Function-Correcting Codes for Symbol-Pair Read Channels

Function-correcting codes (FCCs) are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we develop the theory of FCCs over symbol-pair read channels. We introduce the notion of function-correcting symbol-pair codes (FCSPCs) and aim to find their optimal redundancy. To this end, we introduce the notion of irregular-pair-distance codes and derive upper and lower bounds on the optimal redundancy in terms of the shortest length of the irregular-pair-distance codes. We then simplify these bounds and employ these general results to specific functions including pair-locally binary functions, pair weight functions and pair weight distribution functions. In addition, we provide some general constructions for FCSPCs. Lastly, by comparison with classical symbol-pair codes, we find that the theory of FCSPCs developed in our paper really reduces the redundancy under the condition that the receiver can recover certain attribute of the message.