Efficient balancing of q-ary sequences with parallel decoding

Constructions for constant-weight ICI-free codes

“…The rest of the paper will be organized as follows: In Section II, we will present a construction for constant-weight ICIfree codes that is similar to the balancing of q-ary codewords (see [6] for more details on binary balancing and [9] for details on q-ary balancing). We then calculate the coding rate of this construction.…”

On m-ary balanced codes with parallel decoding

“…An m-ary balanced code is a block code of length n such that each codeword is balanced. The m-ary balanced codes can be used to detect unidirectional errors, to reject the low frequencies in digital communication systems, and so on [9], [4], [7]. The problem is to convert the information words into balanced words using the minimum possible redundancy.…”

“…Many researchers have given various efficient implementations of this complementation method for both binary and m-ary case [2], [1], [8], [9], [10], [11], [7], [5]. In the parallel decoding implementation of Knuth's complementation method, the check symbol C directly encodes the number h b of bits complemented.…”

“…Note also that the smaller is the set of balancing functions the lower is the redundancy of the coding scheme. In [7], an m-ary generalization is given for the simple parallel decoding scheme which uses p = mk balancing functions. In Section II an improved m-ary generalization which uses only p = (m − 1)k + m mod 2 < mk balancing functions is given and so a lower redundancy is obtained.…”

“…Using r check digits, the simple parallel decoding scheme in [7] can balance k ≤ 1 m r (m − 1)r/2 m information digits; whereas, the scheme given in Section II improves on the scheme in [7] because it can balance…”