In this work, we consider the minimum distance properties and convergence thresholds of 3-dimensional turbo codes (3D-TCs), recently introduced by Berrou et al.. Here, we consider binary 3D-TCs while the original work of Berrou et al. considered double-binary codes. In the first part of the paper, the minimum distance properties are analyzed from an ensemble perspective, both in the finite-leng...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding algorithms with nonexponential complexity known for RM codes. Decoding performance is further enhanced by using intermediate code lists and permutation procedures....

In this paper, we show a manner to use properties of the permutation group on some binary linear codes to improve the decoding algorithms. We search especially for particular permutations and we prove bounds on dimension of a special subcode of the idempotent subcode. This σ-subcode can have very lower dimension in practice than the original code. We give several examples at the end and explain...

Let A be a finite or countable alphabet and let θ be a literal (anti)morphism onto A∗ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under θ (θ-invariant for short). We establish a formula which allows to embed any non-complete θ-invariant code into a complete one: this brings a positive answer to the open ...

We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our previous work for vexillary permutations. We also analyze general tilings of Elnitsky’s polygon, and demonstrate that these are closely related to the pattern...

Let A2(n, d) be the maximum size of a binary code of length n and minimum distance d. In this paper we present the following new lower bounds: A2(18, 4) ≥ 5632, A2(21, 4) ≥ 40960, A2(22, 4) ≥ 81920, A2(23, 4) ≥ 163840, A2(24, 4) ≥ 327680, A2(24, 10) ≥ 136, and A2(25, 6) ≥ 17920. The new lower bounds are a result of a systematic computer search over transitive permutation groups.

A length-n Cayley permutation p of a total ordered set S is a length-n sequence of elements from S, subject to the condition that if an element x appears in p then all elements y < x also appear in p. In this paper, we give a Gray code list for the set of length-n Cayley permutations. Two successive permutations in this list di er at most in two positions.

In this paper, we study the contribution of compiler optimizations to energy reduction. In particular, we are interested in the impact of loop optimizations in terms of performance and power tradeoffs. Both low-level loop optimizations at code generation (back-end) phase, such as loop unrolling and software pipelining, and high-level loop optimizations at program analysis and transformation pha...