Related papers: Windowed Decoding of Spatially Coupled Codes
We address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…
Low-density parity-check (LDPC) convolutional codes (or spatially-coupled codes) were recently shown to approach capacity on the binary erasure channel (BEC) and binary-input memoryless symmetric channels. The mechanism behind this…
We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding…
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…
Polar codes have gained significant attention in channel coding for their ability to approach the capacity of binary input discrete memoryless channels (B-DMCs), thanks to their reliability and efficiency in transmission. However, existing…
In this paper, we consider quantized decoding of LDPC codes on the binary symmetric channel. The binary message passing algorithms, while allowing extremely fast hardware implementation, are not very attractive from the perspective of…
The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. As near capacity-approaching codes, Low-Density Parity-Check (LDPC) codes possess several advantages over…
We study the performance of polarizing codes over a degraded symmetric wiretap channel under a total variation distance (TVD) secrecy constraint. We show that the leakage can be bounded by the sum of the TVDs of the bit-channels…
Noise in quantum computing is countered with quantum error correction. Achieving optimal performance will require tailoring codes and decoding algorithms to account for features of realistic noise, such as the common situation where the…
This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than…
Window decoding, first proposed to reduce decoding complexity for real-time decoding, is an essential component to realize scalable, universal-fault tolerant computation. Prior work has focused on improving throughput through…
In this chapter, we show how the use of differential coding and the presence of phase slips in the transmission channel affect the total achievable information rates and capacity of a system. By means of the commonly used QPSK modulation,…
We address the problem of converting large-scale high-dimensional image data into binary codes so that approximate nearest-neighbor search over them can be efficiently performed. Different from most of the existing unsupervised approaches…
We propose a new class of error correction codes for low-delay streaming communication. We consider an online setup where a source packet arrives at the encoder every $M$ channel uses, and needs to be decoded with a maximum delay of $T$…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
In the conventional successive cancellation (SC) decoder for polar codes, all the future bits to be estimated later are treated as random variables. However, polar codes inevitably involve frozen bits, and their concatenated coding schemes…
We derive the optimum second-order coding rates, known as second-order capacities, for erasure and list decoding. For erasure decoding for discrete memoryless channels, we show that second-order capacity is $\sqrt{V}\Phi^{-1}(\epsilon_t)$…
Codes based on sparse matrices have good performance and can be efficiently decoded by belief-propagation (BP). Decoding binary stabilizer codes needs a quaternary BP for (additive) codes over GF(4), which has a higher check-node complexity…
Kudekar et al. proved that the belief-propagation (BP) performance for low-density parity check (LDPC) codes can be boosted up to the maximum-a-posteriori (MAP) performance by spatial coupling. In this paper, spatial coupling is applied to…
Fast fading wireless networks with delayed knowledge of the channel state information have received significant attention in recent years. An exception is networks where channels are spatially correlated. This paper characterizes the…