Related papers: Decay of Correlations for Sparse Graph Error Corre…
Sparse Regression Codes (SPARCs) are capacity-achieving codes introduced for communication over the Additive White Gaussian Noise (AWGN) channels and were later extended to general memoryless channels. In particular it was shown via…
Short survey about code on the graph by example of hardware friendly quasi-cycle LDPC code. We consider two main properties of code: weight enumerator (well known from classic code theory) and Trapping sets pseudocodewords weight spectrum…
We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…
Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin…
Construction of error-correcting codes achieving a designated minimum distance parameter is a central problem in coding theory. In this work, we study a very simple construction of binary linear codes that correct a given number of errors…
This paper considers the problem of covert communication with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly sub-optimal, and simultaneously to ensure that the…
We consider lossy compression of a binary symmetric source by means of a low-density generator-matrix code. We derive two lower bounds on the rate distortion function which are valid for any low-density generator-matrix code with a given…
Motivated by hyper-reliable low-latency communication in 6G, we consider error control coding for short block lengths in multi-antenna fading channels. In general, the channel fading coefficients are unknown at both the transmitter and…
We study the problem of estimating vector-valued variables from noisy "relative" measurements. This problem arises in several sensor network applications. The measurement model can be expressed in terms of a graph, whose nodes correspond to…
Low correlation (finite length) sequences are used in communications and remote sensing. One seeks codebooks of sequences in which each sequence has low aperiodic autocorrelation at all nonzero shifts, and each pair of distinct sequences…
Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic…
We study faulty successive cancellation decoding of polar codes for the binary erasure channel. To this end, we introduce a simple erasure-based fault model and we show that, under this model, polarization does not happen, meaning that…
Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations…
Error correction code (ECC) is an integral part of the physical communication layer, ensuring reliable data transfer over noisy channels. Recently, neural decoders have demonstrated their advantage over classical decoding techniques.…
This study investigates the problem of learning linear block codes optimized for Belief-Propagation decoders significantly improving performance compared to the state-of-the-art. Our previous research is extended with an enhanced system…
Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…
A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed…
We consider transmission of two independent and separately encoded sources over a two-user binary-input Gaussian multiple-access channel. The channel gains are assumed to be unknown at the transmitter and the goal is to design an…
For reliable transmission across a noisy communication channel, classical results from information theory show that it is asymptotically optimal to separate out the source and channel coding processes. However, this decomposition can fall…
Cross-correlation is a popular signal processing technique used in numerous location tracking systems for obtaining reliable range information. However, its efficient design and practical implementation has not yet been achieved on mote…