Enumeration encoding and decoding algorithms for pyramid cubic lattice and trellis codes

A pyramid source code is a code that assigns equal-length binary strings to all reproduction codevectors of equal (weighted) ε₁ norm. A pyramid source encoding is partitioned into two concatenated mappings; the first from source word to reproduction codeword within a codebook; the second from the reproduction codevector to a binary string. The first mapping allows distortion and is accomplished using lattice quantization or trellis-coded quantization. The second mapping is noiseless and is denoted as enumeration. Efficient pyramid enumeration encoding and decoding algorithms are presented, for use with fixed-rate or variable-rate pyramid lattice and trellis codes