Method and apparatus for constructing asymptotically optimal second

Abstract

An encoding apparatus for constructing an asymptotically optimal coding scheme for second order DC-constrained channels is disclosed. A first encoding function block breaks an input data stream into equal sized vectors of length m bits. A sign designation bit is then attached to each vector to make vectors of length m+1 bits. r redundancy bits are added to each vector, to produce balanced vectors of length m+1+r bits. A first moment is calculated for each vector. A determination is made whether the addition of this vector's first moment value to an accumulated running sum of all the vectors' first moments effectively drives the running sum in the direction of zero. If is does then that vector's first moment is added to the accumulated running sum of first moments and the vector is added to the output array. If not, then the value of that vector's first moment is inverted before being added to the accumulated running sum, and the individual bits of this vector get inverted, and the sign designation bit of that vector gets toggled so as to indicate upon decoding that the bits of this vector have been involved. This encoding process is repeated until all the first moments of all the individual vectors of the balanced array have been calculated and a total accumulated running sum of all the first moments has been determined. A last balanced vector is produced, whose first moment value is added to the value of the total accumulation running first moment sum to drive the final first moment sum to zero. The output array of such vectors is then second-order DC-free, and the above described encoder is asymptotically optimal for second order DC-constrained channels.