investigated for the binary input discrete memoryless channels. Those

channels are the binary asymmetric channel (BAC), including the two

special cases of the binary symmetric channel (BSC) and the Z-channel

(ZC). The binary erasure channel (BEC) is a common used channel with

ternary output. For the asymmetric channels, a general BAC, it is

shown that so-called

The optimal (in the sense of minimum average error probability, using

maximum likelihood decoding) code structure is derived for the ZC in

the cases of two, three, and four codewords and an arbitrary finite

blocklength. For the symmetric channels, the BSC and the BEC, the

optimal code structure is derived with at most three codewords and an

arbitrary finite blocklength, a statement for linear optimal codes

with four codes is also given.

The derivation of these optimal codes relies heavily 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

that is not based on the union bound or other approximations.

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

[-] --__|__ /__\ /__ Senior Researcher & Lecturer, ETH Zurich, Switzerland

_|_ -- --|- _ / / Adj. Professor, National Chiao Tung University (NCTU), Taiwan

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

Last modified: Tue Aug 20 06:28:40 UTC+8 2013