Related papers: Maximum-likelihood Soft-decision Decoding for Bina…
This paper studies maximum likelihood(ML) decoding in error-correcting codes as rational maps and proposes an approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion, which will be denoted by $p$ in the…
Due to their capacity-achieving property, polar codes have become one of the most attractive channel codes. To date, the successive cancellation list (SCL) decoding algorithm is the primary approach that can guarantee outstanding…
The classical majority-logic decoder proposed by Reed for Reed-Muller codes RM(r, m) of order r and length 2^m, unfolds in r+1 sequential steps, decoding message symbols from highest to lowest degree. Several follow-up decoding algorithms…
In this paper, we investigate learning-based maximum likelihood (ML) detection for uplink massive multiple-input and multiple-output (MIMO) systems with one-bit analog-to-digital converters (ADCs). To overcome the significant dependency of…
This paper discusses bit-level soft decoding of triple-parity Reed-Solomon (RS) codes through automorphism permutation. A new method for identifying the automorphism groups of RS binary images is first developed. The new algorithm runs…
Guessing random additive noise decoding (GRAND) is a recently proposed decoding paradigm particularly suitable for codes with short length and high rate. Among its variants, ordered reliability bits GRAND (ORBGRAND) exploits soft…
The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies of algebraic soft-decision decoding with infinite cost are first studied…
Maximum Likelihood (ML) decoding of forward error correction codes is known to be optimally accurate, but is not used in practice as it proves too challenging to efficiently implement. Here we introduce a ML decoder called SGRAND, which is…
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is…
We present the first theoretical framework that connects predictive coding (PC), a biologically inspired local learning rule, with the minimum description length (MDL) principle in deep networks. We prove that layerwise PC performs…
In this paper, we present a sequential sampling-based algorithm for the two-stage distributionally robust linear programming (2-DRLP) models. The 2-DRLP models are defined over a general class of ambiguity sets with discrete or continuous…
Recently, rate-$1/\omega$ zero-terminated and tail-biting convolutional codes (ZTCCs and TBCCs) with cyclic-redundancy-check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short…
We present novel decoding schemes for hard and soft decision decoding of block codes using the minimal weight codewords of the dual code. The decoding schemes will be described for cyclic codes where polynomials can be used, however, the…
This paper presents a comprehensive guide to designing minimal trellises for both non-degenerate and degenerate decoding of quantum stabilizer codes. For non-degenerate decoding, various strategies are explored, leveraging insights from…
Recent advances in large language models (LLMs) show potential for clinical applications, such as clinical decision support and trial recommendations. However, the GPT-4 LLM predicts an excessive number of ICD codes for medical coding…
We propose a decoder for Trellis-Constrained Codes, a super-class of Turbo- and LDPC codes. Inspired by amplitude amplification from quantum computing, we attempt to amplify the relative likelihood of the most likely codeword until it…
A dual-layer multiple-input multiple-output (MIMO) system with multi-level modulation is considered. A computationally efficient soft-input soft-output receiver based on the exact max-log maximum a posteriori (max-log-MAP) principle is…
The minimum weight matching (MWM) and maximum likelihood decoding (MLD) are two widely used and distinct decoding strategies for quantum error correction. For a given syndrome, the MWM decoder finds the most probable physical error…
Multi-stage stochastic linear programs (MSLPs) are notoriously hard to solve in general. Linear decision rules (LDRs) yield an approximation of an MSLP by restricting the decisions at each stage to be an affine function of the observed…
This paper is concerned with the ordered statistic decoding with local constraints (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly…