Catálogo de publicaciones - libros

This paper addresses the problem of threshold traitor tracing for digital content where, by embedding appropriate digital patterns into the distributed content, it is possible to trace and identify the source of unauthorised redistribution.

We use a set of marking assumptions where the adversaries have varying powers to change or erase coordinates of the fingerprint where their individual fingerprints differ–and consider the implications. We propose new codes derived from combinatorial designs–and develop a method for concatenating these codes to filter out the false positives and defend against some of the attacks considered.

We examine the well-known problem of determining the capacity of multi-dimensional run-length-limited constrained systems. By recasting the problem, which is essentially a combinatorial counting problem, into a probabilistic setting, we are able to derive new lower and upper bounds on the capacity of (0,)-RLL systems. These bounds are better than all previously-known bounds for ≥ 2, and are even tight asymptotically. Thus, we settle the open question: what is the rate at which the capacity of (0,)-RLL systems converges to 1 as → ∞? While doing so, we also provide the first ever non-trivial upper bound on the capacity of general (,)-RLL systems.

This paper compares two approaches to reliable communication over fading channels using low-density parity check (LDPC) codes. The particular model considered is the block fading channel with independent channel realizations. The first approach uses a block interleaver to create independent sub-channels that are encoded using irregular LDPC codes with rates specified by the appropriate capacity values; this first approach uses a decision feedback structure wherein decoded data are used as pilots to estimate the channel prior to the next round of decoding. The second approach uses a combined graph describing both the channel and the code to iteratively estimate the channel and decode data. For comparable channels, it is shown that the decision-feedback approach provides better performance when a long delay is acceptable, while the iterative receiver provides better performance when more stringent delay constraints are imposed.

We study the design of structured Tanner codes with low error-rate floors on the AWGN channel. The design technique involves the “doping” of standard LDPC (proto-)graphs, by which we mean Hamming or recursive systematic convolutional (RSC) code constraints are used together with single-parity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good” graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult. Lastly, we perform a simple complexity analysis of our Tanner codes and examine the performance of lower-complexity, suboptimal Hamming-node decoders.

This paper is the first part of a sequence of two papers that present algebraic constructions of quasi-cyclic LDPC codes for AWGN, binary random and burst erasure channels. In this paper, a class of quasi-cyclic LDPC codes for both AWGN and binary random erasure channels is constructed based on finite fields and special vector representations of finite field elements.

This paper is the second part of a sequence of two papers that present several algebraic methods for constructing quasi-cyclic (QC) LDPC codes for AWGN, binary random and burst erasure channels. In the first paper, we presented a class of QC-LDPC codes for both the AWGN and binary random erasure channels. The construction of this class of QC-LDPC codes is based on finite fields and location vector representations of finite field elements. In this paper, we presented two other algebraic methods for constructing QC-LDPC codes for the AWGN, binary random and burst erasure channels.

This paper presents two new methods for constructing quasi-cyclic LDPC codes using certain special classes of balanced incomplete block designs constructed based on finite fields. The codes constructed perform well with iterative decoding over both AWGN and binary erasure channels.

It is shown that long enough extended -error correcting BCH codes are spanned by its lightest words of weight 2 + 2. The proof follows from an upper bound on the number of words of weight 2 + 2 in any subcode of of codimension 1.

The Feng-Rao bound gives good estimates of the minimum distance of a large class of codes. In this work we are concerned with the problem of how to extend the Feng-Rao bound so that it deals with all the generalized Hamming weights. The problem was solved by Heijnen and Pellikaan in [7] for a large family of codes that includes the duals of one-point geometric Goppa codes and the -ary Reed-Muller codes, but not the Feng-Rao improved such ones. We show that Heijnen and Pellikaan’s results holds for the more general class of codes for which the traditional Feng-Rao bound can be applied. We also establish the connection to the Shibuya-Sakaniwa bound for generalized Hamming weights ([15], [16], [17], [18], [19] and [20]). More precisely we show that the Shibuya-Sakaniwa bound is a consequence of the extended Feng-Rao bound. In particular the extended Feng-Rao bound gives always at least as good estimates as does the Shibuya-Sakaniwa bound.

Dirty paper coding are relevant for wireless networks, multiuser channels, and digital watermarking. We show that the problem of dirty paper is essentially equivalent to some classes of constrained memories, and we explore the binary so-called nested codes, which are used for efficient coding and error-correction on such channels and memories.