Related papers: Improved Lower Bounds for Secure Codes and Related…
We approach index coding as a special case of rate-distortion with multiple receivers, each with some side information about the source. Specifically, using techniques developed for the rate-distortion problem, we provide two upper bounds…
The model of the quantum protocols sealing a classical bit is studied. It is shown that there exist upper bounds on its security. For any protocol where the bit can be read correctly with the probability $\alpha $, and reading the bit can…
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage…
Parent-identifying schemes provide a way to identify causes from effects for some information systems such as digital fingerprinting and group testing. In this paper, we consider combinatorial structures for parent-identifying schemes.…
As a crucial technique for integrated circuits (IC) test response compaction, $X$-compact employs a special kind of codes called $X$-codes for reliable compressions of the test response in the presence of unknown logic values ($X$s). From a…
In this paper, we investigate the encoding circuit size of Hamming codes and Hadamard codes. To begin with, we prove the exact lower bound of circuit size required in the encoding of (punctured)~Hadamard codes and (extended)~Hamming codes.…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
Subspace codes form the appropriate mathematical setting for investigating the Koetter-Kschischang model of fault-tolerant network coding. The Main Problem of Subspace Coding asks for the determination of a subspace code of maximum size…
In this paper we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find the average quantum enumerators of the ensembles of finite…
Efficient decoding is crucial to high-throughput and power-sensitive wireless communication scenarios. A theoretical analysis of the performance-complexity tradeoff toward low-complexity decoding is required for a better understanding of…
The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding…
Codes defined on graphs and their properties have been subjects of intense recent research. On the practical side, constructions for capacity-approaching codes are graphical. On the theoretical side, codes on graphs provide several…
We consider the problem of communication efficient secure distributed matrix multiplication. The previous literature has focused on reducing the number of servers as a proxy for minimizing communication costs. The intuition being, that the…
This paper presents general bounds on the highest achievable rate for list-decodable insertion-deletion codes. In particular, we give novel outer and inner bounds for the highest achievable communication rate of any insertion-deletion code…
In the two-part paper, we consider the problem of secure network coding when the information rate and the security level can change over time. To efficiently solve this problem, we put forward local-encoding-preserving secure network…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
Subspace codes are the $q$-analog of binary block codes in the Hamming metric. Here the codewords are vector spaces over a finite field. They have e.g. applications in random linear network coding, distributed storage, and cryptography. In…
The main result here is a characterisation of binary $2$-neighbour-transitive codes with minimum distance at least $5$ via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of…
We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…