On the BICM Capacity

Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor

Coded Parity Packet Transmission Method for Two Group Resource Allocation

Gap value control is investigated when the number of source and parity packets is adjusted in a concatenated coding scheme whilst keeping the overall coding rate fixed. Packet-based outer codes which are generated from bit-wise XOR combinations of the source packets are used to adjust the number of both source packets. Having the source packets, the number of parity packets, which are the bit-wise XOR combinations of the source packets can be adjusted such that the gap value, which measures the gap between the theoretical and the required signal-to-noise ratio (SNR), is controlled without changing the actual coding rate. Consequently, the required SNR reduces, yielding a lower required energy to realize the transmission data rate. Integrating this coding technique with a two-group resource allocation scheme renders efficient utilization of the total energy to further improve the data rates. With a relatively small-sized set of discrete data rates, the system throughput achieved by the proposed two-group loading scheme is observed to be approximately equal to that of the existing loading scheme, which is operated with a much larger set of discrete data rates. The gain obtained by the proposed scheme over the existing equal rate and equal energy loading scheme is approximately 5 dB. Furthermore, a successive interference cancellation scheme is also integrated with this coding technique, which can be used to decode and provide consecutive symbols for inter-symbol interference (ISI) and multiple access interference (MAI) mitigation. With this integrated scheme, the computational complexity is signi cantly reduced by eliminating matrix inversions. In the same manner, the proposed coding scheme is also incorporated into a novel fixed energy loading, which distributes packets over parallel channels, to control the gap value of the data rates although the SNR of each code channel varies from each other

Coded Parity Packet Transmission Method for Two Group Resource Allocation

Gap value control is investigated when the number of source and parity packets is adjusted in a concatenated coding scheme whilst keeping the overall coding rate fixed. Packet-based outer codes which are generated from bit-wise XOR combinations of the source packets are used to adjust the number of both source packets. Having the source packets, the number of parity packets, which are the bit-wise XOR combinations of the source packets can be adjusted such that the gap value, which measures the gap between the theoretical and the required signal-to-noise ratio (SNR), is controlled without changing the actual coding rate. Consequently, the required SNR reduces, yielding a lower required energy to realize the transmission data rate. Integrating this coding technique with a two-group resource allocation scheme renders efficient utilization of the total energy to further improve the data rates. With a relatively small-sized set of discrete data rates, the system throughput achieved by the proposed two-group loading scheme is observed to be approximately equal to that of the existing loading scheme, which is operated with a much larger set of discrete data rates. The gain obtained by the proposed scheme over the existing equal rate and equal energy loading scheme is approximately 5 dB. Furthermore, a successive interference cancellation scheme is also integrated with this coding technique, which can be used to decode and provide consecutive symbols for inter-symbol interference (ISI) and multiple access interference (MAI) mitigation. With this integrated scheme, the computational complexity is signi cantly reduced by eliminating matrix inversions. In the same manner, the proposed coding scheme is also incorporated into a novel fixed energy loading, which distributes packets over parallel channels, to control the gap value of the data rates although the SNR of each code channel varies from each other