On row-by-row coding for 2-D constraints

TL;DR

This paper introduces a row-by-row, sliding-block decodable encoder-decoder for large families of 2-D constraints by transforming them into simpler 1-D constraints and utilizing a network flow-based perturbation of Markov chains.

Contribution

It presents a novel encoding scheme converting 2-D constraints into independent 1-D constraints with a network flow approach for perturbation, enabling efficient parallel encoding.

Findings

Effective encoding for large 2-D constraints.

Use of a network flow to optimize perturbation.

Fast implementation of enumerative coder.

Abstract

A constant-rate encoder--decoder pair is presented for a fairly large family of two-dimensional (2-D) constraints. Encoding and decoding is done in a row-by-row manner, and is sliding-block decodable. Essentially, the 2-D constraint is turned into a set of independent and relatively simple one-dimensional (1-D) constraints; this is done by dividing the array into fixed-width vertical strips. Each row in the strip is seen as a symbol, and a graph presentation of the respective 1-D constraint is constructed. The maxentropic stationary Markov chain on this graph is next considered: a perturbed version of the corresponding probability distribution on the edges of the graph is used in order to build an encoder which operates in parallel on the strips. This perturbation is found by means of a network flow, with upper and lower bounds on the flow through the edges. A key part of the encoder is an enumerative coder for constant-weight binary words. A fast realization of this coder is shown, using floating-point arithmetic.