probability, using maximum likelihood decoding) with a small number of

codewords are investigated for the binary asymmetric channel (BAC),

including the two special cases of the binary symmetric channel (BSC)

and the Z-channel (ZC), both with arbitrary cross-over

probabilities. For the ZC, the optimal code structure for an arbitrary

finite blocklength is derived in the cases of two, three, and four

codewords and conjectured in the case of five codewords. For the BSC,

the optimal code structure for an arbitrary finite blocklength is

derived in the cases of two and three codewords and conjectured in the

case of four codewords. For a general BAC, the best codebooks under

the assumption of a threshold decoder are derived for the case of two

codewords. The derivation of these optimal codes relies on a new approach

of constructing and analyzing the codebook matrix not row-wise

(codewords), but

definition of interesting code families that is recursive in the

blocklength $n$ and admits their

performance. This allows for a comparison of the average error

probability between all possible codebooks.

finite blocklength, flip codes, maximum likelihood (ML) decoder,

minimum average error probability, optimal codes, weak flip codes,

Z-channel.

-||- _|_ _|_ / __|__ 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: Thu Sep 5 10:18:56 UTC+8 2013