Consider an extended version of noisy source coding in which the compressed data must be transmitted over an imperfect (forward) channel before being further processed. An interesting criterion for designing the quantizer in such cases is to maximize the end-to-end transmission rate. As then finding the globally optimal solution via the naive brute-force search is practically infeasible, a number of routines have been proposed aiming at providing complexity-wise tractable procedures at the expense of converging to local optima. In this paper, we study the relation between two particular devised heuristics appeared in completely different applications and prove their algorithmic equivalence through an in-depth analytical investigation of their counterpart algorithmic steps. We further substantiate our presented line of argumentation by means of computer-generated simulations.