Performance of Multistage Universal Decoder for Given Linear Codes over Additive Noise Channels

We propose a multilevel coding and multistage decod-ing scheme which is universal for a class of additive noise channels. Then, for a given pair of binary linear codes, we show an upper bound of the decoding er-ror probability. Further, we clarify the condition that the proposed coding and decoding scheme achieves the capacity of the channel and that the decoding error probability vanishes exponentially with code length. 1