…
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions…
In this paper, the performance of signaling strategies with high peak-to-average power ratio is analyzed in both coherent and noncoherent fading channels. Two recently proposed modulation schemes, namely on-off binary phase-shift keying and…