Ángela I. Barbero

The Weight Hierarchy of Hermitian Codes

We compute the complete weight hierarchies of all Hermitian codes. The tools used are the arithmetic of Hermitian curves and the order bound on the generalized Hamming weights.

Cycle-logical treatment for "Cyclopathic" networks

This correspondence addresses the problem of finding the network encoding equations for error-free networks with multiple sources and sinks. Previous algorithms could not cope with cyclic networks. Networks that are cyclic in three different senses are considered in this correspondence, and two extensions of the polynomial time Linear Information Flow (LIF) algorithm are presented. The first algorithm will produce the network encoding equations for a network which can be cyclic, unless the actual flow paths form cycles. The second algorithm will work also when the flow paths form simple cycles. Finally an example of a third kind of cyclic network, where the previous algorithms will fail, is given. However, a binary encoding is provided also in this case.

Weight hierarchy of a product code

Formulas to compute the first members of the weight hierarchy of a product code are given and proved. Basic patterns for the supports of subcodes in which the minimum cardinalities can be found are presented. Hence, formulas for every term of the hierarchy can be given, and the proof for each case will be a generalization of the proofs shown here. >

Constrained codes for passive RFID communication

This paper1 addresses coding for power transfer, modulation, and error control for the reader-to-tag channel in near-field passive radio frequency identification (RFID) systems using inductive coupling as a power transfer mechanism. Different assumptions on channel noise (including two different models for bit-shifts, insertions and deletions, and additive white Gaussian noise) are discussed. In particular, we propose a discretized Gaussian shift channel for the reader-to-tag channel in passive RFID systems, and design some new simple codes for error avoidance on this channel model. Finally, some simulation results are presented to compare the proposed codes to the Manchester code and two previously proposed codes for the bit-shift channel model.

Heuristic Algorithms for Small Field Multicast Encoding

We explore and present heuristic algorithms that, for a given network, attempt to minimize the field size required for encoding

Modulation codes for reader-tag communication on inductively coupled channels

In this paper we study and compare methods for representing information for transmission on inductively coupled channels. We introduce combined runlength and power constraints on modulation codes for such channels, calculate the capacities of these new constraints, and propose new codes that meet the constraints.

Coding for Inductively Coupled Channels

Inductive coupling is a technique wherein one device (the reader) induces an electrical current in another device (the tag), thereby providing not only power for the tag, but also a communication channel. In this paper, we focus exclusively on the reader-to-tag channel. The first part of this paper presents modulation codes that possess a high minimum and a high average power. This is important, since the tag gets its entire power from the received signal, and the information should be modulated in a way that maximizes the power transferred to the tag. The presented modulation codes compare favorably to codes used in radio frequency identification applications today. The second part of the paper describes modulation codes with some error-correcting capabilities. In fact, most errors in the reader-to-tag channel are due to incorrect timing. Here, we propose to model the timing errors in the reader-to-tag communication channel by a simple bit-shift channel, and we will present optimal (in the sense of maximizing the code rate for a given block length) single bit-shift error-correcting codes for this simple bit-shift channel that also have large average power.

Coding for a Bit-Shift Channel with Applications to Inductively Coupled Channels

In this work, we will consider coding for a bitshift channel with applications to inductively coupled channels. Inductive coupling is a technique wherein one device (the reader) induces an electrical current in another device (the tag), thereby providing not only power for the tag, but also a communications channel. Most errors in the reader-to-tag channel are due to incorrect timing. In this work, we propose to model the timing errors in the reader-to-tag communications channel by a simple bit-shift channel. We will present optimal single bit-shift error-correcting codes for this simple bit-shift channel that also have large average power. This is important, since the tag gets its entire power from the received signal, and the information should be modulated in a way that maximizes the power transferred to the tag.

Near-Field Passive RFID Communication: Channel Model and Code Design

This paper discusses a new channel model and code design for the reader-to-tag channel in near-field passive radio frequency identification (RFID) systems using inductive coupling as a power transfer mechanism. If the receiver resynchronizes its internal clock each time a bit is detected, the bit-shift channel used previously in the literature to model the reader-to-tag channel needs to be modified. In particular, we propose a discretized Gaussian shift channel as a new channel model in this scenario. We introduce the concept of quantifiable error avoidance, which is much simpler than error correction. The capacity is computed numerically, and we also design some new simple codes for error avoidance on this channel model based on insights gained from the capacity calculations. Finally, some simulation results are presented to compare the proposed codes to the Manchester code and two previously proposed codes for the bit-shift channel model.

Maximum Likelihood Decoding of Codes on the Z-channel

The aim of this paper is to extend some basic concepts related to the Maximum Likelihood decoding of codes on the Z-channel, which is a particular, but very important, example of an asymmetric channel. We study distance properties of linear codes over the Z-channel, in order to define a suitable metric for the implementation of a Maximum Likelihood decoder on the channel. A combinatorial expression for an approximation on the probability of incorrect Maximum Likelihood decoding is also provided, and comparisons are given to evaluate the tightness of the estimation, when a Hamming code, a Turbo code and an LDPC code are used for communicating over the Z-channel.