The i-vector is a low dimensional representation of Gaussian mixture model (GMM) mean supervector derived through factor analysis and forms the most dominant approach for speaker verification (SV). In our earlier work, we have proposed the sparse coding of the GMM mean supervectors over KSVD learned speaker dictionary for SV. With joint factor analysis (JFA) based prior session/channel compensation the proposed approach is noted to provide a viable alternative to the i-vector approach. In this work, we propose two extensions to earlier presented approach. Firstly, the block sparsity introduced in finding the speaker representations. Secondly, a novel session/channel compensation explored through joint sparse coding over speaker-channel dictionaries which avoids the need of JFA completely. The proposed approach is noted to provide 0.59 percent relative improvement in EER when evaluated on NIST 2003 speaker recognition evaluation data set.