Almost-Certainly Runlength-Limiting Codes

Abstract

Standard runlength-limiting codes — nonlinear codes defined by trellises — have the disadvantage that they disconnect the outer errorcorrecting code from the bit-by-bit likelihoods that come out of the channel. I present two methods for creating transmissions that, with probability extremely close to 1, both are runlength-limited and are codewords of an outer linear error-correcting code (or are within a very small Hamming distance of a codeword). The cost of these runlength-limiting methods, in terms of loss of rate, is significantly smaller than that of standard runlength-limiting codes. The methods can be used with any linear outer code; low-density parity-check codes are discussed as an example.

The cost of the method, in terms of additional redundancy, is very small: a reduction in rate of less than 1% is sufficient for a code with blocklength 4376 bits and maximum runlength 14.