Distributed scalar quantizers for subband allocation

Efficient downlink resource allocation (e.g., subbands in OFDMA/LTE) requires channel state information (e.g., subband gains) local to each user be transmitted to the base station (BS). Lossy encoding of the relevant state may result in suboptimal resource allocations by the BS, the performance cost of which may be captured by a suitable distortion measure. This problem is an indirect distributed lossy source coding problem with the function to be computed representing the optimal resource allocation, and the distortion measuring the cost of suboptimal allocations. In this paper we investigate the use of distributed scalar quantizers for lossy encoding of state, where the BS wishes to compute the index of the user with the largest gain on each subband. We prove the superiority of a heterogeneous (across users) quantizer design over the optimal homogeneous quantizer design, even though the source variables are i.i.d.