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Most of the world's digital data is currently encoded in a sequential form, and compression methods for sequences have been studied extensively. However, there are many types of non-sequential data for which good compression techniques are…
Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binary-input/symmetric-output channels. The case of non-symmetric channels is tackled either by the LDPC coset code…
Bitmap indexes are commonly used in databases and search engines. By exploiting bit-level parallelism, they can significantly accelerate queries. However, they can use much memory, and thus we might prefer compressed bitmap indexes.…
We study codes that are list-decodable under insertions and deletions. Specifically, we consider the setting where a codeword over some finite alphabet of size $q$ may suffer from $\delta$ fraction of adversarial deletions and $\gamma$…
State-constrained signal codes directly encode modulation signals using signal processing filters, the coefficients of which are constrained over the rings of formal power series. Although the performance of signal codes is defined by these…
Rate-compatible error-correcting codes (ECCs), which consist of a set of extended codes, are of practical interest in both wireless communications and data storage. In this work, we first study the lower bounds for rate-compatible ECCs,…
Communication overhead is one of the major performance bottlenecks in large-scale distributed computing systems, in particular for machine learning applications. Conventionally, compression techniques are used to reduce the load of…
This paper addresses the problem of data compression with local decoding and local update. A compression scheme has worst-case local decoding $d_{wc}$ if any bit of the raw file can be recovered by probing at most $d_{wc}$ bits of the…
One of the main difficulties of scaling current localization systems to large environments is the on-board storage required for the maps. In this paper we propose to learn to compress the map representation such that it is optimal for the…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their…
This paper proposes two novel schemes of wideband compressive spectrum sensing (CSS) via block orthogonal matching pursuit (BOMP) algorithm, for achieving high sensing accuracy in real time. These schemes aim to reliably recover the…
In magnetic-recording systems, consecutive sections experience different signal to noise ratios (SNRs). To perform error correction over these systems, one approach is to use an individual block code for each section. However, the…
We present an optimal method for encoding cluster assignments of arbitrary data sets. Our method, Random Cycle Coding (RCC), encodes data sequentially and sends assignment information as cycles of the permutation defined by the order of…
Byte-Pair Encoding (BPE) is a widely used method for subword tokenization, with origins in grammar-based text compression. It is employed in a variety of language processing tasks such as machine translation or large language model (LLM)…
In many important applications -- such as search engines and relational database systems -- data is stored in the form of arrays of integers. Encoding and, most importantly, decoding of these arrays consumes considerable CPU time.…
We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. We introduce an $\ell_2$ regularized formulation of CS which we…
Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem…
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…