Srikanth Pai | Indian Institute of Science (original) (raw)

Papers by Srikanth Pai

The set of all subspaces of F_q^n is denoted by P_q(n). The subspace distance d_S(X,Y) = (X)+ (Y)... more The set of all subspaces of F_q^n is denoted by P_q(n). The subspace distance d_S(X,Y) = (X)+ (Y) - 2(X ∩ Y) defined on P_q(n) turns it into a natural coding space for error correction in random network coding. A subset of P_q(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of P_q(n). Braun, Etzion and Vardy conjectured that the largest cardinality of a linear code, that contains F_q^n, is 2^n. In this paper, we prove this conjecture and characterize the maximal linear codes that contain F_q^n.

— The binary coding theory and subspace codes for random network coding exhibit similar structure... more — The binary coding theory and subspace codes for random network coding exhibit similar structures. The method used to obtain a Singleton bound for subspace codes mimic the technique used in obtaining the Singleton bound for binary framework that captures these similarities. As a first step towards answering this question, we use the lattice framework proposed in [1]. A lattice is a partially ordered set in which any two elements have a least upper bound and a greatest lower bound. A ‘lattice scheme ’ is defined as a subset of a lattice. In this paper, we derive a Singleton bound for lattice schemes and obtain Singleton bounds known for binary codes and subspace codes as special cases. The lattice framework gives additional insights into the behaviour of Singleton bound for subspace codes. We also obtain a new upper bound on the code size for non-constant dimension

In this paper, we will employ the technique used in the proof of classical Singleton bound to der... more In this paper, we will employ the technique used in the proof of classical Singleton bound to derive upper bounds for rank metric codes and Ferrers diagram rank metric codes. These upper bounds yield the rank distance Singleton bound and an upper bound presented by Etzion and Silberstein respectively. Also we introduce generalized Ferrers diagram rank metric code which is a Ferrers diagram rank metric code where the underlying rank metric code is not necessarily linear. A new Singleton bound for generalized Ferrers diagram rank metric code is obtained using our technique.

IEEE Transactions on Information Theory, 2015

2009 First UK-India International Workshop on Cognitive Wireless Systems (UKIWCWS), 2009

Abstract In this article, we consider the setting of one-shot spectrum hole detection for a unifo... more Abstract In this article, we consider the setting of one-shot spectrum hole detection for a uniformly distributed secondary network under fading and path loss. We separate the sensors that are used to detect spectral holes from the secondary transmitters, thus ...

2013 IEEE International Symposium on Information Theory, 2013

The set of all subspaces of F n q is denoted by Pq(n). The subspace distance dS(X, Y ) = dim(X) +... more The set of all subspaces of F n q is denoted by Pq(n). The subspace distance dS(X, Y ) = dim(X) + dim(Y ) − 2 dim(X ∩ Y ) defined on Pq(n) turns it into a natural coding space for error correction in random network coding.

The binary coding theory and subspace codes for random network coding exhibit similar structures.... more The binary coding theory and subspace codes for random network coding exhibit similar structures. The method used to obtain a Singleton bound for subspace codes mimic the technique used in obtaining the Singleton bound for binary codes.This motivates the question of whether there is an abstract framework that captures these similarities. As a first step towards answering this question, we use the lattice framework proposed by Braun in [1]. A lattice is a partially ordered set in which any two elements have a least upper bound and a greatest lower bound. A lattice scheme is defined as a subset of a lattice. In this paper, we derive a Singleton bound for lattice schemes and obtain Singleton bounds known for binary codes and subspace codes as special cases. The lattice framework gives additional insights into the behavior of Singleton bound for subspace codes. We also obtain a new upper bound on the code size for non-constant dimension codes. The plots of this bound along with plots of the code sizes of known non-constant dimension codes in the literature reveal that our bound is tight for certain parameters of the code.

In this article, we consider the setting of one-shot spectrum hole detection for a uniformly dist... more In this article, we consider the setting of one-shot spectrum hole detection for a uniformly distributed secondary network under fading and path loss. We separate the sensors that are used to detect spectral holes from the secondary transmitters, thus allowing each secondary transmitter to benefit from the decisions of multiple (shared)sensors. The detection performance of the sensors varies with the distance from the primary transmitter. Thus a secondary listens to different average number of sensors as it moves around the cell, making the fusion rule complicated. We coin the term communicating shaping function f that is used by the sensors to modulate the coverage area of the sensors. A shaping function is designed heuristically so that the area of coverage normalised by the detection probability of the sensors is the same throughout the cell. This makes the average number of communicating sensors seen by a secondary invariant to the location of the secondary users, allowing a fixed location-invariant fusion rule to be employed at the secondary transmitter.

Arxiv preprint arXiv:1001.3107, Jan 1, 2010

The set of all subspaces of F_q^n is denoted by P_q(n). The subspace distance d_S(X,Y) = (X)+ (Y)... more The set of all subspaces of F_q^n is denoted by P_q(n). The subspace distance d_S(X,Y) = (X)+ (Y) - 2(X ∩ Y) defined on P_q(n) turns it into a natural coding space for error correction in random network coding. A subset of P_q(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of P_q(n). Braun, Etzion and Vardy conjectured that the largest cardinality of a linear code, that contains F_q^n, is 2^n. In this paper, we prove this conjecture and characterize the maximal linear codes that contain F_q^n.

— The binary coding theory and subspace codes for random network coding exhibit similar structure... more — The binary coding theory and subspace codes for random network coding exhibit similar structures. The method used to obtain a Singleton bound for subspace codes mimic the technique used in obtaining the Singleton bound for binary framework that captures these similarities. As a first step towards answering this question, we use the lattice framework proposed in [1]. A lattice is a partially ordered set in which any two elements have a least upper bound and a greatest lower bound. A ‘lattice scheme ’ is defined as a subset of a lattice. In this paper, we derive a Singleton bound for lattice schemes and obtain Singleton bounds known for binary codes and subspace codes as special cases. The lattice framework gives additional insights into the behaviour of Singleton bound for subspace codes. We also obtain a new upper bound on the code size for non-constant dimension

In this paper, we will employ the technique used in the proof of classical Singleton bound to der... more In this paper, we will employ the technique used in the proof of classical Singleton bound to derive upper bounds for rank metric codes and Ferrers diagram rank metric codes. These upper bounds yield the rank distance Singleton bound and an upper bound presented by Etzion and Silberstein respectively. Also we introduce generalized Ferrers diagram rank metric code which is a Ferrers diagram rank metric code where the underlying rank metric code is not necessarily linear. A new Singleton bound for generalized Ferrers diagram rank metric code is obtained using our technique.

IEEE Transactions on Information Theory, 2015

2009 First UK-India International Workshop on Cognitive Wireless Systems (UKIWCWS), 2009

Abstract In this article, we consider the setting of one-shot spectrum hole detection for a unifo... more Abstract In this article, we consider the setting of one-shot spectrum hole detection for a uniformly distributed secondary network under fading and path loss. We separate the sensors that are used to detect spectral holes from the secondary transmitters, thus ...

2013 IEEE International Symposium on Information Theory, 2013

The set of all subspaces of F n q is denoted by Pq(n). The subspace distance dS(X, Y ) = dim(X) +... more The set of all subspaces of F n q is denoted by Pq(n). The subspace distance dS(X, Y ) = dim(X) + dim(Y ) − 2 dim(X ∩ Y ) defined on Pq(n) turns it into a natural coding space for error correction in random network coding.

The binary coding theory and subspace codes for random network coding exhibit similar structures.... more The binary coding theory and subspace codes for random network coding exhibit similar structures. The method used to obtain a Singleton bound for subspace codes mimic the technique used in obtaining the Singleton bound for binary codes.This motivates the question of whether there is an abstract framework that captures these similarities. As a first step towards answering this question, we use the lattice framework proposed by Braun in [1]. A lattice is a partially ordered set in which any two elements have a least upper bound and a greatest lower bound. A lattice scheme is defined as a subset of a lattice. In this paper, we derive a Singleton bound for lattice schemes and obtain Singleton bounds known for binary codes and subspace codes as special cases. The lattice framework gives additional insights into the behavior of Singleton bound for subspace codes. We also obtain a new upper bound on the code size for non-constant dimension codes. The plots of this bound along with plots of the code sizes of known non-constant dimension codes in the literature reveal that our bound is tight for certain parameters of the code.

In this article, we consider the setting of one-shot spectrum hole detection for a uniformly dist... more In this article, we consider the setting of one-shot spectrum hole detection for a uniformly distributed secondary network under fading and path loss. We separate the sensors that are used to detect spectral holes from the secondary transmitters, thus allowing each secondary transmitter to benefit from the decisions of multiple (shared)sensors. The detection performance of the sensors varies with the distance from the primary transmitter. Thus a secondary listens to different average number of sensors as it moves around the cell, making the fusion rule complicated. We coin the term communicating shaping function f that is used by the sensors to modulate the coverage area of the sensors. A shaping function is designed heuristically so that the area of coverage normalised by the detection probability of the sensors is the same throughout the cell. This makes the average number of communicating sensors seen by a secondary invariant to the location of the secondary users, allowing a fixed location-invariant fusion rule to be employed at the secondary transmitter.

Arxiv preprint arXiv:1001.3107, Jan 1, 2010