Low Complexity Factorial Pulse Coding of MDCT Coefficients using Approximation of Combinatorial Functions

Factorial pulse coding, a method which is known to efficiently code an information signal using unit magnitude pulses, involves computation of combinatorial functions. These computations are highly complex as they require many multiply and divide operations on multi-precision numbers, especially when the length of a signal is large or many unit magnitude pulses are used for coding. In this paper, we propose a very low complexity method for approximation of these combinatorial functions. The approximate functions satisfy a property which preserves unique decode-ability of the factorial packing encoding/decoding algorithm. The low complexity computation enables use of factorial packing in encoding/decoding of 144 MDCT coefficients using 28 unit magnitude pulses for the audio coding mode of the EVRC-WB speech coding standard without affecting the number of bits required for coding.