It is well known that an (n, k) code can be used to store information in a distributed storage system with n nodes/disks. If the storage capacity of each node/disk is normalized to one unit, the code can be used to store k units of information, where n > k. If the code used is maximum distance separable (MDS), then the storage system can tolerate up to (n−k) disk failures (erasures), since the ...

The problem of minimizing the trellis complexity of a code by coordinate permutation is studied. Three measures of trellis complexity are considered: the total number of states, the total number of edges, and the maximum state complexity of the trellis. The problem is proven NP-hard for all three measures, provided the eld over which the code is speciied is not xed. We leave open the problem of...

The automorphism group of a binary doubly-even self-dual code is always contained in the alternating group. On the other hand, given a permutation group G of degree n there exists a doubly-even self-dual G-invariant code if and only if n is a multiple of 8, every simple self-dual F2G-module occurs with even multiplicity in F n 2 , and G is contained in the alternating group.

We report on our experiences with the implementation of a parallel algorithm to compute the cycle structure of a permutation given as an oracle. As a sub-problem, the cycle structure of a modified permutation given as a table that is partitioned over N hard disks has to be computed. While a minor point during algorithm design and analysis, we spent most time to implement and tune this particula...

Recent advances in technology have produced a requirement for new implementations of good error-correcting codes. Such applications of codes also require efficient encoding and decoding methods. The method of permutation decoding was first developed by Jessie MacWilliams in the early 60’s and can be used when a linear code has a sufficiently large automorphism group to ensure the existence of a...

This paper introduces and studies the notion of an equidistant frequency permutation array (EFPA). An EFPA of length n = mλ, distance d and size v is defined to be a v×n array T such that 1) each row is a multipermutation on a multiset of m symbols, each repeated with frequency λ, and 2) the Hamming distance between any two distinct rows of T is precisely d. Such an array generalizes the well-s...

This paper introduces a new concept by which it is possible to design and implement arithmetic processors using permutation networks. To demonstrate this concept, several optoelectronic arithmetic units combining optical directional coupler switches and cyclic permutation networks are designed. The designs show that addition, subtraction, and multiplication can all be performed in O(log n) time...

In this paper, by using the notion of fuzzy subsets, the concept of F-permutation is introduced. Then by applying this notion the concepts of presentation of an F-polygroup, graph of an F-permutation and F-permutation matrices are investigated.

In this paper, we present a fully pipelined LDPC decoder for 802.11n standard that supports variable block sizes and multiple code rates. The proposed architecture utilizes features of Quasi-Cyclic LDPC codes and layered decoding to reduce memory bits and interconnection complexity through efficient utilization of permutation network for forward and backward interconnection routing. Permutation...

—An algorithm for finding the starting state of a feedback tailbiting encoder is proposed, based solely on the properties of the encoder state diagram. With this approach, conditions for the existence of a tailbiting code generated by such an encoder are naturally tested in the process of preparing a certain permutation table for the starting state determination algorithm. A tailbiting failure ...