Related papers: Two-Dimensional Tail-Biting Convolutional Codes
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…
As a typical example of bandwidth-efficient techniques, bit-interleaved coded modulation with iterative decoding (BICM-ID) provides desirable spectral efficiencies in various wireless communication scenarios. In this paper, we carry out a…
Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper we discuss several graph-cover-based methods for deriving families of time-invariant…
For finite coupling lengths, terminated spatially coupled low-density parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in conjunction…
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with…
The relation between parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Using the principle of tailbiting, compact…
We propose two approximate algorithms for MAP decoding on tail-biting trellises. The algorithms work on a subset of nodes of the tail-biting trellis, judiciously selected. We report the results of simulations on an AWGN channel using the…
A low-density parity-check (LDPC) code is a linear block code described by a sparse parity-check matrix, which can be efficiently represented by a bipartite Tanner graph. The standard iterative decoding algorithm, known as belief…
Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of…
Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutional codes (CCs) with cyclic redundancy check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths.…
In this paper we propose, implement, and test the first practical decomposition algorithms for the width parameters treecut width and treedepth. These two parameters have recently gained a lot of attention in the theoretical research…
We present a new family of low-density parity-check (LDPC) convolutional codes that can be designed using ordered sets of progressive differences. We study their properties and define a subset of codes in this class that have some desirable…
In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given $p,\epsilon>0$, we study (i) The $p$-bounded constraint: a binary vector of size $m$ is said to be $p$-bounded if its weight is at most…
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A class of these codes was introduced by Roth, who also…
In this work, we consider the minimum distance properties and convergence thresholds of 3-dimensional turbo codes (3D-TCs), recently introduced by Berrou et al.. Here, we consider binary 3D-TCs while the original work of Berrou et al.…
An algorithm for exact maximum likelihood(ML) decoding on tail-biting trellises is presented, which exhibits very good average case behavior. An approximate variant is proposed, whose simulated performance is observed to be virtually…
Topological quantum codes are favored because they allow qubit layouts that are suitable for practical implementation. An $N$-qubit topological code can be decoded by minimum-weight perfect matching (MWPM) with complexity…
Convolutional codes are error-correcting linear codes that utilize shift registers to encode. These codes have an arbitrary block size and they can incorporate both past and current information bits. DNA codes represent DNA sequences and…
Spatially coupled low-density parity-check (SC-LDPC) codes can achieve the channel capacity under low-complexity belief propagation (BP) decoding, however, there is a non-negligible rate-loss because of termination effects for practical…
Most design approaches for trellis-coded quantization take advantage of the duality of trellis-coded quantization with trellis-coded modulation, and use the same empirically-found convolutional codes to label the trellis branches. This…