Binary subblock energy-constrained codes: Bounds on code size and asymptotic rate

The subblock energy-constrained codes (SECCs) have recently been shown to be suitable candidates for simultaneous energy and information transfer, where bounds on SECC capacity were presented for communication over noisy channels. In this paper, we study binary SECCs with given error correction capability, by considering codes with a certain minimum distance. Binary SECCs are a class of constrained codes where each codeword is partitioned into equal sized subblocks, and every subblock has weight exceeding a given threshold. We present several upper and lower bounds on the optimal SECC code size, and also derive the asymptotic Gilbert-Varshamov (GV) and sphere-packing bounds for SECCs. A related class of codes are the heavy weight codes (HWCs) where the weight of each codeword exceeds a given threshold. We show that for a fixed subblock length, the asymptotic rate for SECCs is strictly lower than the corresponding rate for HWCs when the relative distance of the code is small. The rate gap between HWCs and SECCs denotes the penalty due to imposition of weight constraint per subblock, relative to the codeword based weight constraint.