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Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
By presenting an approximated performance-complexity tradeoff (PCT) algorithm,a low-complexity non-binary low density parity check (LDPC) code over q-ary-input symmetric-output channel is designed in this manuscript which converges faster…
Joint network-channel codes (JNCC) can improve the performance of communication in wireless networks, by combining, at the physical layer, the channel codes and the network code as an overall error-correcting code. JNCC is increasingly…
In a distributed space-time coding scheme, based on the relay channel model, the relay nodes co-operate to linearly process the transmitted signal from the source and forward them to the destination such that the signal at the destination…
In this paper, we investigate the performance of a class of spatially coupled codes, namely partially information coupled turbo codes (PIC-TCs) over the binary erasure channel (BEC). This class of codes enjoy flexible code rate adjustment…
We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new…
We study near optimal error correction codes for real-time communication. In our setup the encoder must operate on an incoming source stream in a sequential manner, and the decoder must reconstruct each source packet within a fixed playback…
Low-density parity-check (LDPC) codes together with belief propagation (BP) decoding yield exceptional error correction capabilities in the large block length regime. Yet, there remains a gap between BP decoding and maximum likelihood…
Unrolling a decoding algorithm allows to achieve extremely high throughput at the cost of increased area. Look-up tables (LUTs) can be used to replace functions otherwise implemented as circuits. In this work, we show the impact of…
Leakage outside of the qubit computational subspace poses a threatening challenge to quantum error correction (QEC). We propose a scheme using two leakage-reduction units (LRUs) that mitigate these issues for a transmon-based surface code,…
When statistical inversion of a lag profile is used to determine an incoherent scatter target, the posterior variance of the estimated target can be used to determine how well a certain set of transmission codes perform. In this work we…
Recent studies have shown that distributed storage systems can achieve significant space savings by adapting redundancy levels to varying disk failure rates. This adaptation is performed via code conversion, wherein data encoded under an…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
NOMA) technique based on an algebraic design is studied. We propose an improved low-density spreading (LDS) sequence design based on projective geometry. In terms of its bit error rate (BER) performance, our proposed improved LDS code set…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
Can modifying the training data distribution guide optimizers toward solutions with improved generalization when training large language models (LLMs)? In this work, we theoretically analyze an in-context linear regression model with…
Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes over integer residue rings and analyze their performance with respect to the Lee metric. Their…
A general lossless joint source-channel coding scheme based on linear codes is proposed and then analyzed in this paper. It is shown that a linear code with good joint spectrum can be used to establish limit-approaching joint source-channel…
The throughput benefits of random linear network codes have been studied extensively for wirelined and wireless erasure networks. It is often assumed that all nodes within a network perform coding operations. In energy-constrained systems,…
Low Density Parity Check (LDPC) codes are linear error correcting codes used in communication systems for Forward Error Correction (FEC). But, intensive computation is required for encoding and decoding of LDPC codes, making it difficult…