Fast and simple algorithm of a parity checker for a large residue numbers is presented. A new set of RNS moduli with 2r-(2l1) form for fast modular multiplication is proposed. The proposed RNS moduli has a large dynamic range for a large RNS number. The parity of a residue number can be checked by the Chinese remainder theorem (CRT). A CRT-based parity checker is simply organized by the Montgomery reduction method (MRM), implemented by using multipliers and the carry-save adder array. We present a fast parity checker with minimal hardware processed in three clock cycles for 32-bit RNS modulus set.

Two implementation schemes for a two-step SOVA (Soft Output Viterbi Algorithm) decoder are proposed and verified in a chip. One uses the combination of trace back (TB) logic to find the survivor state and double trace back logic to find the weighting factor of a two-step SOVA. The other is that the reliability values are divided by a scaling factor in order to compensate for the distortion brought by overestimating those values in SOVA. We introduced a fixed scaling factor of 0.25 or 0.33 for a rate 1/3 and designed an 8-state Turbo decoder with a 256-bit frame size to lower the reliability values. The implemented architecture of the two-step SOVA decoder allows important savings in area and high-speed processing compared with the one-step SOVA decoder using register exchange (RE) or trace-back (TB) method. The chip is fabricated using 0.65 µm gate array at Samsung Electronics and it shows higher SNR performance by 2 dB at the BER 10-4 than that of a two-step SOVA decoder without a scaling factor.

Bluetooth is a common wireless technology that is widely used as a connection medium between various consumer electronic devices. The receivers mostly adopt the Viterbi algorithm to improve a bit error rate performance but are hampered by heavy hardware complexity and computational load due to a coherent detection and searching for the unknown modulation index. To address these challenges, a non-coherent maximum likelihood estimation detector with an eight-state Viterbi is proposed for Gaussian frequency-shift keying symbol detection against an irrational modulation index, without any knowledge of prior information or assumptions. The simulation results showed an improvement in the performance compared to other ideal approaches.