Performance bounds in constrained sequence coding
Jonathan J. Ashley · 1987
Adler, Coppersmith, and Hassner (see IEEE-IT 29 5-22) present methods for coding arbitrary n-ary sequences into certain constrained systems of sequences, those with finite memory, defined by labelled directed graphs. An example is the run-length-limited system for the magnetic recording channel. Their codes have limited error propagation because the decoders are sliding block with a finite window length. In Part I, we present upper bounds on the necessary length of the decoder window. The bounds are linear in the memory, anticipation, and number of states of the original constraint graph presenting the constrained system. Certain applications require the use of digital codes whose encoded signal sequences have zero spectral density, or spectral nulls, at certain frequencies. Any finite state code having a spectral null at a rational multiple f of the bit frequency must have digital signal sequences any of whose running digital sums at f is bounded in modulus by a fixed c $\geq$ 0 (MS). In Part II, we bound possible code rates in terms of c.