Related papers: Efficient Decoding of Partial Unit Memory Codes of…
In the framework of write-once memory (WOM) codes, it is important to distinguish between codes that can be decoded directly and those that require that the decoder knows the current generation to successfully decode the state of the…
We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical…
Polar codes are an exciting new class of error correcting codes that achieve the symmetric capacity of memoryless channels. Many decoding algorithms were developed and implemented, addressing various application requirements: from…
In this letter, we propose a two-stage design method to construct memory efficient mutual information-maximizing quantized min-sum (MIM-QMS) decoder for rate-compatible low-density parity-check (LDPC) codes. We first develop a modified…
We propose a novel scheme for rate-compatible arbitrary-length polar code construction for the additive white Gaussian noise (AWGN) channel. The proposed scheme is based on the concept of non-uniform channel polarization. The original polar…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes such as cyclic codes, Reed-Solomon codes, and Reed-Muller codes have nice decoding algorithms.…
Polar codes asymptotically achieve the symmetric capacity of memoryless channels, yet their error-correcting performance under successive-cancellation (SC) decoding for short and moderate length codes is worse than that of other modern…
The classical family of $[n,k]_q$ Reed-Solomon codes over a field $\F_q$ consist of the evaluations of polynomials $f \in \F_q[X]$ of degree $< k$ at $n$ distinct field elements. In this work, we consider a closely related family of codes,…
In this paper, the performance of quadratic residue (QR) codes of lengths within 100 is given and analyzed when the hard decoding, soft decoding, and linear programming decoding algorithms are utilized. We develop a simple method to…
We propose a new partial decoding algorithm for $m$-interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m+1}}$ at all code rates $R$, in time polynomial in the code…
Precoded polar product codes are proposed, where selected component codes enable successive cancellation list decoding to generate bit-wise soft messages efficiently for iterative decoding while targeting optimized distance spectrum as…
Recently, a novel variation of polar codes known as polarization-adjusted convolutional (PAC) codes has been introduced by Ar{\i}kan. These codes significantly outperform conventional polar and convolutional codes, particularly for short…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…
The classical Reed-Muller codes over a finite field $\mathbb{F}_q$ are based on evaluations of $m$-variate polynomials of degree at most $d$ over a product set $U^m$, for some $d$ less than $|U|$. Because of their good distance properties,…
In this paper, we provide a new approach to the analytical estimation of the bit-error rate (BER) for convolutional codes for Viterbi decoding in the binary symmetric channel (BSC). The expressions we obtained for lower and upper BER bounds…
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep…
We study uniquely decodable codes and list decodable codes in the high-noise regime, specifically codes that are uniquely decodable from $\frac{1-\varepsilon}{2}$ fraction of errors and list decodable from $1-\varepsilon$ fraction of…
Quantum computation promises significant computational advantages over classical computation for some problems. However, quantum hardware suffers from much higher error rates than in classical hardware. As a result, extensive quantum error…
The recently proposed recursive projection-aggregation (RPA) decoding algorithm for Reed-Muller codes has received significant attention as it provides near-ML decoding performance at reasonable complexity for short codes. However, its…