|| Polar shaping codes for costly noiseless and noisy channels
||Karthik Nagarjuna Tunuguntla, Paul H. Siegel, University of California, San Diego, United States|
||D6-S2-T2: Polar Codes IV
||Monday, 19 July, 22:20 - 22:40
||Monday, 19 July, 22:40 - 23:00
We propose a shaping code based on polar codes. For a costly noiseless channel, we show that the total cost of the proposed polar shaping code approaches the optimal total cost as block length grows. We also consider shaping for costly noisy discrete memoryless channels (DMCs). We first give an upper bound on the rate that can be achieved with a specified symbol occurrence probability distribution over a DMC. Then we formulate an optimization problem whose solution gives a lower bound on the optimal total cost for a costly noisy DMC. We compute the lower bound for the costly $M$-ary erasure channel. Finally, we propose polar shaping codes for costly noisy channels that achieve the lower bound by adapting polar codes for asymmetric channels proposed by Honda and Yamamoto.