• Huffman Code (optimal prefix-free code) • Shannon-Fano code • Shannon-Fano-Elias code • Arithmetic code (can handle a sequence of symbols) In general, the first three codes do not achieve the optimal rate H(X), and there are no immediate extensions of these codes to rate-optimal codes for a sequence of symbols. On the other hand, arithmetic coding is rate-optimal. However, all these schemes a...

We consider a direct sequence (DS-) code division multiple access (CDMA) system with orthogonally multiplexed pilot signals and minimum mean squared error (MMSE) data and channel estimation. Both flat and frequency-selective fading channels are considered. Large system analysis is used to optimize the pilot-to-data power ratio (PDR) and the code rate for a fixed bandwidth expansion. Specificall...

This paper introduces an explicit institution of bankruptcy into a general equilibrium model of endogenous ̄nancial markets with asymmetric information. The institution of bankruptcy is modelled as a set of rules that determine if an agent is eligible to have his debts discharged. Those rules are called a bankruptcy code. Given a bankruptcy code, we allow free entry of intermediaries o®ering al...

In this paper we study generalized weights as an algebraic invariant of a code. We first describe anticodes in the Hamming and in the rank metric, proving in particular that optimal anticodes in the rank metric coincide with Frobenius-closed spaces. Then we characterize both generalized Hamming and rank weights of a code in terms of the intersection of the code with optimal anticodes in the res...

Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, we first build a bridge between locally repairable code and packing. As an application of this bridge, some optimal locally repairable codes can be obtained by packings, which gives optimal locally repairable codes with flexible parameters. Index Terms Distributed storage, loc...

A simple construction of quaternary hermitian self-orthogonal codes with parameters [2n + 1, k + 1] and [2n + 2, k + 2] from a given pair of self-orthogonal [n, k] codes, and its link to quantum codes is considered. As an application, an optimal quaternary linear [28, 20, 6] dual containing code is found that yields a new optimal [[28, 12, 6]] quantum code.

The distance-3 cyclic lowest-density MDS array code (called the C-Code) is a good candidate for RAID 6 because of its optimal storage efficiency, optimal update complexity, optimal length, and cyclic symmetry. In this paper, the underlying connections between C-Codes (or quasi-C-Codes) and starters in group theory are revealed. It is shown that each C-Code (or quasi-C-Code) of length 2n can be ...

Abstmct We reveal an equivalence relation between the construction of a new class of low density MDS array codes, that we call B-Code, and a combinatorial problem known as perfect one-factorization of complete graphs. We use known perfect one-factors of complete graphs to create constructions and decoding algorithms for both B-Code and its dual code. B-Code and its dual are optimal in the sense...

This paper describes the theory behind and implementation of wburg, a code-generator generator that accepts tree grammars as input and produces a code generator that emits an optimal parse of an IR tree in just a single bottom-up pass. Furthermore, wburg eliminates the need for an explicit IR tree altogether. The grammars that wburg-generated parsers can parse are a proper subset of those that ...

.’ parallel concatenated convolutional coding scheme consists of two constituent systematic convolutional encoders linked by an interleaver. The information bits at the input of the first encoder are scrambled by the interleaver before entering the second encoder. The codewords of the parallel concatenated code consist of the information bits followed by the parity check bits of both encoders. ...