Efficient Encoding of Constrained Block Codes
Kees A. Schouhamer Immink, Kui Cai · IEEE Communications Letters · 2021
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.