and is shown to contain many beautiful properties. In particular, the

subfamily of

linear codes, i.e., they possess some

Different from linear codes that only exist for a number of

codewords

can be defined for an arbitrary

flip codes are related to

families maximize the minimum Hamming distance and meet the Plotkin

bound. However, while the binary nonlinear Hadamard codes have only

been shown to possess good Hamming-distance properties, the fair weak

flip codes are proven to be globally optimal — in the sense of

minimizing the error probability, and under the assumption that the

optimal codes can be constructed recursively in blocklength

all linear or nonlinear codes for the binary erasure channel (BEC) for

many values of the blocklength n and for

optimality results are conjectured.

Moreover, some applications to known bounds on the error probability

for a finite blocklength is introduced for comparison, while as

blocklength n going to infinity, the error exponent of a BEC for a

fixed number of codewords is also discussed.

The results in this work are founded upon a new powerful tool for the

analysis and generation of block codes: the column-wise approach to

the codebook matrix.

flip codes, maximum likelihood (ML) decoder, minimum average error

probability, optimal codes, weak flip codes.

-||- _|_ _|_ / __|__ Stefan M. Moser

[-] --__|__ /__\ /__ Senior Scientist, ETH Zurich, Switzerland

_|_ -- --|- _ / / Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan

/ \ [] \| |_| / \/ Web: https://moser-isi.ethz.ch/

Last modified: Sat Jun 1 09:32:14 UTC+8 2013