On the Broadcast Rate of Index Coding Problems with Symmetric and Consecutive Interference

A single unicast index coding problem (SUICP) with symmetric and consecutive interference (SCI) has K messages and K receivers, the kth receiver R
_k
wanting the kth message x
_k
and having interference I
_k
= {x
_k-U-m
, . . . , x
_k-m-2
, x
_k-m-1
}∪ {x
_k+m+1
, x
_k+m+2
, . . . , x
_k+m+D
} and side-information K
_k
= (I
_k
∪x
_k
)
^c
. In this paper, we derive a lowerbound on the broadcast rate of single unicast index coding problem with symmetric and consecutive interference (SUICP(SCI)). In the SUICP(SCI), if m = 0, we refer this as single unicast index coding problem with symmetric and neighboring interference (SUICP(SNI)). In our previous work, we gave the construction of near-optimal vector linear index codes for SUICP(SNI) with arbitrary K, D, U. In this paper, we convert the SUICP(SCI) into SUICP(SNI) and give the construction of near-optimal vector linear index codes for SUICP(SCI) with arbitrary K, U, D and m. The constructed codes are independent of field size. The near-optimal vector linear index codes of SUICP(SNI) is a special case of near-optimal vector linear index codes constructed in this paper for SUICP(SCI) with m = 0. We give an upperbound on the broadcast rate of SUICP(SCI). We derive the capacity of SUICP(SCI) for some special cases.