On decoding of multi-level MPSK modulation codes

The decoding problem of multi-level block modulation codes is investigated. The hardware design of soft-decision Viterbi decoder for some short length 8-PSK block modulation codes is presented. An effective way to reduce the hardware complexity of the decoder by reducing the branch metric and path metric, using a non-uniform floating-point to integer mapping scheme, is proposed and discussed. The simulation results of the design are presented. The multi-stage decoding (MSD) of multi-level modulation codes is also investigated. The cases of soft-decision and hard-decision MSD are considered and their performance are evaluated for several codes of different lengths and different minimum squared Euclidean distances. It is shown that the soft-decision MSD reduces the decoding complexity drastically and it is suboptimum. The hard-decision MSD further simplifies the decoding while still maintaining a reasonable coding gain over the uncoded system, if the component codes are chosen properly. Finally, some basic 3-level 8-PSK modulation codes using BCH codes as component codes are constructed and their coding gains are found for hard decision multistage decoding

Comparison of channel coding schemes for molecular communications systems

Future applications for nano-machines, such as drug-delivery and health monitoring, will require robust communications and nanonetworking capabilities. This is likely to be enabled via the use of molecules, as opposed to electromagnetic waves, acting as the information carrier. To enhance the reliability of the transmitted data, Euclidean geometry low density parity check (EG-LDPC) and cyclic Reed-Muller (C-RM) codes are considered for use within a molecular communication system for the first time. These codes are compared against the Hamming code to show that an s = 4 LDPC (integer s ≥ 2) has a superior coding gain of 7.26 dBs. Furthermore, the critical distance and energy cost for a coded system are also taken into account as two other performance metrics. It is shown that when considering the case of nano-to nano-machines communication, a Hamming code with m = 4, (integer m ≥ 2) is better for a system operating between 10-6 and 10-3 bit error rate (BER) levels. Below these BERs,s = 2 LDPC codes are superior, exhibiting the lowest energy cost. For communication between nano-to macro-machines, and macro-to nano-machines, s = 3 LDPC and s = 2 LDPC are the best options respectively

On the computation of the linear complexity and the k-error linear complexity of binary sequences with period a power of two

The linear Games-Chan algorithm for computing the linear complexity c(s) of a binary sequence s of period ℓ = 2n requires the knowledge of the full sequence, while the quadratic Berlekamp-Massey algorithm only requires knowledge of 2c(s) terms. We show that we can modify the Games-Chan algorithm so that it computes the complexity in linear time knowing only 2c(s) terms. The algorithms of Stamp-Martin and Lauder-Paterson can also be modified, without loss of efficiency, to compute analogues of the k-error linear complexity for finite binary sequences viewed as initial segments of infinite sequences with period a power of two. We also develop an algorithm which, given a constant c and an infinite binary sequence s with period ℓ = 2n, computes the minimum number k of errors (and the associated error sequence) needed over a period of s for bringing the linear complexity of s below c. The algorithm has a time and space bit complexity of O(ℓ). We apply our algorithm to decoding and encoding binary repeated-root cyclic codes of length ℓ in linear, O(ℓ), time and space. A previous decoding algorithm proposed by Lauder and Paterson has O(ℓ(logℓ)2) complexity