Rates of constant-composition codes that mitigate intercell interference

The Capacity of Count-Constrained ICI-Free Systems

“…For ε > 0, let S q;a,b (p, ε) denote the subset of S q;a,b consisting of all words w ∈ S q;a,b in which the number of occurrences of each symbol s ∈ Σ lies in the interval 1 Since only the sizes of Σ, L, and H will matter, we identify the constrained system by the sizes of these sets. The capacity (or the asymptotic information rate) of S q;a,b under the count constraint specified by p is defined as 2 cap(S q;a,b , p)…”

Constrained codes for intercell interference mitigation and dynamic thresholding in flash memories

“…Our objectives are to find good bounds for the asymptotic rates and efficient encoding/decoding algorithms for high-rate codes. [14,15]. In this chapter, we present some of these results again for completeness and also provide some new results in more general cases.…”

“…Our first contribution in this topic is an explicit formula for the cardinality of A(n; w, I(a, b)) which has been presented in [14].…”

“…The proof of Theorem 1 has been presented in [14] and will be presented in Section 2.2 for completeness. The significance of the term B m (n, s 3 ) is explained therein.…”

“…We are now interested in finding the asymptotic rates R(ρ, I(a, b)) for general ρ and I(a, b). We solved this problem in some special cases and presented the result in [14]. In this dissertation, we solve the problem in general for all ρ and I(a, b).…”