Related papers: Constructing Linear Encoders with Good Spectra
We study zero-error unicast index-coding instances, where each receiver must perfectly decode its requested message set, and the message sets requested by any two receivers do not overlap. We show that for all these instances with up to…
Joint source-channel coding is a compelling paradigm when low-latency and low-complexity communication is required. This work proposes a theoretical framework that integrates classification and anomaly detection within the conventional…
This paper studies the random-coding exponent of joint source-channel coding for the multiple-access channel with correlated sources. For each user, by defining a threshold, the messages of each source are partitioned into two classes. The…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…
Joint encryption-encoding schemes have been released to fulfill both reliability and security desires in a single step. Using Low Density Parity Check (LDPC) codes in joint encryption-encoding schemes, as an alternative to classical linear…
Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes such as cyclic codes, Reed-Solomon codes, and Reed-Muller codes have nice decoding algorithms.…
Source and channel coding over multiuser channels in which receivers have access to correlated source side information is considered. For several multiuser channel models necessary and sufficient conditions for optimal separation of the…
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…
A single input multiple output (SIMO) multiple access channel, with a large number of transmitters sending symbols from a constellation to the receiver of a multi-antenna base station, is considered. The fundamental limits of joint decoding…
We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed,…
This paper asks a basic question: how much training is required to beat a universal source coder? Traditionally, there have been two types of source coders: fixed, optimum coders such as Huffman coders; and universal source coders, such as…
Constrained codes are used to eliminate error-prone patterns in various practical systems. Recently, we introduced efficient binary symmetric lexicographically-ordered constrained (LOCO) codes and asymmetric LOCO (A-LOCO) codes to increase…
Binary convolutional coding (BCC) has been a cornerstone of the IEEE 802.11 wireless LAN standard since its inception, and it remains relevant today across the full generational arc from the legacy 802.11a/g through Wi-Fi 6 (802.11ax) and…
Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a…
A new coding scheme for image transmission over noisy channel is proposed. Similar to standard image compression, the scheme includes a linear transform followed by successive refinement scalar quantization. Unlike conventional schemes, in…
Cyclic codes are the most studied subclass of linear codes and widely used in data storage and communication systems. Many cyclic codes have optimal parameters or the best parameters known. They are divided into simple-root cyclic codes and…
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 $-$…
We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems,…
One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…