Related papers: Code optimization, frozen glassy phase and improve…
Much progress has been made on decoding algorithms for error-correcting codes in the last decade. In this article, we give an introduction to some fundamental results on iterative, message-passing algorithms for low-density parity check…
A packing lemma is proved using a setting where the channel is a binary-input discrete memoryless channel $(\mathcal{X},w(y|x),\mathcal{Y})$, the code is selected at random subject to parity-check constraints, and the decoder is a joint…
Low-density parity-check (LDPC) codes on symmetric memoryless channels have been analyzed using statistical physics by several authors. In this paper, statistical mechanical analysis of LDPC codes is performed for asymmetric memoryless…
We describe some pseudorandom properties of binary linear codes achieving capacity on the binary erasure channel under bit-MAP decoding (as shown in Kudekar et al this includes doubly transitive codes and, in particular, Reed-Muller codes).…
Certifying quantum properties from the probability distributions they induce is an important task for several purposes. While this framework has been largely explored and used for quantum states, its extrapolation to the level of channels…
-We develop a polar coding scheme for empirical coordination in a two-node network with a noisy link in which the input and output signals have to be coordinated with the source and the reconstruction. In the case of non-causal encoding and…
A model of low-temperature polar liquids is constructed that accounts for configurational heat capacity, entropy, and the effect of a strong electric field on the glass transition. The model is based on Pad{\'e}-truncated perturbation…
In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if…
It is shown that some well-known and some new cyclic codes with orthogonal parity-check equations can be constructed in the finite-field transform domain. It is also shown that, for some binary linear cyclic codes, the performance of the…
It was recently shown that spatial coupling of individual low-density parity-check codes improves the belief-propagation threshold of the coupled ensemble essentially to the maximum a posteriori threshold of the underlying ensemble. We…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
We present a novel decoding algorithm for q-ary low-density parity-check codes, termed symbol message passing. The proposed algorithm can be seen as a generalization of Gallager B and the binary message passing algorithm by Lechner et al.…
This paper considers density evolution for lowdensity parity-check (LDPC) and multi-edge type low-density parity-check (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three singleparameter…
Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF). This decoder displays sub-optimal performance in practice and requires very…
Density evolution is one of the most powerful analytical tools for low-density parity-check (LDPC) codes and graph codes with message passing decoding algorithms. With channel symmetry as one of its fundamental assumptions, density…
We propose an approach toward understanding the spin glass phase at zero and low temperature by studying the stability of a spin glass ground state against perturbations of a single coupling. After reviewing the concepts of flexibility,…
Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to…
The min-sum approximation is widely used in the decoding of polar codes. Although it is a numerical approximation, hardly any penalties are incurred in practice. We give a theoretical justification for this. We consider the common case of a…
The spectrum of nucleons and their parity partners is studied as a function of temperature spanning the deconfinement transition. We analyse our results using the correlation functions directly, exponential fits in the hadronic phase, and…
A theoretical concept is presented for the screening of several magnetic moments locally exchange coupled to conduction electrons in a metallic nanostructure. We consider a quantum confined multi-impurity Kondo model which exhibits the…