On the construction of maximal prefix-synchronized codes

Abstract

We present a systematic procedure for mapping data sequences into codewords of a prefix-synchronized code (PS-code), as well as for performing the inverse mapping. A PS-code, proposed by Gilbert (1960), belongs to a subclass of comma-free codes and is useful to recover word synchronization when errors have occurred in the stream of codewords. A PS-code is defined as a set of codewords with the property that each codeword has a known sequence as a prefix, followed by a coded data sequence in which this prefix is not allowed to occur. The largest PS-code among all PS-codes of the same code length is called a maximal prefix-synchronized code (MPS-code). We develop an encoding and decoding algorithm for Gilbert's MPS-code with a prefix of the form 11...10 and extend the algorithm to the class PS-codes of which the prefix is self-uncorrelated. The computational complexity of the entire mapping process is proportional to the length of the codewords.