THE CAPACITY AND CODING GAIN OF CERTAIN CHECKERBOARD CODES

We define a checkerboard code as a two-dimensional binary code that sa tisfies some constraint, e.g., every binary one must be surrounded by eight zeros, and then investigate the capacity for each of several dif ferent constraints. Using a recursive construction we develop a series of loose bounds on the capacity. These bounds, in turn, lead to conje cturally precise estimates of the capacity by the use of a numerical c onvergence-speeding technique called Richardson extrapolation. Finally , using the value of the capacity, we define and compute a measure of coding gain which allows us to compare checkerboard codes to simple co ding schemes.