Designing Optimal Multiresolution Quantizers with Error Detecting Codes

This paper investigates the design of optimal multiresolution vector quantizers for broadcast channels with cyclic redundancy checks (CRC). Given a CRC-coded broadcast system with multiresolution vector quantization (MRVQ), a closed-form formula for the weighted end-to-end distortion (EED) is first derived under random index assignment. The closed-form expression is then further utilized to identify necessary optimality conditions to minimize the EED, from which an iterative algorithm is proposed for quantization design. Experiments conducted under both the point-to-point and broadcast channels demonstrate that for a wide range of channel error probability, inclusion of CRC significantly reduces the EED without sacrificing bandwidth. Further analyses are conducted to determine the best tradeoff between bits allocated for source quantization and CRC error detection.