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This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
Compression of inverted lists with methods that support fast intersection operations is an active research topic. Most compression schemes rely on encoding differences between consecutive positions with techniques that favor small numbers.…
This study presents a novel model for invertible sentence embeddings using a residual recurrent network trained on an unsupervised encoding task. Rather than the probabilistic outputs common to neural machine translation models, our…
Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…
Despite recent advancements in packet loss concealment (PLC) using deep learning techniques, packet loss remains a significant challenge in real-time speech communication. Redundancy has been used in the past to recover the missing…
Interleaved Reed-Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed-Solomon codes. Usually, these codewords are decoded…
Generalized Reed-Solomon (RS) codes are a common choice for efficient, reliable error correction in memory and communications systems. These codes add $2t$ extra parity symbols to a block of memory, and can efficiently and reliably correct…
Finding desired information from large data set is a difficult problem. Information retrieval is concerned with the structure, analysis, organization, storage, searching, and retrieval of information. Index is the main constituent of an IR…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
Folded Reed-Solomon (FRS) and univariate multiplicity codes are prominent polynomial codes over finite fields, renowned for achieving list decoding capacity. These codes have found a wide range of applications beyond the traditional scope…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
Maximum rank distance codes denoted MRD-codes are the equivalent in rank metric of MDS-codes. Given any integer $q$ power of a prime and any integer $n$ there is a family of MRD-codes of length $n$ over $\FF{q^n}$ having polynomial-time…
Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
Compared to real-valued signals, complex-valued signals provide a unique and intuitive representation of the phase of real physical systems and processes, which holds fundamental significance and is widely applied across many fields of…
We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence…
The classical majority-logic decoder proposed by Reed for Reed-Muller codes RM(r, m) of order r and length 2^m, unfolds in r+1 sequential steps, decoding message symbols from highest to lowest degree. Several follow-up decoding algorithms…