Related papers: Performance Analysis based on Density Evolution on…
This study focuses on the efficiency of message-passing-based decoding algorithms for polar and low-density parity-check (LDPC) codes. Both successive cancellation (SC) and belief propagation (BP) decoding algorithms are studied {in} the…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
Inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First an inner bound is derived using a two phase encoding scheme with…
We consider distributed Luby transform (DLT) codes for efficient packet transmission in a multi-way relay network, where the links are modeled as erasure channels. Density evolution is applied for asymptotic performance analysis, and…
We derive the density evolution equations for non-binary low-density parity-check (LDPC) ensembles when transmission takes place over the binary erasure channel. We introduce ensembles defined with respect to the general linear group over…
This short paper explores density evolution (DE) for low-density parity-check (LDPC) codes at signal-to-noise-ratios (SNRs) that are significantly above the decoding threshold. The focus is on the additive white Gaussian noise channel and…
Compute-and-forward relaying is effective to increase bandwidth efficiency of wireless two-way relay channels. In a compute-and-forward scheme, a relay tries to decode a linear combination composed of transmitted messages from other…
We introduce a new method for decoding short and moderate length linear block codes with dense parity-check matrix representations of cyclic form, termed multiple-bases belief-propagation (MBBP). The proposed iterative scheme makes use of…
In this paper, we propose a new class of quantized message-passing decoders for LDPC codes over the BSC. The messages take values (or levels) from a finite set. The update rules do not mimic belief propagation but instead are derived using…
We investigate error propagation in sliding window decoding of braided convolutional codes (BCCs). Previous studies of BCCs have focused on iterative decoding thresholds, minimum distance properties, and their bit error rate (BER)…
Expectation Propagation is a generalization to Belief Propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal…
We present a comprehensive analysis of fidelity decay and error accumulation in faulty quantum circuit models. Our work devises an analytical bound for the average fidelity between desired and faulty output states, accounting for errors…
Belief propagation is a fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles.…
Superposition codes are efficient for the Additive White Gaussian Noise channel. We provide here a replica analysis of the performances of these codes for large signals. We also consider a Bayesian Approximate Message Passing decoder based…
Error correction code is a major part of the communication physical layer, ensuring the reliable transfer of data over noisy channels. Recently, neural decoders were shown to outperform classical decoding techniques. However, the existing…
In this paper, we present the block Markov superposition transmission of BCH (BMST-BCH) codes, which can be constructed to obtain a very low error floor. To reduce the implementation complexity, we design a low complexity iterative…
The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some…
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
This paper proposes a quasi-belief propagation decoder for BCH codes that systematically integrates domain knowledge--specifically, channel noise variance, the cyclic property of the codes, and the deliberate redundancy in their…