Transmission Lengths That Maximize Throughput of Variable-Length Coding & ACK/NACK Feedback

Variable-length (VL) coding sends an initial codeword followed by subsequent transmissions of incremental redundancy (IR) sent when the decoder indicates through feedback that it has not yet identified a reliable codeword. VL coding is a staple of modern communication to handle fading, and recent theoretical analysis and applications have demonstrated its value on non-fading channels for applications that require short blocklengths. To maximize throughput in a VL setting, the length of each IR transmission should be optimized. Sequential differential optimization (SDO) computes transmission lengths that optimize throughput by minimizing average blocklength. SDO produces a family of solutions that each maximize throughput for a specified maximum number of transmissions. This paper considers the average number of feedback transmissions per message as an alternative metric for the cost of the feedback resource. A Lagrangian approach provides a new SDO solution that jointly minimizes both the average blocklength and the average number of feedback transmissions associated with a message. The mapping of real-valued SDO solutions to the necessarily integer transmission lengths is also addressed.