Near Shannon limit decoding for 1% packet error rate

In this paper a hierarchical decoding structure is proposed. With this decoding structure, we can near optimally decode a rate 1/2 convolutional code with memory length of 30 in a short packet format (300 information bits). The simulation results show that on Gaussian channels the packet drop rate of 1% can be achieved at the cost of: (a) the E_b/N₀ requirement is 1 dB away from the Shannon limit (where the rate loss due to the tail bits has not been considered) and (b) average computational complexity is about the same as a few thousand state Viterbi algorithm, but the maximum computational complexity could be high. Compared with the Shannon´s sphere packing lower bound, for a packet drop rate of 1% the terminated rate 1/2 convolutional codes with m=14, 19 and 25 are nearly perfect (just under 1 dB of imperfectness, after consideration of the rate loss and the Shannon limit shift due to the tail bits and 3 parity bits), where the peak complexity for the hierarchical decoder is similar to that of the 1024, 4096 and 16384 state Viterbi decoder for m=14, 19 and 25, respectively