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We propose a new code design that aims to distribute an LDPC code over a relay channel. It is based on a split-and-extend approach, which allows the relay to split the set of bits connected to some parity-check of the LDPC code into two or…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
In this paper we prove threshold saturation for spatially coupled turbo codes (SC-TCs) and braided convolutional codes (BCCs) over the binary erasure channel. We introduce a compact graph representation for the ensembles of SC-TC and BCC…
Non-binary low-density parity-check (LDPC) codes have some advantages over their binary counterparts, but unfortunately their decoding complexity is a significant challenge. The iterative hard- and soft-reliability based majority-logic…
Low decoding latency and complexity are two important requirements of channel codes used in many applications, like machine-to-machine communications. In this paper, we show how these requirements can be fulfilled by using some special…
Spatially-Coupled (SC)-LDPC codes are known to have outstanding error-correction performance and low decoding latency. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, in…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
Low-density parity-check (LDPC) codes are an important feature of several communication and storage applications, offering a flexible and effective method for error correction. These codes are computationally complex and require the…
This paper presents a design technique for obtaining regular time-invariant low-density parity-check convolutional (RTI-LDPCC) codes with low complexity and good performance. We start from previous approaches which unwrap a low-density…
Most existing works on analyzing the performance of a random ensemble of low-density parity-check (LDPC) codes assume that the degree distributions of the two ends of a randomly selected edge are independent. In the paper, we take one step…
Low-density parity-check codes, a class of capacity-approaching linear codes, are particularly recognized for their efficient decoding scheme. The decoding scheme, known as the sum-product, is an iterative algorithm consisting of passing…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
In this paper, we propose a class of codes, referred to as random staircase generator matrix codes (SGMCs), which have staircase-like generator matrices. In the infinite-length region, we prove that the random SGMC is capacity-achieving…
We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits…
The performance of low-density parity-check (LDPC) codes at high signal-to-noise ratios (SNRs) is known to be limited by the presence of certain sub-graphs that exist in the Tanner graph representation of the code, for example trapping sets…
The use of multiple Reconfigurable Intelligent Sur- faces (RIS) has gained attention in 6G networks to enhance coverage. However, the feasibility of deploying multiple RIS relies on efficient channel estimation and reduced pilot overhead.…
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…
Low density parity check (LDPC) codes, initially discovered by Gallager, exhibit excellent performance in iterative decoding, approaching the Shannon limit. MDS array codes, with favorable algebraic structures, are codes suitable for…
Quantum low-density parity-check (qLDPC) codes are a promising construction for drastically reducing the overhead of fault-tolerant quantum computing (FTQC) architectures. However, all of the known hardware implementations of these codes…
A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the…