7 problems

Consider a minimal convolutional code with $m$ memory elements and a degree-$v$ distance-spectrum-optimal CRC code, used together under serial list Viterbi decoding at a fixed SNR.…

Let $m$ be the degree of the CRC code, and let $\operatorname{P}^{1}_{\operatorname{UE}}$ and $\operatorname{P}^{1}_{\operatorname{F}}$ denote, respectively, the undetected-error p…

For $k\ge 6$, let $X_{t,k,m}$ be the set of integers $n$ in the interval … for which $S_{n,k}$ is not proper, and let $n(k,m)$ be the paper's designated value. Translated-block con…

For $k\ge 6$, let $X_{t,k,m}$ be the set of integers $n$ in the interval … for which $S_{n,k}$ is not proper, and let $n(k,1)$ be the paper's designated value. First-block conjectu…

Let $\theta(k)$ be the threshold, let $\theta_1(k)$ be the explicit upper-bound quantity, and let $\vartheta(k)$ be the positive real number defined in the paper. Sharp-bound conje…

Let $\theta(k)$ be the threshold studied in the paper, and let $\theta_2(k)$ be its implicit lower bound. Implicit-bound conjecture. The equality … should hold for all $k$. Computa…

Let $K(m)$ denote the relevant minimum code parameter and let $\underline{\omega}(m)$ denote the lower bound defined in the paper. Exactness conjecture. … The claim is motivated by…