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Array low density parity check (LDPC) codes are high-rate codes that can achieve good error rate performance in additive white Gaussian noise (AWGN) channels. However, array LDPC codes do not support arbitrary code lengths, because the code length of an array LDPC code with good error rate performance is limited to a multiple of a prime number. This paper proposes Size Compatible (SC)-array LDPC codes; they achieve good error rate performance while supporting arbitrary code lengths. We conduct computer simulations to evaluate the block error rate (BLER) performance of SC-array LDPC codes in AWGN channels. We also evaluate the corresponding performance of SC-array LDPC coded multiband OFDM systems for data transmission rates over 1 Gbps in the UWB multipath channel model CM 3. We show that if the submatrix size is a nonprime number, SC-array LDPC codes achieve better error rate performance than the conventional array LDPC codes in AWGN channels. We also show that the SC-array LDPC codes achieve better error rate performance than the punctured array LDPC codes in AWGN channels. We also show that if the submatrix size is a prime number, SC-array LDPC codes achieve the same error rate performance as conventional array LDPC codes in AWGN channels. Moreover, we show that for multiband OFDM systems with data transmission rates of over 1 Gbps, SC-array LDPC codes achieve better error rate performance than conventional array LDPC codes.

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Abstract-The paper presents results of collision probability evaluation of a one-to-many reversible mapping between user space and IPv6 address space which is developed to improve of IPv6 addresses generation in a local area network (LAN). Each time a user accesses the network, a dynamic unicast IPv6 address is given via DHCPv6 (Dynamic Host Configuration Protocol for IPv6) server to protect users from unwanted behavior analysis exploiting IPv6 addresses, thus protecting user privacy. This IPv6 address is generated dynamically using CFB (Cipher Feedback) mode of AES (Advanced Encryption Standard) algorithm based on user identity. The dynamic address can be uniquely linked to user if the need arises to allow network administrator to identify user based on captured IPv6 address during any security event. Checksum has been used for validation of probability of coincidental match of randomly generated Interface Id or generated by some other mechanism. The collision probability of the one-to-many reversible mapping for stateful IPv6 address assignment is evaluated using birthday paradox. The results show that the collision probability is very small indeed. The one-tomany reversible mechanism may be incorporated as an extension to the current DHCPv6 software.