ON OVERFLOW AND UNDERFLOW PROBLEMS IN BUFFER-INSTRUMENTED VARIABLE-LENGTH CODING OF FIXED-RATE MEMORYLESS SOURCES

Variable-length coding schemes can be used in entropy encoding of finite-alphabet sources, but to transmit these codes over a synchronous channel requires a buffer. Since this buffer is of finite size, it is subject to both overflow and underflow. The buffer behavior is studied with particular application to Huffman coding of the outputs of an optimum uniform-threshold quantizer driven by a memoryless Gaussian source. Fairly general upper and lower bounds on the average terminal time are developed. Under certain conditions, the tightness of these bounds is verified, and asymptotic formulas are developed. As an example, an encoding scheme using Huffman codes in conjunction with uniform quantization of memoryless Gaussian sources is considered, and the buffer behavior is studied as a function of the buffer size and output rate.