Three strongly sequential, lossless compression schemes, one with linearly growing per-letter computational complexity, and two with fixed per-letter complexity, are presented and analyzed for memoryless sources with abruptly changing statistics. The first method, which improves on Willems' weighting approach, asymptotically achieves a lower bound on the redundancy, and hence is optimal. The second scheme achieves redundancy of O (log N=N) when the transitions in the statistics are large, and O (log log N= log N) otherwise. The third approach always achieves redundancy of O (log N=N). Obviously, the two fixed complexity approaches can be easily combined to achieve the better redundancy between the two. Simulation results support the analytical bounds derived for all the coding schemes.

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Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive indices in increasing order of first occurrence.

Abstract-Three strongly sequential, lossless compression schemes, one with linearly growing per-letter computational complexity, and two with fixed per-letter complexity, are presented and analyzed for memoryless sources with abruptly changing statistics. The first method, which improves on Willems' weighting approach, asymptotically achieves a lower bound on the redundancy, and hence is optimal. The second scheme achieves redundancy of O (log N=N ) when the transitions in the statistics are large, and O (log log N= log N ) otherwise. The third approach always achieves redundancy of O ( log N=N ). Obviously, the two fixed complexity approaches can be easily combined to achieve the better redundancy between the two. Simulation results support the analytical bounds derived for all the coding schemes.