An implementation of Elias coding for input-restricted channels

Abstract

Ahstrurt-An implementation of Elias coding for input-restricted channels is presented and analyzed. This is a variabk-to-fixed length coding method that uses finite-precision arithmetic and can work at rates arbitrarily close to channel capacity as the precision is increased. The method offers a favorable tradeoff between complexity and coding efficiency. For example, in experiments with the 12, 7 1 runlength constrained channel, a coding efficiency of 0.9977 is observed, which is significantly better than what is achievable by other known methods of comparable complexity.

Lossless sliding-block compression of constrained systems

“…The reader can verify that the sets E 0 , E (1) 1 , E (2) 1 , E (1) 2 , and E (2) 2 have total weights 15, 15, 7, 16, and 16, respectively, as desired (in fact, the weights of E (1) 2 and E (2) 2 are forced to be 16).…”

“…Recall that the capacity, cap(S), of a constraint S is de ned by cap(S) = lim !1 (1=`) log jS`j ; (2) where the limit is known to exist 12, Section 3.2.1] (hereafter all logarithms are taken to base 2). Since jS qm j jS q j m for any choice of positive integers q and m, it follows that cap(S) = lim m!1 (1=(qm)) log jS qm j (1=q) log jS q j ; that is, the limit in the right-hand side of (2) is taken over elements each of which is an upper bound on cap(S).…”

“…A state splitting of a graph G (called an out-splitting in 12, Section 4.1] and sometimes called a round of state splitting) is obtained by partitioning the set, E u , of outgoing edges from each state u of G into N = N(u) disjoint sets, E u = E (1) u E (2) u E (N) u ;…”

“…(5) replacing u by descendant states u (1) ; u (2) ; : : : ; u (N) , assigning E (r) u as outgoing edges from u (r) , and replicating all edges incoming to a state v to each of its descendants v (r) .…”

“…The resulting split graph H will have ve states, 0, 1 (1) , 1 (2) , 2 (1) , and 2 (2) , and the induced (A H ; n)-super-vector is The following modi cation of Proposition 4.4 of 12] shows that in general there always is an x-consistent splitting whenever we need one. Proposition 4 Let G be an irreducible graph which does not have out-degree at most n and let x be an (A G ; n)-super-vector.…”