Efficient Encoding of Constrained Block Codes

Abstract

We present coding methods for generating $\ell$ -symbol constrained codewords taken from a set, $\mathcal{\mathcal { S }}$ , of allowed codewords. In standard practice, the size of the set $\mathcal{S}$ , denoted by $M=|\mathcal{S}|$ , is truncated to an integer power of two, which may lead to a serious waste of capacity. We present an efficient and low-complexity coding method for avoiding the truncation loss, where the encoding is accomplished in two steps: first, a series of binary input (user) data is translated into a series of $M$ -ary symbols in the alphabet $\mathbb{M}=\{0, \ldots, M-1\}$ . Then, in the second step, the $M$ -ary symbols are translated into a series of admissible $\ell$ -symbol words in $\mathcal{S}$ by using a small look-up table. The presented construction of Pearson codes and fixed-weight codes offers a rate close to capacity. For example, a 255B320B balanced code, where 255 source bits are translated into 32 10-bit balanced codewords, has a rate 0.1% below capacity.