Related papers: Fountain Uncorrectable Sets and Finite-Length Anal…

We investigate the reasons behind the superior performance of belief propagation decoding of non-binary LDPC codes over their binary images when the transmission occurs over the binary erasure channel. We show that although decoding over…

Fountain codes are becoming increasingly important for data transferring over dedicated high-speed long-distance network. However, the encoding and decoding complexity of traditional fountain codes such as LT and Raptor codes are still…

The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for…

The capacity of unifilar finite-state channels in the presence of feedback is investigated. We derive a new evaluation method to extract graph-based encoders with their achievable rates, and to compute upper bounds to examine their…

Stopping sets, and in particular their numbers and sizes, play an important role in determining the performance of iterative decoders of linear codes over binary erasure channels. In the 2004 Shannon Lecture, McEliece presented an…

We consider the compound capacity of polar codes under successive cancellation decoding for a collection of binary-input memoryless output-symmetric channels. By deriving a sequence of upper and lower bounds, we show that in general the…

In this first part, a computable outer bound is proved for the multiterminal source coding problem, for a setup with two encoders, discrete memoryless sources, and bounded distortion measures.

Two finite volume methods are derived and applied to the solution of problems of incompressible flow. In particular, external inviscid flows and boundary-layer flows are examined. The firstmethod analyzed is a cell-centered finite volume…

The bit-wise unequal error protection problem, for the case when the number of groups of bits $\ell$ is fixed, is considered for variable length block codes with feedback. An encoding scheme based on fixed length block codes with erasures…

In this paper we present a thorough analysis of non binary LDPC codes over the binary erasure channel. First, the decoding of non binary LDPC codes is investigated. The proposed algorithm performs on-the-fly decoding, i.e. it starts…

In this paper, we use reinforcement learning to find effective decoding strategies for binary linear codes. We start by reviewing several iterative decoding algorithms that involve a decision-making process at each step, including…

The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure,…

In most error correction coding (ECC) frameworks, the typical error metric is the bit error rate (BER) which measures the number of bit errors. For this metric, the positions of the bits are not relevant to the decoding, and in many noise…

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…

We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…

In this paper, the design of irregular turbo codes for the binary erasure channel is investigated. An analytic expression of the erasure probability of punctured recursive systematic convolutional codes is derived. This exact expression…

To address the issue of increased bit error rates during the later stages of linear search in denoising diffusion error correction codes, we propose a novel method that optimizes denoising diffusion error correction codes (ECC) using cosine…

In this paper, we present a novel way for solving the main problem of designing the capacity approaching irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC). The proposed method is much simpler, faster,…

This paper studies the mismatched decoding problem for binary-input discrete memoryless channels. An example is provided for which an achievable rate based on superposition coding exceeds the LM rate (Hui, 1983; Csisz\'ar-K\"orner, 1981),…

Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the…