Upper Bound on the Efficiency of dc-Constrained Codes

Abstract

We derive the limiting efficiencies of dc-constrained codes. Given bounds on the running digital sum (RDS), the best possible coding efficiency η, for a K-ary transmission alphabet, is η = log <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</inf> /log <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> K, where λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</inf> is the largest eigenvalue of a matrix which represents the transitions of the allowable states of RDS. Numerical results are presented for the three special cases of binary, ternary and quaternary alphabets.