This paper presents a secure integer arithmetic code that owns the capabilities of compression and encryption simultaneously. It is quite different from the randomized arithmetic code, the interval splitting arithmetic code, and the secure arithmetic code. All of them are applied to float-point arithmetic coding. Instead of float-point implementation, integer implementation is more popular since it can decrease the computational cost of arithmetic coding without inducing significant compression loss. During the implementation of integer arithmetic coding, we find that it is possible to lower the instantaneous entropy through the adjustment of interval size. Hence, we can design a secure integer arithmetic code (SIAC) with high security, and the compression efficiency of this code is almost the same or even higher than that of the traditional integer arithmetic code (TIAC).

Variable length codes (VLCs) are widely adopted in many compression standards due to their good coding efficiency on average codeword length. However, an inherent problem with a VLC is that an error of even one bit can cause serious error propagation and thus loss of synchronization at the receiver, which would lead to a series of non-correctly decoded symbols. Reversible variable length codes (RVLCs) were introduced to significantly mitigate this phenomenon. In this work, a method to find an optimal RVLC in terms of the minimum average codeword length is first formulated as a tree-searching problem, and then, instead of performing an exhaustive search, an A*-based construction algorithm is proposed to find an optimal RVLC. The proposed algorithm has been applied to several benchmarks for sources and has found respective optimal symmetric and asymmetric RVLCs.

Let A = {a1,a2,..., a26} be a set of 26 English alphabets with probabilities P = {p1,p2,... ,p26} and C be the corresponding Huffman code that has 26 codewords {c1,c2,... ,c26} with average codeword length 4.15573. The respective lengths of the codewords are given by {lscr1,lscr2,...,lscr26}. According to P, a concatenation of 1000 symbols randomly generated from A is Huffman encoded into a bitstream x of length M and x is further encoded into a bitstream y of length N by a binary (2,1,6) convolutional code with octal generator sequence 554 and 744. Then, y is BPSK modulated and sent over an AWGN channel. Let r = (r1, r2,..., rN) denote the received bitstream. This work assumes that no bits are deleted by the channel, and that the side information N is known at the receiver.

A novel two-variable modularized fast polynomial transform (FPT) algorithm is presented. In this method, only fast polynomial transforms and fast Fourier transforms of the same length are required. The modularity, regularity, and easy extensibility of the proposed algorithm make it of great practical value in computing multidimensional discrete Fourier transforms (DFTs).>