Related papers: Bounds and Constructions for $\overline{3}$-Strong…
In this paper, we compare the finite-length performance of protograph-based spatially coupled low-density parity-check (SC-LDPC) codes and LDPC block codes (LDPC-BCs) over GF(q). In order to reduce computational complexity and latency, a…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
Polar codes are a new class of block codes with an explicit construction that provably achieve the capacity of various communications channels, even with the low-complexity successive-cancellation (SC) decoding algorithm. Yet, the more…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
This paper considers the cognitive interference channel (CIC) with two transmitters and two receivers, in which the cognitive transmitter non-causally knows the message and codeword of the primary transmitter. We first introduce a discrete…
Intersecting codes are a classical object in coding theory whose rank-metric analogue has recently been introduced. Although the definition formally parallels the Hamming-metric case, the structure and parameter constraints of rank-metric…
Typically, unsupervised segmentation of speech into the phone and word-like units are treated as separate tasks and are often done via different methods which do not fully leverage the inter-dependence of the two tasks. Here, we unify them…
Linear-programming pseudocodewords play a pivotal role in our understanding of the linear-programming decoding algorithms. These pseudocodewords are known to be equivalent to the graph-cover pseudocodewords. The latter pseudocodewords, when…
We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new…
In this paper, we explore the application of semidefinite programming to the realm of quantum codes, specifically focusing on codeword stabilized (CWS) codes with entanglement assistance. Notably, we utilize the isotropic subgroup of the…
Polar codes are a class of channel capacity achieving codes that has been selected for the next generation of wireless communication standards. Successive-cancellation (SC) is the first proposed decoding algorithm, suffering from mediocre…
A code is called a $q$-query locally decodable code (LDC) if there is a randomized decoding algorithm that, given an index $i$ and a received word $w$ close to an encoding of a message $x$, outputs $x_i$ by querying only at most $q$…
Codes constructed from connected spatially coupled low-density parity-check code (SC-LDPCC) chains are proposed and analyzed. It is demonstrated that connecting coupled chains results in improved iterative decoding performance. The…
This work presents a high throughput and energy efficient multicore (MC) successive cancellation (SC) decoder architecture for polar codes. SC is a low-complexity decoding algorithm with a set of sequential operations. The sequential…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
Color codes present distinct advantages for fault-tolerant quantum computing, such as high encoding rates and the transversal implementation of Clifford gates. However, existing matching-based decoders for the color codes such as the…
We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of…
The study of subblock-constrained codes has recently gained attention due to their application in diverse fields. We present bounds on the size and asymptotic rate for two classes of subblock-constrained codes. The first class is binary…
We propose randomized frameproof codes for content protection, which arise by studying a variation of the Boneh-Shaw fingerprinting problem. In the modified system, whenever a user tries to access his fingerprinted copy, the fingerprint is…
In this paper, we highlight the class of spatially coupled codes and discuss their applicability to long-haul and submarine optical communication systems. We first demonstrate how to optimize irregular spatially coupled LDPC codes for their…