Related papers: A New Permutation Decoding Method for Reed-Muller …
We propose a new coding scheme, called the delayed coding (DC) scheme, for channels with insertion, deletion, and substitution (IDS) errors. The proposed scheme employs delayed encoding and non-iterative detection and decoding strategies to…
We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of…
In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
This note presents a descending method that allows us to classify quotients of Reed-Muller codes of lenghth 128 under the action of the affine general linear group.
This brief introduces a hardware complexity reduction method for successive cancellation list (SCL) decoders. Specifically, we propose to use a sorting scheme so that L paths with smallest path metrics are also sorted according to their…
Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure based on sorting the scalar components. Using a codebook comprising several permutation codes as subcodes preserves the…
Reed--Muller (RM) codes are known to achieve capacity on binary symmetric channels (BSC) under the Maximum a Posteriori (MAP) decoder. However, it remains an open problem to design a capacity achieving polynomial-time RM decoder. Due to a…
We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…
Automorphism-ensemble decoding is applied to the Plotkin constituents of Reed-Muller codes, resulting in a new soft-decision decoding algorithm with state-of-the-art performance versus complexity trade-offs.
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…
A low-complexity tree search approach is presented that achieves the maximum-likelihood (ML) decoding performance of Reed-Muller (RM) codes. The proposed approach generates a bit-flipping tree that is traversed to find the ML decoding…
We consider hard-decision iterative decoders for product codes over the erasure channel, which employ repeated rounds of decoding rows and columns alternatingly. We derive the exact asymptotic probability of decoding failure as a function…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques. An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly…
We obtain a new coding and decoding method using the generalized Pell $(p,i)$ -numbers. The relations among the code matrix elements, error detection and correction have been established for this coding theory. We give two new blocking…
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…
This paper considers '$\delta$-almost Reed-Muller codes', i.e., linear codes spanned by evaluations of all but a $\delta$ fraction of monomials of degree at most $d$. It is shown that for any $\delta > 0$ and any $\varepsilon>0$, there…
An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine variety codes is proposed. Our procedure is achieved by…
Modular quantum computing architectures require error correction schemes that remain effective in the presense of noisy inter-processor operations. We introduce a distributed quantum error correction framework based on approximate codes to…