Method and apparatus for the representation and processing of genome sequence data, produced by genome sequencing machines, when aligned on one or more reference sequences. Sequence reads are coded by aligning them with respect to pre-existing or constructed reference sequences. After the alignment, the coding process is composed of a classification of the reads into data classes, followed by the coding of each data class in terms of a multiplicity of descriptors layers. Specific source models and entropy coders are used for the coding of the sub-sets of descriptors used to represent each data class.