Related papers: Systematic Bernoulli Generator Matrix Codes
A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for…
In this paper we are concerned with the asymptotic analysis of nonbinary spatially-coupled low-density parity-check (SC-LDPC) ensembles defined over GL$\left(2^{m}\right)$ (the general linear group of degree $m$ over GF$\left(2\right)$).…
We compute the code parameters for binary linear codes obtained by greedy constructing the parity check matrix. Then we show that these codes improve the Gilbert-Varshamov (GV) bound on the code size and rate. This result counter proves the…
Bosonic encodings of quantum information offer hardware-efficient, noise-biased approaches to quantum error correction relative to qubit register encodings. Implementations have focused in particular on error correction of stored, idle…
We consider codes for channels with extreme noise that emerge in various low-power applications. Simple LDPC-type codes with parity checks of weight 3 are first studied for any dimension $m\rightarrow\infty.$ These codes form modulation…
We introduce BiGR, a novel conditional image generation model using compact binary latent codes for generative training, focusing on enhancing both generation and representation capabilities. BiGR is the first conditional generative model…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse…
Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse…
The loop series provides a formal way to write down corrections to the Bethe entropy (and/or free energy) of graphical models. We provide methods to rigorously control such expansions for low-density parity-check codes used over a highly…
Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Theoretical framework for dealing with general symmetric…
Ensuring extremely high reliability in channel coding is essential for 6G networks. The next-generation of ultra-reliable and low-latency communications (xURLLC) scenario within 6G networks requires frame error rate (FER) below $10^{-9}$.…
We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
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…
In this paper we consider regular low-density parity-check codes over a binary-symmetric channel in the decoding regime. We prove that up to a certain noise threshold the bit-error probability of the bit-sampling decoder converges in mean…
We introduce a new family of binary linear codes suitable for steganographic matrix embedding. The main characteristic of the codes is the staircase random block structure of the generator matrix. We propose an efficient list decoding…
Quantum computers theoretically are able to solve certain problems more quickly than any deterministic or probabilistic computers. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, one has to…
For LDPC codes operating over additive white Gaussian noise channels and decoded using message-passing decoders with limited precision, absorbing sets have been shown to be a key factor in error floor behavior. Focusing on this scenario,…