1. A method for data storage, comprising: in a system that includes a host having a host memory and a memory controller that is separate from the host and stores data for the host in a non-volatile memory including multiple memory cells; allocating a portion of the host memory for use by the memory controller; sending a storage request, by the memory controller to the host, instructing the host to store, in the allocated portion of the host memory, information items relating to respective groups of the memory cells of the non-volatile memory; storing, by the host, in the allocated portion of the host memory, the information items relating to the respective groups of the memory cells responsive to the storage request sent by the memory controller; receiving, by the memory controller, from the host a command that causes the memory controller to access a given group of the memory cells; sending, in response to the command, a retrieval request, by the memory controller to the host processor, instructing the host to retrieve from the allocated portion of the host memory by the memory controller a respective information item relating to the given group of the memory cells; retrieving, by the host, from the allocated portion of the host memory, the information items relating to the respective groups of the memory cells responsive to the retrieval request sent by the memory controller; and accessing the given group of the memory cells using the retrieved information item.