Related papers: Recursive List Decoding for Reed-Muller Codes
A successive cancellation (SC) decoder with inactivations is proposed as an efficient implementation of SC list (SCL) decoding over the binary erasure channel. The proposed decoder assigns a dummy variable to an information bit whenever it…
A novel adaptive binary decoding algorithm for LDPC codes is proposed, which reduces the decoding complexity while having a comparable or even better performance than corresponding non-adaptive alternatives. In each iteration the variable…
A simple algorithm for decoding both errors and erasures of Reed-Solomon codes is described.
The recently introduced polar codes constitute a breakthrough in coding theory due to their capacityachieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures…
In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…
We show that expander codes, when properly instantiated, are high-rate list recoverable codes with linear-time list recovery algorithms. List recoverable codes have been useful recently in constructing efficiently list-decodable codes, as…
In this paper, we show that the projective Reed-Muller~(PRM) codes form a family of locally correctable codes~(LCC) in the regime of low query complexities. A PRM code is specified by the alphabet size $q$, the number of variables $m$, and…
A new permutation decoding approach for polar codes is presented. The complexity of the algorithm is similar to that of a successive cancellation list (SCL) decoder, while it can be implemented with the latency of a successive cancellation…
A novel permuted fast successive-cancellation list decoding algorithm with fast Hadamard transform (FHT-FSCL) is presented. The proposed decoder initializes $L$ $(L\ge1)$ active decoding paths with $L$ random codeword permutations sampled…
An iterated refinement procedure for the Guruswami-Sudan list decoding algorithm for Generalised Reed-Solomon codes based on Alekhnovich's module minimisation is proposed. The method is parametrisable and allows variants of the usual list…
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…
Define the codewords of the Tensor Reed-Muller code $\mathsf{TRM}(r_1,m_1;r_2,m_2;\dots;r_t,m_t)$ to be the evaluation vectors of all multivariate polynomials in the variables $\left\{x_{ij}\right\}_{i=1,\dots,t}^{j=1,\dots m_i}$ with…
We consider the problem of erasure/list decoding using certain classes of simplified decoders. Specifically, we assume a class of erasure/list decoders, such that a codeword is in the list if its likelihood is larger than a threshold. This…
In this paper, we consider the problem of recursively designing uniquely decodable ternary code sets for highly overloaded synchronous code-division multiple-access (CDMA) systems. The proposed code set achieves larger number of users $K <…
The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or non-identical quantum noise. In this work, we…
This paper considers the input-constrained binary memoryless symmetric (BMS) channel, without feedback. The channel input sequence respects the $(d,\infty)$-runlength limited (RLL) constraint, which mandates that any pair of successive $1$s…
Algebraic space-time coding allows for reliable data exchange across fading multiple-input multiple-output channels. A powerful technique for decoding space-time codes in Maximum-Likelihood (ML) decoding, but well-performing and widely-used…
The successive cancellation list decoding algorithm for polar codes yields near-optimal decoding performance at the cost of high implementation complexity. The successive cancellation stack algorithm has been shown to provide similar…
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…
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…