Related papers: Capacity Achieving Codes From Randomness Condenser…
We explain how to optimize finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn based on a finite-length scaling result to…
Spatially-Coupled LDPC (SC-LDPC) ensembles achieve the capacity of binary memoryless channels (BMS), asymptotically, under belief-propagation (BP) decoding. In this paper, we study the BP decoding of these code ensembles over a BMS channel…
We construct a channel coding scheme to achieve the capacity of any discrete memoryless channel based solely on the techniques of polar coding. In particular, we show how source polarization and randomness extraction via polarization can be…
Locally decodable channel codes form a special class of error-correcting codes with the property that the decoder is able to reconstruct any bit of the input message from querying only a few bits of a noisy codeword. It is well known that…
To better understand the wireless network design with a large number of hops, we investigate a line network formed by general discrete memoryless channels (DMCs), which may not be identical. Our focus lies on Generalized Batched Network…
Consider communication over the binary erasure channel BEC using random low-density parity-check codes with finite-blocklength n from `standard' ensembles. We show that large error events is conveniently described within a scaling theory,…
The problem of mismatched decoding for discrete memoryless channels is addressed. A mismatched cognitive multiple-access channel is introduced, and an inner bound on its capacity region is derived using two alternative encoding methods:…
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).…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
Recently, the authors showed that Reed-Muller (RM) codes achieve capacity on binary memoryless symmetric (BMS) channels with respect to bit error rate. This paper extends that work by showing that RM codes defined on non-binary fields,…
In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE…
We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…
This paper considers the performance of Reed-Muller (RM) codes transmitted over binary memoryless symmetric (BMS) channels under bitwise maximum-a-posteriori (bit-MAP) decoding. Its main result is that, for a fixed BMS channel, the family…
We investigate the duality of the binary erasure channel (BEC) and the binary defect channel (BDC). This duality holds for channel capacities, capacity achieving schemes, minimum distances, and upper bounds on the probability of failure to…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
We propose an iterative method for approximately computing the capacity of discrete memoryless channels, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and…
Consider a binary linear code of length $N$, minimum distance $d_{\text{min}}$, transmission over the binary erasure channel with parameter $0 < \epsilon < 1$ or the binary symmetric channel with parameter $0 < \epsilon < \frac12$, and…
The capacity of a channel with an energy-harvesting (EH) encoder and a finite battery remains an open problem, even in the noiseless case. A key instance of this scenario is the binary EH channel (BEHC), where the encoder has a unit-sized…
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations…
Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general,…