A Cyclic Placement Strategy for Multi-Access Coded Caching

We investigate the multi-access coded caching problem, which involves <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> files, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> users, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> caches. Each user can access <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> adjacent caches in a cyclic manner. We present a novel coded placement scheme for the case of cache size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M=\displaystyle \frac{K-1}{KL}$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\displaystyle \frac{K-1}{L}$</tex> is an integer. The scheme is based on coded placement and involves cyclic placement in caches. We show that the scheme achieves a lower worst-case transmission rate than existing schemes in some cases when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N\leq K-L$</tex>. As for the case of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N &gt; K-L$</tex>, for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N &gt; 2,L=K-1$</tex> and cache size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M \in\left[0, \frac{1}{K}\right]$</tex>, our proposed achievable scheme is another way to achieve the optimal memory-rate tradeoff, in addition to the scheme proposed by Namboodiri and Rajan.