LDPC codes for the q-ary bit-measurement channel

In this paper, we introduce a new channel model we term the q-ary bit-measurement channel (QBMC). This channel models a memory device, where q-ary symbols (q = 2^s) are stored in the form of current/voltage levels. The symbols are read by measuring a single bit from the symbol in each read step, starting from the most significant bit. An error event occurs when not all the symbol bits are known, e.g., due to a premature termination of the read sequence. To deal with such error events, we propose the use of GF(q) low-density parity-check (LDPC) codes and analyze their iterative-decoding performance. In particular, we show how to exploit the algebraic structure of the QBMC channel for efficient analysis, and study the effect of the Tanner graph's edge-label distribution on the decoding performance. It is shown that for q = 4 the optimal correction of single-bit erasures is achieved by a distribution different from the uniform distribution on the non-zero elements of GF(4).