Let $A(n, d)$ denote the maximum size of a binary code of length $n$ and minimum Hamming distance $d$ . Studying $A(n, d)$ , including efforts to determine it as well to derive bounds on $A(n, d)$ for large $n$ ’s, is one of the most fundamental subjects in coding theory. In this paper, we explore new lower and upper bounds on $A(n, d)$ in the large-minimum distance regime, in particular, when $d = n/2 - \Omega (\sqrt {n})$ .
Generalized integrated interleaved (GII) codes are essential to next-generation digital communication and storage systems since they can achieve very high decoding throughput with low complexity. Only hard-decision GII decoding has been considered in previous work. To further improve the error-correcting capability, soft-decision decoding algorithms utilizing the channel probability information need to be developed. The decoding of GII codes constructed based on BCH codes consists of multiple rounds of BCH decoding.
The bee-identification problem, formally defined by Tandon, Tan, and Varshney (2019), requires the receiver to identify “bees” using a set of unordered noisy measurements. In this previous work, Tandon, Tan, and Varshney studied error exponents and showed that decoding the measurements jointly results in a significantly larger error exponent. In this work, we study algorithms related to this joint decoder. First, we demonstrate how to perform joint decoding efficiently.
Reed-Muller (RM) codes achieve the capacity of general binary-input memoryless symmetric channels and are conjectured to have a comparable performance to that of random codes in terms of scaling laws. However, such results are established assuming maximum-likelihood decoders for general code parameters. Also, RM codes only admit limited sets of rates. Efficient decoders such as successive cancellation list (SCL) decoder and recently-introduced recursive projection-aggregation (RPA) decoders are available for RM codes at finite lengths.
In this paper, we first formulate a novel Chase Guruswami-Sudan algorithm which list corrects not only all errors among the Chase flipping symbols but also the number of errors up to the enhanced Johnson bound among remaining positions, for Reed-Solomon and $q$ -ary BCH codes. The enhanced Johnson bound is induced by shortening the code without those Chase flipping symbols. We next devise a novel Chase Kötter-Vardy algorithm for soft decision decoding of Reed-Solomon codes.
Motivated by applications in distributed storage, the notion of a locally recoverable code (LRC) was introduced a few years back. In an LRC, any coordinate of a codeword is recoverable by accessing only a small number of other coordinates. While different properties of LRCs have been well-studied, their performance on channels with random erasures or errors has been mostly unexplored. In this paper, we analyze the performance of LRCs over such stochastic channels.
We propose a new compression scheme for genomic data given as sequence fragments called reads. The scheme uses a reference genome at the decoder side only, freeing the encoder from the burdens of storing references and performing computationally costly alignment operations. The main ingredient of the scheme is a multi-layer code construction, delivering to the decoder sufficient information to align the reads, correct their differences from the reference, validate their reconstruction, and correct reconstruction errors.
Let $[q\rangle $ denote the integer set $\{0,1, {\ldots },q-1\}$ and let ${{\mathbb {B}}}=\{0,1\}$ . The problem of implementing functions $[q\rangle \rightarrow {{\mathbb {B}}}$ on content-addressable memories (CAMs) is considered. CAMs can be classified by the input alphabet and the state alphabet of their cells; for example, in binary CAMs, those alphabets are both ${{\mathbb {B}}}$ , while in a ternary CAM (TCAM), both alphabets are endowed with a “don’t care” symbol.
Distributed filtering is crucial in many applications such as localization, radar, autonomy, and environmental monitoring. The aim of distributed filtering is to infer time-varying unknown states using data obtained via sensing and communication in a network. This paper analyzes continuous-time distributed filtering with sensing and communication constraints. In particular, the paper considers a building-block system of two nodes, where each node is tasked with inferring a time-varying unknown state.
In literature, PIBMA, a linear-feedback-shift-register (LFSR) decoder, has been shown to be the most efficient high-speed decoder for Reed-Solomon (RS) codes. In this work, we follow the same design principles and present two high-speed LFSR decoder architectures for binary BCH codes, both achieving the critical path of one multiplier and one adder. We identify a key insight of the Berlekamp algorithm that iterative discrepancy computation involves only even-degree terms.